class xii physics (042)
TRANSCRIPT
Physics (042) / XII / TERM-1 /2021-22
KENDRIYA VIDYALAYA SANGATHAN
AHMEDABAD REGION
STUDY MATERIAL
TERM-1
CLASS XII
PHYSICS (042)
Session 2021-22
Physics (042) / XII / TERM-1 /2021-22
INSPIRATION
Shri(Dr) Jaydeep Das
Deputy Commissioner
KVS RO Ahmedabad
Smt Shruti Bhargava
Assistant Commissioner
KVS RO Ahmedabad
MENTOR
Shri Avijit Panda
Principal
Kendriya Vidyalaya,Sabarmati
Physics (042) / XII / TERM-1 /2021-22
CONTENT DEVELOPEMENT TEAM S.NO. Name of Teacher Designation Name of KV 1 Mrs. Vandana Badola PGT Physics NO.1 SHAHIBAUG AHMEDABAD
2 Mr. R N Singh PGT Physics NO.1 SHAHIBAUG AHMEDABAD
3 Mr. Bhupesh Kumar Nagoda PGT Physics AHMEDABAD CANTT
4 Mr. R H Parmar PGT Physics SAC AHMEDABAD
5 Mr. M P Dabi PGT Physics ONGC CHANDKHEDA
6 Mr. T C Agrawal PGT Physics ONGC CHANDKHEDA
7 Mr. Gurmeet Singh PGT Physics HIMMATNAGAR
8 Mrs. Anju Kumari PGT Physics AFS WADSAR
9 Mr. Praveen Nogia PGT Physics BSF DANTIWADA
10 Mr. S K Devrani PGT Physics SEC 30 GANDHINAGAR
11 Mr. Sandeep Kumar Koli PGT Physics SEC 30 GANDHINAGAR
12 Mr. Bhoor Singh Meena PGT Physics CANTT GANDHINAGAR
13 Mr. Shabbir Hingorja PGT Physics CRPF GANDHINAGAR
14 Mrs. Anjana PGT Physics NO 1 AFS BHUJ
15 Mr. Akhilesh Suryavanshi PGT Physics NO 2 BHUJ CANTT
16 Mr. Deepak Kumar Singhal PGT Physics AFS NALIYA
17 Mr. Viswanath PGT Physics DHRANGADHRA
18 Mr. Yaksh Deep PGT Physics PORBANDAR
19 Mr. Sahil Aneja PGT Physics BHAVNAGAR PARA
20 Mr. Ranjay Kumar Sharma PGT Physics RAJKOT
21 Mr. Om Prakash Yadav PGT Physics RAJKOT
22 Mr. Mukesh Kumar PGT Physics NO 1 AFS JAMNAGAR
23 Ms. Suryakant Vats PGT Physics NO 1 AFS JAMNAGAR
24 Mr. Ram PGT Physics INF LINES JAMNAGAR
25 Dr Neeraj Singh PGT Physics AFS II JAMNAGAR
26 Mr. Umesh Kumar PGT Physics INS VALSURA
27 Mr. Pinkesh Rathod PGT Physics AFS SAMANA
28 Mr. Naveen Kumar PGT Physics DIU
29 Mr. Rakesh Kumar PGT Physics NO 1 BARODA
30 Mr. S V Singh PGT Physics EME BARODA
31 Mr. Sudhir Bhootda PGT Physics EME BARODA
32 Mr. Sanjeev Chaddha PGT Physics AFS BARODA
33 Mr. J K Jain PGT Physics AFS BARODA
34 Mrs. Sangeeta Arora PGT Physics ONGC BARODA
35 Mr. Chitresh Pandya PGT Physics DAHOD
36 Mr. C M Sharma PGT Physics ONGC ANKLESHWAR
37 Mr. V K Pathak PGT Physics NO 1 SURAT
38 Mr. Pawan Kumar PGT Physics KRIBHCO SURAT
39 Mr. R M Shukla PGT Physics ONGC SURAT
40 Mr. A P Singh PGT Physics SILVASSA
41 Mr. P K Sah PGT Physics VV NAGAR
42 Mrs. Anju PGT Physics ONGC MEHSANA
43 Mr. Kamlesh Kumar PGT Physics RAILWAY GANDHIDHAM
44 Mr. Balwant Kumar PGT Physics AHMEDABAD CANTT
45 Mr. Vikas Sharma PGT Physics SABARMATI
Physics (042) / XII / TERM-1 /2021-22
PHYSICS
Class-XII
INDEX
S.No Particulars 1 SYLLABUS (TERM-1)
2 Deleted Topics (TERM-1)
3 Question Paper Design (TERM-1)
4 Chapter-1; Electric Charge and Field
5 Chapter-2; Electric Potential and Capacitance
6 Chapter-3; Current Electricity
7 Chapter-4; Moving Charges and Magnetism
8 Chapter-5; Magnetism and Matter
9 Chapter-6; Electromagnetic Induction
10 Chapter-7; Alternating Current
11 CBSE Sample Paper(TERM-1) with Answer key 2021-22
*Every Chapter Contains: 1. Gist of Lesson
2. Multiple Choice Questions with Answer key
3. Assertion and Reason Question with Answer key
4. Case Study Based Questions with Answer key
Physics (042) / XII / TERM-1 /2021-22
SYLLABUS
TERM-1 Session 2021-22
PHYSICS, CLASS-XII
UNIT Chapters Marks
Unit 1 Chapter 1: Electric Charges and Fields
Chapter 2: Electric Potential and Capacitance
17
Unit 2 Chapter 3: Current Electricity
Unit 3 Chapter 4: Moving Charges and Magnetism
Chapter 5: Magnetism and Matter
18
Unit 4 Chapter 6: Electromagnetic Induction
Chapter 7: Alternating Current
Total 35
Physics (042) / XII / TERM-1 /2021-22
DELETED TOPICS (For Session 2021-22)
PHYSICS(042)
CLASS XII
TERM-1
S.No Name of the Chapter Deleted Topics
1 Electric Charges &
Fields
uniformly charged thin spherical shell (field inside and
outside).
2 Electric Potential &
Capacitance No topic is deleted
3 Current Electricity Carbon resistors, colour code for carbon resistors;
series and parallel combinations of resistors
4 Moving Charges and
Magnetism
Cyclotron
5 Magnetism and Matter magnetic field intensity due to a magnetic dipole (bar
magnet) along its axis and perpendicular to its axis,
torque on a magnetic dipole (bar magnet) in a
uniform magnetic field;
Para-, dia- and ferro - magnetic substances, with
examples. Electromagnets and factors affecting their strengths, permanent magnets.
6 Electromagnetic Induction
No topic is deleted
7 Alternating Current power factor, wattless current
Physics (042) / XII / TERM-1 /2021-22
QUESTION PAPER DESIGN TERM-1 EXAM
2021-22
CHAPTER 1
ELECTRIC CHARGE & FIELD
GIST OF LESSON:
Coulombโs Law of Electrostatics
Electrostatic force of interaction acting between two stationary point charges is given by
๐น = 1
4๐๐0.๐1๐2
๐2
where q1, q2 are magnitude of point charges, r is the distance between them and ฮตo is
permittivity of free space.
Here, 1 / 4ฯฮตo = 9 x 10 9 N-m2/C2
The value of ฮตo is 8.85 X 10-12 C2 / N-mC2.
If there is another medium between the point charges except air or vacuum, then ฮตo is
replaced by ฮตoK or ฮตoฮตr or ฮต.
where K or ฮตr is called dielectric constant or relative permittivity of the medium.
K = ฮตr = ฮต / ฮตo where, ฮต = permittivity of the medium.
For air or vacuum, K = 1 For water, K = 81 For metals, K = โ
Coulomb Law implies:
Force on q1 due to q2 = โ Force on q2 due to q1
F12 = โ F21
The forces due to two point charges are parallel to the line joining point charges; such forces
are called central forces and electrostatic forces are conservative forces.
Electric Field:
The space in the surrounding of any charge in which its influence can be experienced by
other charges is called electric field.
Electric Field Lines
โAn electric field line is an imaginary line or curve drawn through a region of space so that
its tangent at any point is in the direction of the electric field vector at that point. The
relative closeness of the lines at some place give an idea about the intensity of electric field
at that point.โ
Two lines can never intersect.
Electric field lines always begin on a positive charge and end on a negative charge and do
not start or stop in mid space.
Electric Field Intensity (E)
The electrostatic force acting per unit positive charge on a point in electric field is called
electric field intensity at that point.
Electric field intensity ๐ธ =๐น
๐
Its SI unit is NC-1 or V/m and its dimension is [MLT-3 A-1].
It is a vector quantity and its direction is in the direction of electrostatic force acting on
positive charge.
Electric field intensity due to a point Charge:
due to a point charge q at a distance r is given by
Magnitude - ๐ธ = 1
4๐๐0.
๐
๐2
Properties of Electric Field Lines:
Electric lines of force are the imaginary lines drawn in electric field at Which a positive test
charge will move if it is free to do so.
Electric lines of force start from positive charge and terminate on negative charge.
A tangent drawn at any point on electric field represents the direction of electric field at
that point.
Two electric lines of force never intersect each other.
Electric lines of force are always perpendicular to an equipotential surface.
Electric Flux (ฯE)
Electric flux over an area is equal to the total number of electric field lines crossing this area.
Electric flux through a small area element dS is given by
ฯE = E. dS
where E= electric field intensity and dS = area vector.
Its SI unit is Nm2C-1.
Gaussโs Theorem:
The electric flux over any closed surface is 1 / ฮตo times the total charge enclosed by that
surface, i.e.,
โ ๐ธ = โฎ ๐ธ. ๐๐ = ๐๐๐
๐0 where Qin = Net Charge enclosed in the surface.
Note: If a charge q is placed at the centre of a cube, then total electric flux linked with the
whole cube = q / ฮตo, electric flux linked with one face of the cube = q / 6 ฮตo.
Electric Field Intensity due to an Infinite Line Charge
๐ธ = ๐
2๐๐0๐ ( Direction โRadially outwards for q > 0 and inwards or q<0)
where ฮป is linear charge density and r is distance from the line charge.
Electric Field Near an Infinite Plane Sheet of Charge:
E = ฯ / 2 ฮตo
where ฯ = surface charge density.
If infinite plane sheet has uniform thickness, then
E = ฯ / ฮตo
Electric Dipole:
An electric dipole consists of two point charges of equal magnitude and opposite sign
separated by a very small distance. e.g., a molecule of HCL, a molecule of water etc.
Electric Dipole Moment p = q (2a)
Its SI unit is โcoulomb-metreโ and its dimension is [LTA).
It is a vector quantity and its direction is from negative charge towards positive charge.
Electric Field Intensity and Potential due to an Electric Dipole
(i) On Axial Line
Electric field intensity ๐ธ = 1
4 ๐ ๐๐
2 ๐๐
(๐2 โ ๐2)2
If r > > 2a, then ๐ธ = 1
4 ๐ ๐๐
2 ๐
๐3 ( Short Dipole)
Electric potential ๐ = 1
4 ๐ ๐๐
๐
๐2 โ ๐2
If r > > 2a, then ๐ = 1
4 ๐ ๐๐
๐
๐ ( Short Dipole)
(ii) On Equatorial Line
Electric field intensity ๐ธ = 1
4 ๐ ๐๐
๐
(๐2 + ๐2)3/2
If r > > 2a, then ๐ธ = 1
4 ๐ ๐๐
๐
๐3 ( Short Dipole)
Electric potential V = 0
(iii) At any Point along a Line Making ฮธ Angle with Axis
Electric field intensity ๐ธ = 1
4 ๐ ๐๐ ๐ โ1+3๐๐๐ 2๐
๐3
Electric potential ๐ = 1
4 ๐ ๐๐
๐๐๐๐ ๐๐๐ ๐
๐2โ ๐2๐๐๐ 2 ๐
If r > > 2a, then ๐ = 1
4 ๐ ๐๐ ๐๐๐๐ ๐๐๐ ๐
๐2 ( Short Dipole)
Torque:
Torque acting on an electric dipole placed in uniform electric field is given by
ฯ = pEsin ฮธ or ฯ = p x E
When ฮธ = 90ยฐ, then โฯmax = pE (Maximum)
When electric dipole is parallel to electric field, it is in stable equilibrium and when it is anti-
parallel to electric field, it is in unstable equilibrium. ( In this Case Torque = 0)
Dipole in Non-Uniform Electric Field:
When an electric dipole is placed in a non-uniform electric field, then a resultant force as
well as a torque act on it.
Net force on electric dipole = (qE1 โ qE2), along the direction of greater electric field
intensity.
Therefore electric dipole undergo rotational as well as linear motion.
CHAPTER 1
ELECTRIC CHARGE AND FIELD
MULTIPLE CHOICE QUESTIONS:
1. Four charges +8Q, -3Q, +5Q and -10 Q are kept inside a closed surface. What will be
the outgoing flux through the surface
(a) 26 V-m (b) 0 V-m (c) 10 V-m (d) 8 V-m
2. The value of electric field inside a conducting sphere having radius R and charge Q
(a) KQ/R2 (b) KQ/R (c) Zero (d) KQ2/R2
3. Which is vector Quantity among the followingโ
(a) Electric flux (b) Electric charge
(c) Electric field (d) Electric potential
4. The SI unit of electric field is
(a) N/C2 (b) (N/C) x m2 (c) (N/m2) x C (d) N/C
5. The electric field intensity due to infinite charged sheet
(a) ฯ/ฦ0 (b) ฯ/2ฦ0 (c) ฯ/4ฦ0 (d) ฯ/6ฦ0
6. The direction of electric dipole moment
(a) Negative charge to positive charge.
(b) Positive charge to negative charge.
(c) Perpendicular to the line joining two charges.
(d) Positive Charge to positive charge.
7. The direction of electric field due to electric dipole at a point on its equatorial line
(a) Parallel to the direction of dipole moment.
(b) Perpendicular to the direction of dipole moment.
(c) Opposite to the direction of dipole moment.
(d) From Negative to Positive charge.
8. The electric field due to a uniformly charged linear conductor of linear charge
density ฮป at a distance r is -
(a) ฮป/4ฯฦ0r (b) 2ฮป/ฯฦ0r (c) ฮป/ฦ0r (d) ฮป/2ฯ ฦ0r
9. The net torque on a dipole in an uniform electric field is Zero, When the angle
between the dipole movement and magnetic field is -
(a) 300 (b) 600 (c) 900 (d) 00
10. Gauss theorem gives the relation between
(a) Charge and flux (b) Charge and field
(c) Force and flux (d) Dipole movement and electric field.
11. What amount of charge we place at corner point A of the cube of sides a so that
the total flux through the faces of the cube is
(a) q (b) q/2 (c) 2q (d) q/8
12 Four equal charges q are placed at the four comers A, B, C, D of a square of length
a. The magnitude of the force on the charge at B will be
13. In Fig. (i) two negative charges q2 and q3 fixed along the y-axis, exert a net electric
force in the negative-x direction on a charge q1 fixed along the x-axis. If a positive
charge Q is added at (x, 0) in figure (ii), the force on q1
(a) shall increase along the positive x-axis.
(b) shall decrease along the positive x-axis.
(c) shall point along the negative x-axis.
(d) shall increase but the direction changes because of the intersection of Q with q2
and q3
14. The figure here shows electric field lines. The electric field strength at P1 is E1 and
that at P2 is E2 If distance between P1, P2 is r, then which of the following statement
is true?
(a) E1 > E2 (b) E1 < E2 (c) E2 = rE1 (d) E2 = E1/rยฒ
15. Four charges are arranged at the corners of a square ABCD, as shown in the adjoining
figure. The force on the charge kept at the centre O is (a) Zero (b) Along the diagonal AC (c)Along the diagonal BD (d) Perpendicular to side AB
16. Consider a system of three charges q/3, q/3 and โ2q/3 placed at points A, B and C respectively as shown in the figure. Take O to be the centre of the circle of radius R and
angle CAB = 60ยบ
(a) The electric field at point O is q/8ฯฮต0R2
(b) The magnitude of the force between the charges at C and B is q2/54ฯฮต0R2 (c) The potential energy of the system is zero
(d) The potential at point O is q/12ฯฮต0R
17. A hemispherical surface of radius R is kept in a uniform electric field E as shown in
the figure. The flux th rough the curved surface is:
(a) EฯR2 (b) E2ฯR2 (c) E4ฯR2 (d) Zero
18. A thin conducting ring of radius R is given a charge +Q. The electric field at the
centre O of the ring due to the charge on the part AKB of the ring is E. The electric
field at the centre due to the charge on the part ACDB of the ring is
(a) E along KO (b) 3E along OK (c) 3E along KO (d) E along OK
19. Three charges + 3q + q and Q are placed on a straight line with equal separation.
In order to make the net force on q to be zero, the value of Q will be : (a) +3q (b) +2q (c) -3q (d) -4q
20. Which of the following figures represent the electric field lines due to a single
negative charge?
21. The SI unit of electric flux is
(a) N C-1 m-2 (b) N C m-2 (c) N C-2 m2 (d) N C-1 m2
22. Each of the two point charges are doubled and their distance is halved. Force of
interaction becomes p times, where p is :
(a) 1 (b) 4 (c) 1/16 (d) 16
23. A hollow cylinder has a charge q coulomb within it. if ฮฆ is the electric flux in units of
volt meter associated with the curved surface B, the flux linked with the plane
surface A in units of volt meter will be (charge is symmetrically placed within it)
24. Three charges, each +q, are placed at the corners of an isosceles triangle ABC of
sides BC and AC, 2a. D and E are the mid points of BC and CA. The work done in
taking a charge Q from D to E is
(a) (b) (c) zero (d)
25. Figure shows the part of an infinite plane sheet of charge
Which of the following graphs correctly shows the behaviour of electric field
intensity as we move from point O to A.
(a) (b) (c) (d)
26 Three charges + 3q + q and Q are placed on a straight line with equal separation. In
order to make the net force on q to be zero, the value of Q will be :
(a) +3q (b) +2q (c) -3q (d) -4
27 For a point charge, the graph between electric field versus distance is given by :
28 Which one of the following is the unit of electric field?
(a) Coulomb (b) Newton (c) Volt (d) N/C
29 Two charges 3 ร 10-5 C and 5 ร 104 C are placed at a distance 10 cm from each
other. Find the value of electrostatic force acting between them.
(a) 13.5 ร 1011 C (b) 40 ร 10-5 C
(c) 180 ร 109 C (d) 3.05 ร 10-11 C
30 Four charges + 8Q, - 3Q +5Q and -10Q are kept inside a closed surface. What
will be the outgoing flux through the surface.
(a) 26 V-m (b) 0 V-m (c) 10 V-m (d) 8 V-m
31
Electric field lines contracts lengthwise, It shows
(a) repulsion between same charges
(b) Attraction between apposite charges
(c) No relation between force & contraction.
(d) Electric field lines does not moves on straight path.
32 What is the S. I. unit of electric flux?
(a) N/C ร m2
(b) N รm2
(c) N2/C ร m2
(d) N2/C2 ร m2
33 What is the value of minimum force acting between two charges placed at 1 m
apart from each other
(a) Ke2 (b) Ke (c) Ke/4 (d) 2Ke2
34 A glass rod acquires charge by rubbing it with silk cloth. The charge on glass rod
is due to
(a) Friction (b) Conduction (c) Induction (d) Radiation
35
The number of electron-taken out from a body to produce 1 coulomb of charge will
be
(a) 6.25 ร 1018 (b) 625 ร 1018 (c) 6.023 ร 1023 (d) None
36 If sphere of bad conductor is given charge then it is distributed on:
(a) surface (b) inside the surface (c) only inside the surface (d)None
37 Electric field in a cavity of metal:
(a) depends upon the surroundings (b) depends upon the size of cavity
(c) is always zero (d) is not necessarily zero
38 The dielectric constant of a metal is:
(a) 0 (b) 1 (c) โ (d) -1
39 About electric flux :
(a) SI unit is NC -1m 2 (b) itโs a scalar physical quantity.
(c) SI unit is Vm (d) All(a), (b) and (c) are correct.
40 Each of the two point charges are doubled and distance between the two point
charges is also dobled. Force of interaction becomes m times, where m is :
(a) 1 (b) 4 (c) 116 (d) 16
41 Coulombโs law in vector form can be written as
F = (1/4ฯฯต0) (Q1 Q 2 /r 2)r
where ฮต0 is the permitivity of free space. The SI units of ฯต0 will be:
(a) N m2 / C2 (b) N-1 m -2 C2 (c) N m3 / C (d) 2 N m2 / C2
42 The dimensional formula for Charge is :
(a) [MLT 4A 2] (b) [M -1L -3 T 4A 2] (c)[MLT 1 A1 ] (d) None of these
43 If โฎ ๐ . ๐๐ฌ = 0 , inside a surface, that means :-
(a) there is no net charge present inside the surface
(b) Uniform electric field inside the surface
(c) Discontinues field lines inside the surface
(d) Charge present inside the surface
44 A parrot comes and sits on a bare high power line. It will:
(a) experience a mild shock (b) experience a strong shock.
(c) get killed instantaneously (d) not be affected practically
45 If two conducting sphere are connected after charging
separately then:
(a) Electrostatic energy sphere energy will remain conserved
(b) Electrostatic energy charges remains conserved
(c) Electrostatic energy decreases and charge remains conserved
(d) None
46 An electron is sent in an electric field of magnitude 9.1 ร
10 6NC -1. The acceleration produced in it is :
(a) 1.6 ms-2 (b) 1.6 ร 10 18ms -2
(c) 3.2 ร 10 18ms-2 (d) 0.8 ร 1018 ms-2
47 The value of electric field inside a conducting sphere having radius R and charge
Q will be
(a) KQ/ R 2 (b) KQ/ R (c) Zero (d) 2 KQ 2 / R
48 Charge on a body is integral multiple of +e . It is given by the law of -
(a) Conservation of charge (b) Conservation of mass
(c) Conservation of energy (d) Quantisation of charge
49 Charge Q is kept in a sphere of 5 cm first than it is kept in a cube of side 5 cm.
the outgoing flux will be-
(a) More in case of sphere (b) More in case of cube
(c) Same in both case (d) Information Incomplete
50 On charging a neutral Balloon its size -
(a) Increases (b) Decreases
(c) Remains same (d) No relation between charge & size
ANSWER KEY( MCQs):
Q. 1 2 3 4 5 6 7 8 9 10
ANS B C C D B A C D A A
Q. 11 12 13 14 15 16 17 18 19 20
ANS A C A A C B A D A B
Q. 21 22 23 24 25 26 27 28 29 30
ANS D D D b c C B D A B
Q. 31 32 33 34 35 36 37 38 39 40
ANS B A A A A D C C D A
Q. 41 42 43 44 45 46 47 48 49 50
ANS B C A D C B C D C A
ASSERTION AND REASON QUESTIONS:
For question numbers 1 to 24, two statements are given-one labelled Assertion (A) and the
other labelled Reason (R). Select the correct answer to these questions from the codes (a),
(b), (c) and (d) as given below.
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false and R is also false
1 Assertion : The electrostatics force increases with decrease the distance between the
charges.
Reason : The electrostatic force of attraction or repulsion between any two stationary point
charges is inversely proportional to the square of the distance between them
2 Assertion: When a body is charged, its mass changes.
Reason : Charge is quantized.
3 Assertion: The total amount of charge on a body equal to 4 x10-19 C is not possible.
Reason : Experimentally it is established that all free charges are integral multiples of a basic
unit of charge denoted by e. Thus, charge q on a body is always given by q = ne.
4 Assertion: The electrostatics force increases with decrease the distance between the
charges.
Reason : The electrostatic force of attraction or repulsion between any two stationary point
charges is inversely proportional to the square of the distance between them.
5 Assertion: The Coulomb force between two points charges depend upon the dielectric
constant of the intervening medium.
Reason: Coulombโs force varies inversely with the dielectric constant of medium.
6 Assertion: The charge given to a metallic sphere does not depend on whether it is hollow or
solid.
Reason: The charge resides only at the surface of conductor.
7 Assertion: A comb run through oneโs dry hair attracts small bits of paper.
Reason: Molecules in the paper gets polarized by the charged comb resulting in net force of
attraction
8 Assertion: A proton is placed in a uniform electric field, it tends to move along the direction
of electric field.
Reason: A proton placed in a uniform electric field experiences a force.
9 Assertion: Electric field at the surface of a charged conductor is always normal to the surface
at every point.
Reason: Electric field gives the magnitude & direction of electric force F experienced by any
charge placed at any point.
10 Assertion: Electric filed lines do not form closed loops.
Reason: Electric filed lines are always normal to the surface of a conductor.
11 Assertion: Electrostatic forces are conservative in nature.
Reason: Work done by electrostatic force is path dependent.
12 Assertion: A negatively charged body means that the body has gained electrons while a
positively charged body means the body has lost some of its electrons.
R: Charging process involves transfer of electrons.
13 Assertion: If dipole moment of water molecules were zero, then microwave cooking would
not be possible.
Reason: In a microwave oven the water molecules vibrate due to oscillating electric field in
microwave and heat the food.
14 Assertion: Electric field lines are continuous curves in free space.
Reason: Electric field lines start from negative charge and terminate at positive charge.
15 Assertion: A point charge cannot exert force on itself.
Reason: Coulomb force is a central force.
16 Assertion: An electron has negative charge by definition.
R: Charge of a body depends on its velocity.
17 Assertion: Since matter cannot be concentrated at a point, therefore point charge is not
possible.
Reason: An electron is a point charge.
18 Assertion: A finite size charged body may behave like a point charge if it produces an
inverse square electric field.
Reason: Two charged bodies may be considered as point charges if their distance of
separation is very large compared to their dimensions.
19 Assertion: The path traced by a positive charge is a field line.
Reason: A field line can intersect itself.
20 Assertion: If electric flux over a closed surface is negative then the surface encloses net
negative charge.
Reason: Electric flux is independent of the charge distribution inside the surface.
21 Assertion: Particles such as photon or neutrino which have no rest mass are uncharged.
Reason: Charge cannot exist without mass.
22 Assertion: The equilibrium of a charged particle under the action of electrostatic force
alone can never be stable.
Reason: Coulomb force is an action-reaction pair.
23 Assertion: The field in a cavity inside a conductor is zero which causes electrostatic
shielding.
Reason: Dielectric constant of conductors in electrostatics is infinite.
24 Assertion: Though quark particles have fractional electronic charges, the quantum of charge
is still e.
Reason: Quark particles do not exist in Free State.
25 Assertion. In a non-uniform electric field, a dipole will have translatory as well as rotatory
motion.
Reason. In a non-uniform electric field, a dipole experiences a force as well as a torque.
26 Assertion. Net electric field inside a conductor is zero .
Reason. Total positive charge equals to total negative charge in a charged conductor.
27 Assertion: Three equal charges are situated on a circle of radius r such that they form on equilateral triangle, then the electric field intensity at the centre is zero.
Reason:The force on unit positive charge at the centre, due to the three equal charges are represented by the three sides of a triangle taken in the same order. Therefore, electric field intensity at centre is zero.
28 Assertion: The surface densities of two spherical conductors of different radii are equal.
Then the electric field intensities near their surface are also equal.
Reason:Surface density is equal to charge per unit area.
29 Assertion: When a conductor is placed in an external electrostatic field, the net electric field
inside the conductor becomes zero after a small instant of time.
Reason: It is not possible to set up an electric field inside a conductor.
30 Assertion: The electric flux of the electric field โฎ E.dA is zero. The electric field is zero
everywhere on the surface.
Reason:The charge inside the surface is zero.
ANSWERS(Assertion & Reason):
Q.No. ANS Q.No. ANS Q.No ANS
1 A 11 C 21 A
2 B 12 A 22 B
3 A 13 A 23 B
4 A 14 C 24 A
5 A 15 B 25 A
6 A 16 C 26 C
7 A 17 C 27 A
8 B 18 B 28 B
9 B 19 D 29 C
10 B 20 B 30 D
CASE STUDY QUESTIONS:
1 Gold Leaf Electroscope: Gold leaf electroscope has two gold leafs suspended
from a metal(usually brass) stem in a vacuumed glass jar and connected to a
metal cap. The glass is grounded with the help of a metal foil to make it
uncharged. It can be used to: Detect charge: Body under test is touched with the
metal cap.
(i) Neutral atoms contain equal numbers of positive and negative .
(a) Electrons and Protons
(b) Protons and Electrons
(c) Neutrons and Electrons
(d) Protons and Neutrons
(ii) greater the charge on a given body, the divergence in the leaves will beโฆ
(a) smaller (b) greater (c) same (d) first smaller then greater
(iii) Magnitude of force between a pair of proton and proton is F and between a
proton d electron is Fโ thenโฆ
(a) F = Fโ (b) F > Fโ (c) F < Fโ (d) F >> Fโ
(iv) Earthing meansโฆ
(a) to perform an experiment on Earth
(b) to burry the device in the Earth
(c) To put the device on Earth
(d) Process of sharing charges with Earth
(v) If a negatively charged rod touches a conductor, the conductor will be charged
by what method?
(a) Friction (b) Conduction (c) Convection (d) Induction
2 Concept of Electric Field: Electric field is an elegant way of characterizing the
electrical environment of a system of charges. Electric field at a point in the space
around a system of charges tells you the force a unit positive test charge would
experience if placed at that point (without disturbing the system). Electric field is
a characteristic of the system of charges and is independent of the test charge
that you place at a point to determine the field
(i) Which of the following statement is correct? The electric field at a point is
(a) always continuous.
(b) continuous if there is a charge at that point.
(c) discontinuous only if there is a negative charge at that point.
(d) discontinuous if there is a charge at that point
(ii) The force per unit charge is known asโฆ
(a) Electric Field (b) Electric Flux
(c) Electric Current (d) Electric potential.
(iii) The SI unit of electric field isโฆ
(a) N/C (b) V/m (c)V m (d) both (a) and (b)
(iv) A proton of mass โmโplaced in electric field region remains stationary in air
then magnitude of electric field isโฆ
(a) mge (b) mg/e (c) e/mg (d) eยฒg/mยฒ
(v) Electric field is โฆ
(a) Vector (b)Scalar (c) tensor (d) none of the above
3 Electric Charge: When a glass rod is rubbed with silk, the rod acquires one kind
of charge and the silk acquires the second kind of charge. This is true for any pair
of objects that are rubbed to be electrified. Now if the electrified glass rod is
brought in contact with silk, with which it was rubbed, they no longer attract each
other. They also do not attract or repel other light objects as they did on being
electrified. Thus, the charges acquired after rubbing are lost when the charged
bodies are brought in contact. What can you conclude from these observations?
It just tells us that unlike charges acquired by the objects neutralise or nullify each
otherโs effect. Therefore, the charges were named as positive and negative by
the American scientist Benjamin Franklin. We know that when we add a positive
number to a negative number of the same magnitude, the sum is zero. This might
have been the philosophy in naming the charges as positive and negative. By
convention, the charge on glass rod or catโs fur is called positive and that on
plastic rod or silk is termed negative. If an object possesses an electric charge, it
is said to be electrified or charged. When it has no charge it is said to be
electrically neutral.
(i) When you charge a balloon by rubbing it on your hair this is an example of what
method of charging?
(a)Friction (b)Conduction (c)Grounding (d)Induction
(ii) Neutral atoms contain equal numbers of positive __ and negative __.
(a)Electrons and Protons (b)Protons and Electrons
(c)Neutrons and Electrons (d)Protons and Neutrons
(iii) Which particle in an atom can you physically manipulate?
(a)protons (b)electrons
(c)neutrons (d)you can't manipulate any particle in an atom
(iv) If a negatively charged rod touches a conductor, the conductor will be
charged by what method?
(a) Friction (b)Conduction (c)Induction (d)Convection
(v) A negatively charged rod is touched to the top of an electroscope, which on is
correct in the given figure
(a) A (b) B (c) C (d) D
4 Electrostatic Induction: Figure (a) shows an uncharged metallic sphere on an
insulating metal stand. If we Bring a negatively charged rod close to the metallic
sphere, as shown in Fig. (b). As the rod is brought close to the sphere, the free
electrons in the sphere move away due to repulsion and start piling up at the
farther end. The near end becomes positively charged due to deficit of electrons.
This process of charge distribution stops when the net force on the free
electrons inside the metal is zero. Now if we Connect the sphere to the ground
by a conducting wire. The electrons will flow to the ground while the positive
charges at the near end will remain held there due to the attractive force of the
negative charges on the rod, as shown in Fig. (c). Disconnect the sphere from the
ground. The positive charge continues to be held at the near end Fig.(d). if we
remove the electrified rod. The positive charge will spread uniformly over the
sphere as shown in Fig. (e). In this experiment, the metal sphere gets charged by
the process of induction and the rod does not lose any of its charge.
(i) What do you call the process of charging a conductor by bringing it near
another charged object?
(a) Induction (b) Polarisation (c) neutralization (d) conduction
(ii)The negatively charged balloon is brought near the two cans. What happens?
(a)The negative charges in Can B move towards the balloon
(b)The negative charges in Can A move away from the balloon
(c)The positive charges in Can B move towards the balloon
(d)The positive charges in Can A move away from the balloon
(iii) Transferring a charge without touching is ___
(a)Conduction (b)Induction (c)Grounding (d)Newtons 3rd law
(iv) Due to electrostatic induction in aluminum rod due to charged plastic rod,
the total charge on the aluminum rod is
(a)Zero (b)Positive (c) Negative (d) Dual
(v) If we bring charged plastic rod near-neutral aluminum rod, then rods will
(a)Repel each other (b)Attract each other
(c)Remain their position (d)Exchange charges
5
Electric Dipole: The electric field due to a
charge configuration with total charge
zero is not zero, but for distances large
compared to the size of the
configuration, its filed falls off faster than
1/r2, typical of the field due to a single
charge. An electric dipole is the simplest
example of this fact. An electric dipole is
a pair of equal and opposite charges +q
and -q separated by some distance 2a. Its
dipole moment vector p has magnitude
2qa and is in the direction of the dipole axis from -q to +q. The electric field of the
pair of charges can be found out from Coulombโs law and the superposition
principle. The magnitude and the direction of the dipole field depend not only on
the distance r but also on the angle between the position vector r and the dipole
moment p. In some molecules, like H2O, the centers of -ve charges and of +ve
charges do not coincide. So they have permanent dipole moment. Such molecules
are called polar molecules.
(i) What will be the value of electric field at the center of the electric dipole?
(a) Zero
(b) Equal to the electric field due to one charge at Centre
(c) Twice the electric field due to one charge at Centre
(d) Half the value of electric due to one charge at Centre
(ii) If r is the distance of a point from the Centre of a short dipole, then the electric field intensity due to the short dipole remains proportional to
(a) r2 (b) r3 (c) r-2 (d) r-3
(iii) An electric dipole coincides on Z-axis and its midpoint is on origin of the
coordinate system. The electric field at an axial point at a distance z from origin
is Ez and electric field at an equatorial point at a distance y from origin is Ey. Here
z=y>>a, so |Ez|/|Ey| is equal toโฆ
(a) 1 (b)4 (c) 3 (d) 2
(iv) An electric dipole of moment p is placed in a uniform electric field E. The
maximum torque experienced by the dipole isโฆ
(a) pE (b) p/E (c) E/p (d) p . E
(v) The frequency of oscillation of electric dipole having dipole moment p and
rotational inertia I, oscillating in a uniform electric filed E, is given byโฆ
(a) (1/2ฯ) โ๐ผ/๐๐ธ (b) (1/2ฯ) โ๐๐ธ/๐ผ
(c) (2ฯ) โ๐๐ธ/๐ผ (d) (2ฯ) โ๐ผ/๐๐ธ
6 Electric Flux & Gaussโs Theorem: The term electric field flux implies some kind of
flow.
Flux is the property of any vector field. Electric flux is
a
property of Electric field. It is equal to the product of
the given area
and the normal component of the electric filed
through it.
Gaussโs theorem gives a relationship between the
total flux passing
through any closed surface S and the charge q enclosed with in the surface. Its
states that the total flux surface S and the charge q enclosed with in the surface.
It states that the total flux through a closed surface is 1/ฦ0 times the net charge
enclose by the surface.
Mathematically, ษธE = โซ ๐ธ. ๐๐ = ๐/๐
ฦ0
Gaussโs theorem is quite useful in calculating the electric field in problems where
it is possible to choose a closed surface that the electric field E has a normal
component which is either zero
or has a single fixed value at every point on the surface. Symmetry considerations
in many problems make the application of Gaussโs theorem much easier. The
closed surface we choose
(having symmetry consideration in view) to solve a given problem is called
Gaussian surface. Gaussโs theorem is based on inverse square dependence on the
distance contained in Coulombโs law. Any violation of Gaussโs theorem will reflect
a deviation from the inverse square law.
(i) What is the SI unit of electric flux?
(a) (N/C) * m2 (b) N * m2
(c) N/m2 (d)(N2/m2) * C2
(ii)โซ ๐ธ. ๐๐ = 0, inside a surface, that means there is..
(a) Charge present inside the surface.
(b)uniform electric field inside the surface
(c) discontinuous field lines inside the surface
(d) some the charge present inside the surface
(iii) For a given surface the Gaussโs law is stated asโซ ๐ธ. ๐๐ = 0. From this we
can conclude that..
(a) E is necessarily zero on the surface.
(b) E is perpendicular to the surface at every point
(c) the total flux through the surface is zero
(d) the flux is only going out of the surface.
(iv) The electric flux for Gaussian
surface A that encloses the charged
particles in free space isโฆ
(Given q1 = -14nC, q2 = 78.85nC, q3 =
-56nC)
(a)103 Nm2C-1
(b)103 CN-1 m-2
(c) 6.32 x 103 Nm2C-1
(d) 6.32 x 103 CN-1 m-2
(v) Charge q is first kept in a sphere of radius 5 cm and then it is kept in a cube of
side 5 cm.
The outgoing fluxโฆ.
(a) will be more in case of sphere
(b) will be more in case of cube
(c) will be same in both cases
(d) cannot be determined
7 Electric Field Lines: Electric field strength is proportional to the density of lines of
force i.e., electric field strength at a point is proportional to the number of lines
of force cutting a unit area element placed normal to the field at that point. As
illustrated in given figure, the electric field at P is stronger than at Q.
(i) Electric lines of force about a positive point charge are (a) radially outwards (b) circular clockwise (c) radially inwards (d) parallel straight lines
(ii) Which of the following is false for electric lines of force? (a) They always start from positive charge and terminate on negative charges. (b) They are always perpendicular to the surface of a charged conductor. (c) They always form closed loops. (d) They are parallel and equally spaced in a region of uniform electric field.
(iii) Which one of the following patterns of electric line of force is not possible in
field due to stationary charges?
(iv) Electric field lines are curved
(a) in the field of a single positive or negative charge
(b) in the field of two equal and opposite charges.
(c) in the field of two like charges.
(d) both (b) and (c)
(v) The figure below shows the electric field lines due to two positive charges. The magnitudes EA, EB and EC of the electric fields at point A, B and C respectively are related as
(a) EA>EB>EC
(b) EB>EA>EC
(c) EA=EB>EC
(d) EA>EB=EC
8 Torque on Dipole in Uniform electric field: When electric dipole is placed in uniform electric field, its two charges experience equal and opposite forces, which cancel each other and hence net force on electric dipole in uniform electric field is zero. However, these forces are not collinear, so they give rise to some torque on the dipole. Since net force on electric dipole in uniform electric field is zero, so no work is done in moving the electric dipole in uniform electric field. However, some work is done in rotating the dipole against the torque acting on it.
(i) The dipole moment of a dipole in a uniform external field ฤ is B. Then the torque ฯ acting on the dipole is (a) ฯ=p x E (b) ฯ = p. E (c) ฯ = 2(p + E) (d) ฯ = (p + E)
(ii) An electric dipole consists of two opposite charges, each of magnitude 1.0 ฮผC separated by a distance of 2.0 cm. The dipole is placed in an external field of 105 NC-1. The maximum torque on the dipole is (a) 0.2 x 10-3 Nm (b) 1x 10-3 Nm (c) 2 x 10-3 Nm (d) 4x 10-3 Nm
(iii) Torque on a dipole in uniform electric field is minimum when ฮธ is equal to (a) 0ยฐ (b) 90ยฐ (c) 180ยฐ (d) Both (a) and (c)
(iv) When an electric dipole is held at an angle in a uniform electric field, the net force F and torque ฯ on the dipole are (a) F= 0, ฯ = 0 (b) Fโ 0, ฯโ 0 (c) F=0, ฯ โ 0 (d) Fโ 0, ฯ=0
(v) An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle with the direction of the field. Assuming that potential energy of the dipole to be zero when 0 = 90ยฐ, the torque and the potential energy of the dipole will respectively be (a) pEsinฮธ, -pEcosฮธ (b) pEsinฮธ, -2pEcosฮธ (c) pEsinฮธ, 2pEcosฮธ (d) pEcosฮธ, โ pEsinฮธ
ANSWERS (CASE STUDY QUESTIONS):
ANS.(i) ANS.(ii) ANS.(iii) ANS.(iv) ANS.(v)
Q.1 b b a d b
Q.2 b a d b a
Q.3 a b b b C
Q.4 a b b a b
Q.5 c d d a b
Q.6 a a c a c
Q.7 a c c d a
Q.8 a c d c a
CHAPTER 2
ELECTRIC POTENTIAL & CAPACITANCE
GIST OF LESSON:
Electric Potential (V)
Electric potential at any point is equal to the work done per positive charge in carrying it from infinity to
that point in electric field.
Electric potential, V = W / q
Its SI unit is J / C or volt and its dimension is [ML2T-3A-1].
It is a scalar quantity.
Electric potential due to a point charge at a distance r is given by
๐ = 1
4๐๐0.๐
๐
Potential Gradient:
The rate of change of potential with distance in electric field is called potential gradient.
Potential gradient = ๐๐
๐๐
Its unit is V / m.
Relation between potential gradient and electric field intensity is given by
๐ธ = โ๐๐
๐๐
Equipotential Surface
Equipotential surface is an imaginary surface joining the points of same potential in an electric field. So,
we can say that the potential difference between any two points on an equipotential surface is zero. The
electric lines of force at each point of an equipotential surface are normal to the surface.
(i) Equipotential surface may be planer, solid etc. But equipotential surface can never be point size.
(ii) Electric field is always perpendicular to equipotential surface.
(iii) Equipotential surface due to an isolated point charge is spherical.
(iv) Equipotential surface are planer in an uniform electric field.
(v) Equipotential surface due to a line charge is cylindrical.
Properties of Electric Field Lines:
Electric lines of force are the imaginary lines drawn in electric field at which a positive test charge will
move if it is free to do so.
Electric lines of force start from positive charge and terminate on negative charge.
A tangent drawn at any point on electric field represents the direction of electric field at that point.
Two electric lines of force never intersect each other.
Electric lines of force are always perpendicular to an equipotential surface.
Potential Energy:
Potential energy of an electric dipole in a uniform electric field is given by
U = โ pE cosฮธ = p.E
Dipole in Non-uniform Electric Field
When an electric dipole is placed in a non-uniform electric field, then a resultant force as well as a torque
acts on it.
Net force on electric dipole = (qE1 โ qE2), along the direction of greater electric field intensity.
Therefore electric dipole undergoes rotational as well as linear motion.
Electrostatic Potential Energy of Charge System:
(1) Two point charge system, contains charges q1 and q2 separated by a distance r is given by ๐ =
1
4 ฯ ฮตo ๐1๐2
๐
(2) Three point charge system
๐ = 1
4 ฯ ฮตo ๐1๐2
๐12+
1
4 ฯ ฮตo ๐2๐3
๐23+
1
4 ฯ ฮตo ๐1๐3
๐13
Important Points
When charge is given to a soap bubble its size gets increased.
In equilibrium for a charged soap bubble, pressure due to surface tension
= electric pressure due to charging
4T / r = ฯ2 / 2 ฮตo
or 4T / r = 1 / 2 ฮตo (q / 4 ฯr2)2
or q = 8 ฯr โ2 ฮตo rT
where, r is radius of soap bubble and T is surface tension of soap bubble.
Behaviour of a Conductor in an Electrostatic Field:
(i) Electric field at any point inside the conductor is zero.
(ii) Electric field at any point on the surface of charged conductor is directly proportional to the surface
density of charge at that point, but electric potential does not depend upon the surface density of charge.
(iii) Electric potential at any point inside the conductor is constant and equal to potential.
(iv) Direction of electric field at any point on its surface is always normal to the surface.
Electrostatic Shielding:
The process of protecting certain field from external electric field is called, electrostatic shielding.
Electrostatic shielding is achieved by enclosing that region in a closed metallic chamber.
Dielectric
Dielectrics are of two types Non-polar Dielectric the non-polar dielectrics (like N2, O2, benzene, methane)
etc. is made up of non-polar atoms/molecules, in which the centre of positive charge coincides with the
centre of negative charge of the atom/molecule.
Polar Dielectric
The polar dielectric (like H2O, CO2, NH3 etc) are made up of polar atoms/molecules, in which the centre
of positive charge does not coincide with the centre of negative charge of the atom.
Capacitor
A capacitor is a device which is used to store huge charge over it, without changing its dimensions.
When an earthed conductor is placed near a charged conductor, then it decreases its potential and therefore
more charge can be stored over it.
A capacitor is a pair of two conductors of any shape, close to each other and have equal and opposite
charges.
Capacitance of a conductor C = q / V
Its SI unit is coulomb/volt or farad (F)
Its other units are 1 ฮผ F = 10-6 F
1 ฮผฮผ F = 1 pF = 10-12 F
Capacitance of an Isolated Spherical Conductor
C = 4 ฯ ฮตo K R For air K = 1
โด C = 4 ฯ ฮตo R = R / 9x 109
Parallel Plate Capacitor
The parallel plate capacitor consists of two metal plates parallel to each other and separated by a distance d.
Capacitance C = KA ฮตo / d
For air capacitor Co = A ฮตo / d
When a dielectric slab is inserted between the plates partially, then its capacitance.
๐ถ = A ฮตo
(d โ t + t / K)
If a conducting (metal) slab is inserted between the plates, then
๐ถ = A ฮตo
(d โt)
Force Between the Plates of the Capacitor:
The plates of a parallel plate capacitor attract each other with a force
F = Q2 / 2 A ฮตo
Charge Induced:
When a dielectric slab is placed between the plates of a capacitor than charge induced on its side due to
polarization of dielectric is
qโ = q (1 โ 1 / K)
Capacitors Combination:
(i) In Series:
Resultant capacitance = 1 / C = 1 / C1 + 1 / C2 + 1 / C3 + โฆ.
In series charge is same on each capacitor, which is equal to the charge supplied by the source.
If V1, V2, V3,โฆ. are potential differences across the plates of the capacitors then total voltage applied by
the source
V = V1 + V2 + V3 + โฆ.
(ii) In Parallel:
Resultant capacitance C = C1 + C2 + C3 + โฆ.
In parallel potential differences across the plates of each capacitor is same.
If q1, q2, q3 are charges on the plate of capacitors connected in parallel then total charge given by the source
q = q1 + q2 + q3 + โฆ.
Electrostatic Energy Stored in Capacitor:
Electric potential energy of a charged conductor or a capacitor is given by,
๐ = 1
2๐๐ =
1
2๐ถ๐2 =
๐2
2๐ถ Where Q = Charge. V = Potential of Capactor, C = Capacitance
Redistribution of Charge:
When two isolated charged conductors are connected to each other then charge is redistributed in the ratio
of their capacitances.
Common potential ๐ = q1 + q2
C1 + C2 =
C1V1 + C2V2
C1 + C2
Energy loss โ๐ธ = 1
2
๐ถ1๐ถ2(๐1โ๐2)2
(๐ถ1+๐ถ2)
This energy is lost in the form of heat in connecting wires.
CHAPTER-2
ELECTROSTATIC POTENTIAL AND CAPACITANCE
MULTIPLE CHOICE QUESTIONS:
1. When charge is supplied to a conductor, its potential depends upon
(a) the amount of charge (b) Geometry & size of conductor
(c) both (a)&(b) (d) only on(a)
2. A parallel plate capacitor is charged by a battery. Once it is charged battery is removed. Now a dielectric material is inserted between the plates of the capacitor, which of the following does not change?
(a) electric field between the plates (b)potential difference across the plates
(c) charge on the plates (d) energy stored in the capacitor.
3. A dipole is placed parallel to electric field. If W is the work done in rotating the dipole
from 0ยฐ to 60ยฐ, then work done in rotating it from 0ยฐ to 180ยฐis
(a) 2 W (b) 3W
(c) 4 W (d) W/2
4. The variation potential V with r & electric field E with r for a point charge is correctly
shown in the graphs
5. A charge Q is supplied to a metallic conductor. Which is true?
(a) Electric field inside it is same as on the surface.
(b) Electric potential inside is zero.
(c) Electric potential on the surface is zero
(d) Electric potential inside it is constant
6. A parallel plate capacitor C has a charge Q. The actual charges on the plates are
(a) Q, Q (b) Q / 2, Q /2
(c) Q,-Q (d) Q1/2 ,Q2/2
7. Three capacitors of capacitances 1ยตf, 2ยตF & 3ยตF are connected in series and a potential
difference of 11V is applied across the combination them the potential difference
across the plates of 1ยตF capacitor is
(a) 2V (b) 4V (c) 1V (d)6V
8. The electric field at the Centre of a cavity is-
(a) Zero (b) kq /a2 (c) kq/a (d) kq/2a2
9. Two conducting spheres A and B of radii a & b respectively are at the same
potential. The ratio of surface charge densities of A and B is
(a) b/a (b) a/b (c) a2/b2 (d) b2/a2
10. Work done to bring a unit positive charge un-accelerated from infinity to a point
inside electric field is called:
(a) Electric field (b) Electric potential
(c) Capacitance (d) Electric flux
11. Electric potential due to a point charge โq at distance x from it is given by:
(a) Kq/x2 (b) Kq/x
(c) -Kq/x2 (d) -Kq/x
12. Electric field is always:
(a) Parallel to equipotential surface
(b) Perpendicular to equipotential surface
(c) It can be perpendicular and parallel as well
(d) It does not depend on distribution of charge
13. Electric field and electric potential inside a charged
spherical shell:
(a) E = 0; V= 0 (b) E = 0; V โ 0
(c) E โ 0; V= 0 (d) E โ 0; V โ 0
14. Shape of equipotential surface in uniform electric field will be:
(a) Spherical normal to electric field
(b) Random
(c) circular normal to electric field
(d) Equidistant Planes normal to electric field
15. On reducing potential across a capacitor, its capacitance:
(a) Decreases (b) Increases
(c) Remains constant (d) First increases then decreases
16. Energy stored in a in a charged capacitor is given by:
(a) U= CV/2 (b) U = CV2/2
(c) 2CV2 (d) VC2/2
17. A spherical conductor has charge Q on its surface. Radius of the conductor is R. Which of the following is correct? (a) Electric Potential is a non-zero constant (b) Electric Potential is a constant (c) Electric Field is zero (d) Electric Field is a non-zero constant
18. The electrostatic potential on the surface of a charged conducting sphere is 200 V.
Two statements are made in this regard: S1 : At any point inside the sphere, electric intensity is zero. S2 : At any point inside the sphere, the electrostatic potential is 200V. Which of the following is a correct statement? (a) S1 is true but S2 is false. (b) Both S1 & S2 are false. (c) S1 is False but S2 is true. (d) both S1 and S2 are true..
19. In a region of constant potential (a) the electric field is uniform (b) the electric field is zero. (c) there can be no charge inside the region. (d) the electric field shall necessarily change if a charge is placed outside the region.
20. If I place an second uniformly charge shell (Q) of radius R'>R, will the value of potential change at r<R (a) increases (b) decreases (c) constant (d) none of the above
21. The electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius 10 cm surrounding the total charge is 20 Vm. The flux over a concentric sphere of radius 20 cm will be
(a) 20 Vm. (b) 25 Vm. (c) 40 Vm. (d) 200 Vm.
22. A soap bubble is given negative charge, its radius will
(a) Increase (b) decrease (c) remains unchanged (d) fluctuate
23. Three charges Q, +q and +q is placed at the vertices of a right-angled triangle of side
โaโ. The net electrostatic energy of the configuration is zero, if Q is equal to-
(a) -q/(1+โ2) (b) -2q/(2+โ2) (c) -2q (d) +q
24 . The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is (a) proportional to the square root of the distance between the plates.
(b) linearly proportional to the distance between the plates. (c) independent of the distance between the plates. (d) inversely proportional to the distance between the plates.
25. A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system (a) increases by a factor of 4. (b) decreases by a factor of 2. (c) remains the same. (d) increases by a factor of 2.
26. 64 drops each having the capacity C and potential V are combined to form a big drop. If the charge on the small drop is q, then the charge on the big drop will be (a) 2q (b) 4q (c) 16q (d) 64q
27. A parallel plate condenser is connected with the terminals of a battery. The distance between the plates is 6mm. If a glass plate (dielectric constant K = 9) of 4.5 mm is introduced between them, then the capacity will become (a) 2 times. (b) the same. (c) 3 times. (d) 4 times.
28. Two metal plates form a parallel plate capacitor. The distance between the plates is d. A
metal sheet of thickness and of the same area is introduced between the plates. What is the ratio of the capacitance in the two cases? (a) 2 : 1 (b) 3 : 1 (c) 2 : 1 (d) 5 : 1 29. A capacitor of 4 ฮผF is connected as shown in the circuit. The internal resistance and emf of the battery is 0.5 ฮฉ and 2.5 V respectively. The amount of charge on the capacitor plates will be ---
(a) 0 (b) 4 (c) 16 ฮผC (d) 8 ฮผC
30. A capacitor is charged by using a battery which is then disconnected. A dielectric slab then slipped between the plates, which results in (a) reduction of charge on the plates and increase of potential difference across the plates (b) increase in the potential difference across the plate, reduction in stored energy, but no change in the charge on the plates (c) decrease in the potential difference across the plates, reduction in the stored energy, but no change in the charge on the plates. (d) none of these
31. In a parallel plate capacitor, the capacity increases if (a) area of the plate is decreased (b) distance between the plates increases. (c) area of the plate is increased. (d) dielectric constantly decreases
32. A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates (a) increases (b) decreases (c) does not change (d) becomes zero
33. Two identical capacitors are joined in parallel, charged to a potential V, separated and then connected in series; the positive plate of one is connected to the negative of the other. Which of the following is true? (a) The charges on the free plated connected together are destroyed (b) The energy stored in the system increases (c) The potential difference between the free plates is 2V (d) The potential difference remains constant
34. A capacitor has some dielectric between its plates, and the capacitor is connected to a dc source. The battery is now disconnected and then the dielectric is removed, then (a) capacitance will increase (b) energy stored will decrease (c) electric field will increase (d) voltage will decrease
35. Two spherical conductors each of capacity C are charged to potential V and -V. These are then connected by means of a fine wire. The loss of energy is
(a) zero (b) CV2 (c) CV2 (d) 2 CV2
36 .In series combination of capacitors, the net capacitance of combination : (a) increases (b) decreases (c) remains same (d) zero
37 . A slab of material of dielectric constant K has the same area as the plates of a parallel plate capacitor but has a thickness (3/4)d, where d is the separation of the plates. The ratio of the capacitance C (in the presence of the dielectric) to the capacitance C0 (in the absence of the dielectric) is:
(a)
(b)
(c)
(d) 38 . A capacitor is charged by using a battery which remains connected. A dielectric slab is then slipped between the plates, which results in: (a) Reduction of charge on the plates and increase of potential across the plates (b) Increase in the potential difference across the plates, reduction in stored energy, but no change in the charge on the plates (c) Decrease in the potential difference across the plates, reduction in electric field, but no change in the charge on the plates (d) Increase in charge on the plates and no change in potential difference across the plates 39 . In the given figure, three capacitors C1, C2 and C3 are joined to a battery, with symbols having their usual meanings, the correct conditions will be:
(a) Q1 = Q2 = Q3 and V1 = V2 = V3 + V (b) Q1 = Q2 + Q3 and V = V1 + V2 + V3 (c) Q1 = Q2 + Q3 and V = V1 + V2 (d) Q3 = Q2 and V2 = V3 40. Two capacitors, 3 ฮผF and 4 ฮผF, are individually charged across a 6 volt battery. After being disconnected from the battery, they are connected together with the negative plate of one attached to the positive plate of the other. What is the common potential? (a) 6 volt (b) (6/7) volt (c) 2 volt (d) (3/2) volt
41 . Condenser A has a capacity of 15 ฮผF when it is filled with a medium of dielectric constant 15. Another condenser B has a capacity of 1 ฮผF with air between the plates. Both are charged separately by a battery of 100 V. After charging, both are connected in parallel without the battery and the dielectric material being removed. The common potential is now: (a) 400 V (b) 800 V (c) 1200 V (d) 1600 V 42 . In the circuit as shown in the figure:
The effective capacitance between A and B is: (a) 3 ฮผF (b) 2 ฮผF (c) 4 ฮผF (d) 8 ฮผF 43. A network of four capacitors of capacity equal to C1 = C, C2 = 2C, C3 = 3C and C4 = 4C are connected to a battery as shown in the figure. The ratio of the charges on C2 and C4 is:
(a) 4/7 (b) 3/22 (c) 7/4 (d) 22/3 44. In the circuit diagram, potential difference between point A and B is 200 volt, the potential difference between point a and b when the switch S is open, is:
(a) 100 volt (b) volt (c) volt (d) 50 volt
45 . Between the plates of a capacitor, a dielectric slab is slowly removed and then reinserted. The net work done by the system in this process is:
(a) Zero (b) 1
2(๐พ โ 1)๐ถ๐ฅ2
(c) (d) (K โ 1)CV2 ANSWERS MULTIPLE CHOICE QUESTIONS:
Q.NO. ANS Q.NO. ANS Q.NO. ANS Q.NO. ANS Q.NO. ANS
1 C 11 D 21 A 31 C 41 B
2 C 12 B 22 A 32 A 42 C
3 C 13 B 23 B 33 C 43 B
4 B 14 D 24 C 34 C 44 B
5 D 15 C 25 B 35 C 45 A
6 C 16 B 26 D 36 B
7 D 17 A 27 C 37 C
8 A 18 D 28 A 38 D
9 A 19 B & C 29 D 39 C
10 B 20 A 30 C 40 B
ASSERTION & REASONING QUESTIONS:
Note: -These questions consist of two statemcents, each printed as Assertion and Reason.
While answering these questions, you are rbequired to choose any one of the following
four responses.
(a) If both Assertion and Reason are correct and the Reason is a correct explanation of the
Assertion.
(b) If both Assertion and Reason are correct but Reason is not a correct explanation of the
Assertion.
(c) If the Assertion is correct but Reason is incorrect.
(d) If both the Assertion and Reason are incorrect.
1. Assertion: The equatorial plane of the dipole is an equipotential surface.
Reason: The electric potential at any point on equatorial plane is zero.
2. Assertion: The total charge stored in a capacitor is zero.
Reason: The electric field just outside the capacitor is ฯ/ฮต0. Where ฯ is surface charge
density.
3. Assertion: The electric potential at any point on the equatorial plane of a dipole is zero.
Reason: The work done in bringing a unit positive charge from infinity to a point in
equatorial plane is equal for the two charges of the dipole.
4. Assertion: Electric field inside a conductor is zero.
Reason: The electric potential at all points inside the conductor is the same.
5. Assertion: For a charged particle moving from point A to point B, the net work done by an
electrostatic field on the particle is independent of the path connecting point A and B.
Reason: The net work done by a conservative force on an object moving along a closed
loop is zero.
6. Assertion: If the distance between parallel plates of a capacitor is halved and dielectric
constant is three times, then the capacitance becomes six times.
Reason: capacitance of capacitor does not depend upon the nature of the material.
7. Assertion: A parallel plate capacitor is connected across battery through a key. A
dielectric constant K is introduced between the plates. The energy which is stored
becomes K times.
Reason: The surface density of charge on the plate remains constant.
8. Assertion: Two equipotential surfaces cannot intersect each other.
Reason: Two equipotential surfaces are parallel to each other.
9. Assertion: The potential difference between any two points in an electric field depends
on initial and final position.
Reason: Electric field is a conservative field so the work done per unit positive charge
does not depend on the path followed.
10. Assertion: Work done in moving a charge between any two points in an electric field is
independent of the path followed by the charge between these points.
Reason: Electrostatic force is a non-conservative force.
11. Assertion: Electric field is discontinuous across the surface of a spherical charged shell.
Reason: Electric potential is continuous across the surface of a spherical charged shell.
12. Assertion: Polar molecules have permanent dipole moment.
Reason: In polar molecules, the centre of positive and negative charges coincide even
when there is no external electric field.
13. Assertion: Electric energy resides out of the spherical isolated conductor.
Reason: The electric field at any point inside the conductor is zero.
14. Assertion: Dielectric polarisation means formation of positive and negative charges
inside the dielectric.
Reason: Free electrons are formed in this process.
15. Assertion: A dielectric is inserted between the plates of a battery connected to a
capacitor. The energy of the capacitor increases.
Reason: Energy of the capacitor is U = CV2/2.
16. Assertion: When a dielectric slab is gradually inserted between the plates of an isolated
parallel plate capacitor, the energy of the system decreases.
Reason: The electrostatic force between the plates decreases.
ANSWERS(Assertion & Reason):
1. b 2.c 3. d 4. b 5. a 6. c 7.c 8.c
9. a 10.c 11. b 12. c 13.a 14. c 15. a 16. c
CASE STUDY BASED QUESTIONS:
Q1. CAPACITOR: The capacity of a condenser increases both when a conducting slab or an
insulating slab is introduced between the plates of the condenser. In the former case,
electric field inside the conductor is zero and in the latter case, electric field inside the
insulator decreases. Thus potential difference decreases in both cases between the plates of
the condenser and hence capacity of the condenser increases.
Now answer the followings.
1. New capacitance of the capacitor becomes when a dielectric medium of dielectric
constant k is introduced between its plates
(a) K times (b) 1/K times (c) no change (d) K2 times
2. Charge on the capacitor is doubled. Its capacity becomes K times, where K is equal to
(a) 2 (b) 1 (c)1/2 (d) 4
3. Which are the dielectric medium
(a)Air or vacuum (b) mica, glass, ceramic
(c) Paper, Oil, Rubber (d) all the above
4. Energy of a capacitor of capacitance 10ฮผ F having charge 10 ฮผC is
(a) 5ฮผJ (b) 10ฮผJ (c) 15ฮผJ (d) 2.5ฮผJ
5. Capacitor stores which type of energy
(a) kinetic energy (b) potential energy
(c) vibrational energy (d) heat energy
6. Dielectric constant is equal to
(a) Cair / Cmed (b) Cmed / Cair (c) Cair x Cmed (d) none of these
Q2. CAPACITOR: A capacitor contains two oppositely charges metallic conductors at a finite
separation. It is a device by which capacity of storing charge may be varied simply by
changing separation and or medium between the conductors. Capacitance is numerically
equal to charge on the plates of capacitor divided by the potential. Now answer the
followings.
(1) Electric field between plates of capacitor is
(a) Uniform (b) Non โuniform
(c) depends on size of capacitor (d) None of these
(2) Capacitance of capacitor is increased by
(a) Inserting medium between its plates
(b) Decreasing area of its plates
(c) Increasing distance between its plates
(d) None of these
(3) The electric field intensity between plates of capacitor is
(a) ฯ / ฮต0 (b) ฯ / 2ฮต0 (c) 2ฯ / ฮต0 (d) ฯ / 3ฮต0
(4) Energy stored in a capacitor of capacitance 6 ฮผ F having charge on its plate 6 ฮผ C is
(a)3 ฮผ J (b) 6 ฮผ J (c)12 ฮผ J (d)4 ฮผ J
(5) When a number of capacitors are connected in series between two points, all the
capacitors possesses same
(a) capacity (b) Potential (c) charge (d)none of these
(6) On reducing potential across a capacitor, its capacitance
(a) decreases (b) increases (c) remains same (d) none of these
Q3. ELECTROSTATIC POTENTIAL: Electrostatic potential of a charged body represents the
degree of electrification of the body. It determines the flow of electric charge between two
charged bodies placed in contact with each other. The charge always flows from a body of
higher potential to another body at lower potential. The flow of charge stops as soon as the
potential of the two bodies become equal. Now answer the followings.
1. Nm/C is the unit of
(a) Electric potential (b) electric field intensity
(c) electric flux (d) None of these
2. A uniform electric field of 100 N/C exists vertically upward direction. The decrease in
electric potential as one goes up through a height of 5cm is
(a) 20V (b) 120 V (c) 5V (d) zero
Hint* V = E x d
3. Work done to bring a unit positive charge unaccelerated from infinity to a point inside
electric field is called
(a) electric field (b) electric potential (c) capacitance (d) electric flux
4. Two conducting spheres A and B of radii a and b respectively are at the same potential.
The ratio of surface charge densities of A and B is
(a) b/a (b)a/b (c)a2/ b2 (d) b2/ a2
Hint* 4. Q1/q2 =C1V/ C2V =C1/C2 = (4ฯ ฮต0 a/4ฯ ฮต0 b) = a/b
and ฯ1= q/4ฯ a2 then ฯ1/ฯ2 = (q1/q2)x (b/a)2 = b/a
5. Electric potential at a distance of 27 cm from a point charge 9 nC, is given by
(a) 200 V (b) 100 V (c) 300 V (d) 50 V
Hint* V = kQ/R (R = radius of shell)
6. Two charges -6ฮผC and 10ฮผC are placed at distant 18 cm apart. Electric potential at the
midpoint joining these two will be
(a) 4x 105V (b) 4x 104V (c) 4x 103V (d) 4x 106V
Hint* V = k/r ( Q1 +Q2) where r = 9 cm
Q4. Electrostatic Shielding: The electric field inside the cavity is zero, whateverbe the size
and shape of the cavity and whatever be the charge on the conductor and the external
fields in which it might be placed. The electric field inside a charged spherical shell is zero.
But the vanishing of electric field in the (charge-free) cavity of a conductor is , as mentioned
above, a very general result. A related result is that even if the conductor is charged or
charges are induced on a neutral conductor by an external field, all charges reside only on
the outer surface of a conductor with cavity. The proofs of the results noted in Fig.are
omitted here, but we note their important implication. Whatever be the charge and field
configuration outside, any cavity in a conductor remains shielded from outside electric
influence: the field inside the cavity is always zero. This is known as electrostatic shielding.
The effect can be made use of in protecting sensitive instruments from outside electrical
influence.
1. A metallic shell having inner radius R1and outer radii R2 has a point
charge Q kept inside cavity. Electric field in the region R1< r < R2where r is
the distance from the centre is given by a) Depends on the value of r b) Zero c) Constantand nonzeroeverywhere d) Noneoftheabove
2. The electric field inside the cavity is depend on a) Size of the cavity b) Shape of the cavity c) Charge on the conductor d) None of the above
3. Electrostatic shielding is based (a) Electric field inside the cavity of a conductor is less than zero (b) Electric field inside the cavity of a conductor is zero (c) electric field inside the cavity of a conductor is greater than zero (d) electric field inside the cavity of a plastic is zero
4. During the lightning thunderstorm, it is advised to stay a) inside the car b) under trees
c) in the open ground d) on the car
5. Which of the following material can be used to make a Faraday cage (based on electrostatic shielding) a) Plastic b) Glass c) Copper d) Wood
Q5.Electrostatic Potential & Field: Read the passage given below and answer the following questions: The potential at any observation point P of a static electric field is defined as the work done by the external agent (or negative of work done by electrostatic field)in slowly bringing a unit positive point charge from infinity to the observation point. Figure shows the potential variation along the line of charges. Two point charges Q1 and Q2 lie along a line at a distance from each other.
The following questions are multiple choice questions. Choose the most appropriate answer: 1. At which of the points 1, 2 and 3 is the electric field is zero? (a)1 (b) 2 (c) 3 (d) Both (a) and (b)
Hint: Asโ๐๐
๐๐ =Er, the negative of the slope of V versus r curve represents the component of
electric field along r. Slope of curve is zero only at point 3. Therefore, the electric field vector is zero at point 3.
2. The signs of charges Q1 and Q2 respectively are (a) positive and negative (b) negative and positive (c) positive and positive (d) negative and negative Hint: Near positive charge, net potential is positive and near a negative charge, net potential is negative. Thus, charge Q1 is positive and Q2, is negative.
3. Which of the two charges Q1, and Q2 is greater in magnitude? (a) Q2 (b) Q1 (c) Same (d) canโt determined Hint: From the figure, it can be seen that net potential due to two charges is positive everywhere in the region left to charge Q1. Therefore the magnitude of potential due to charge Q1 is greater than due to Q2.
4. Which of the following statement is not true? (a) Electrostatic force is a conservative force. (b) Potential energy of charge q at a point is the work done per unit charge in bringing a charge from any point to infinity. (c) When two like charges lie infinite distance apart, their potential energy is zero. (d) Both (a) and (c).
5. Positive and negative point charges of equal magnitude are kept at (0,0,๐
2) and(0,0,
โ๐
2)
respectively. The work done by the electric fieldwhen another positive point charge is moved from(-a, 0, 0) to (0, a, 0) is (a) positive (b) negative (c) zero (d) depends on the path connecting the initial and final position Hint: It can be seen that potential at the points both A and Bare zero. When the charge is moved from A to B, work done by the electric field on the charge will be zero.
6. Work done in moving a positive charge on a equipotential surface is: (a) negative (b) zero (c) positive (d) infinte
ANSWERS(Case Study Questions):
ANS. 1 ANS. 2 ANS. 3 ANS. 4 ANS. 5 ANS. 6
Q.1 a b d a b b
Q.2 a a a a c c
Q.3 a c b a c a
Q.4 b d b a c โฆโฆ
Q.5 c a b b c b
CHAPTER-3 CURRENT ELECTRICITY
GIST OF LESSON: โข Current carriers โ The charge particles which flow in a definite direction constitutes the electric
current are called current carriers. E.g.: Electrons in conductors, Ions in electrolytes, Electrons and holes in semi-conductors.
โข Electric current is defined as the amount of charge flowing through any cross section of the conductor in unit time. I = Q/t.
โข Current density J = I/A.
โข Ohmโs law: Current through a conductor is proportional to the potential difference across the ends of the conductor provided the physical conditions such as temperature, pressure etc. Remain constant. V ฮฑ I i.e. V = IR, Where R is the resistance of the conductor. Resistance R is the ratio of V & I
โข Resistance is the opposition offered by the conductor to the flow of current.
โข Resistance R = ฯl/A where ฯ is the resistivity of the material of the conductor- length and A area of cross section of the conductor. If l is increased n times, new resistance becomes n2R. If A is increased
n times, new resistance becomes Rn2
1
โข Resistivity ฯ = m/ne2ฯ, Where m, n, e are mass, number density and charge of electron respectively, ฯ-relaxation time of electrons. ฯ is independent of geometric dimensions.
โข Relaxation time is the average time interval between two successive collisions
โข Conductance of the material G =1/R and conductivity ฯ=1/ฯ
โข Drift velocity is the average velocity of all electrons in the conductor under the influence of applied electric field. Drift velocity Vd = (eE/m)ฯ also I = neAvd
โข Mobility (ฮผ) of a current carrier is the ratio of its drift velocity to the applied field dV
E =
โข Effect of temperature on resistance: Resistance of a conductor increase with the increase of
temperature of conductor (1 )T oR R T= + , where ฮฑ is the temperature coefficient of resistance of
the conductor. ฮฑ is slightly positive for metal and conductor, negative for semiconductors and insulators and highly positive for alloys.
โข Cells: E.M.F of a cell is defined as the potential difference between its terminals in an open circuit. Terminal potential difference of a cell is defined as the p.d between its ends in a closed circuit.
โข Internal resistance r of a cell is defined as the opposition offered by the cell to the flow of current.
r = RV
E
โ1 where R is external resistances.
โข Grouping of cells :
i) In series grouping circuit current is given by s
nEI
R nr=
+,
ii) In parallel grouping circuit current is given by p
mEI
r mR=
+ where n, m are number of cells in series
and parallel connection respectively.
โข Kirchhoffโs Rule:
i) Junction Rule:-The algebraic sum of currents meeting at a point is zero. 0I =
ii) Loop rule:-The algebraic sum of potential difference around a closed loop is zero V o=
โข Wheatstone bridge is an arrangement of four resistors arranged in four arms of the bridge and is used to determine the unknown resistance in terms of other three resistances. For balanced
Wheatstone Bridge,P R
Q S=
โข Slide Wire Bridge or Metre Bridge is based on Wheatstone bridge and is used to measure unknown resistance. If unknown resistance S is in the right gap, R
l
ls
โ=
100
โข Potentiometer is considered as an ideal voltmeter of infinite resistance.
โข Principle of potentiometer: The potential drop across any portion of the uniform wire is proportional to the length of that portion of the wire provided steady current is maintained in it i.e. v ฮฑ l
โข Potentiometer is used to (i) compare the e.m.f.s of two cells (ii) determine the internal resistance of a cell and (iii) measure small potential differences.
โข Expression for comparison of e.m.f of two cells by using potentiometer,2
1
2
1
l
l=
where 21, ll are the
balancing lengths of potentiometer wire for e.m.fs 1 and 2 of two cells.
โข Expression for the determination of internal resistance of a cell I is given by Rl
ll
โ
2
21
Where 1l is the balancing length of potentiometer wire corresponding to e.m.f of the cell, 2l that of
terminal potential difference of the cell when a resistance R is connected in series with the cell whose internal resistance is to be determined
โข Expression for determination of potential differenceL
rl
rRV
+=
. where L is the length of the
potentiometer wire, l is balancing length, r is the resistance of potentiometer wire, R is the resistance included in the primary circuit.
โข Jouleโs law of heating states that the amount of heat produced in a conductor is proportional to (i) square of the current flowing through the conductor,(ii) resistance of the conductor and (iii) time for which the current is passed. Heat produced is given by the relation H=I2Rt
โข Electric power: It is defined `as the rate at which work is done in maintaining the current in electric circuit. P =VI = I2R =V2/R. Power P is the product of V & I
โข Electrical energy: The electrical energy consumed in a circuit is defined as the total work done in maintaining the current in an electrical circuit for a given time. Electrical energy = VIt = I2Rt =(V2/R)t = Pt
โข Commercial unit of energy 1KWh= 3.6ร106J
CONCEPT MAP
Flow of Charges
MULTIPLE CHOICE QUESTIONS:
1 Consider a current carrying wire current I in the shape of a circle. Note that as the current
progresses along the wire, the direction of j (current density) changes in an exact manner,
while the current/remain unaffected. The agent that is essentially responsible for is-
(a) source of emf.
(b) electric field produced by charges accumulated on the surface of wire.
(c) the charges just behind a given segment of wire which push them just the right way by
repulsion.
(d) the charges ahead.
2 Which of the following is wrong? Resistivity of a conductor is
(a) independent of temperature.
(b) inversely proportional to temperature.
(c) independent of dimensions of conductor.
(d) less than resistivity of a semiconductor
3 Drift velocity vd varies with the intensity of electric field as per the relation
(a) vd โ E
(b) vd โ 1/E
(c) vd = constant
(d) vd โ Eยฒ
4 For a cell, the graph between the potential difference (V) across the terminals of the cell and
the current (I) drawn from the cell is shown in the figure.
The e.m.f. and the internal resistance of the cell are
(a) 2V, 0.5 ฮฉ
(b) 2V, 0.4 ฮฉ
(c) Greater than 2V, 0.5 ฮฉ
(d)less than 2V, 0.4 ฮฉ
5 When there is an electric current through a conducting wire along its length, then an electric
field must exist
(a) outside the wire but normal to it.
(b) outside the wire but parallel to it.
(c) inside the wire but parallel to it.
(d) inside the wire but normal to it.
6 From the graph between current I and voltage V shown below, identify the portion
corresponding to negative resistance
(a) AB (b) BC (c) CD (d) DE
7 Which of the following I-V graph represents ohmic conductors?
8 The I-V characteristics shown in figure represents
(a) ohmic conductors (b) non-ohmic conductors (c) insulators (d) superconductors
9 . Which of the following is correct for V-I graph of a good conductor?
10 A cell having an emf E and internal resistance r is connected across a variable external
resistance R. As the resistance R is increased, the plot of potential difference V across R is
given by
11 In parallel combination of n cells, we obtain
(a) more voltage (b) more current (c) less voltage (d) less current
12 For measurement of potential difference, a potentiometer is preferred over voltmeter
because
(a) potentiometer is more sensitive than voltmeter.
(b) the resistance of potentiometer is less than voltmeter.
(c) potentiometer is cheaper than voltmeter.
(d) potentiometer does not take current from the circuit.
13 Resistivity of conductor depend on
(a)Temperature of conductor
(b)Length of conductor
(c)Area of conductor
(d)Current in conductor
14 We use alloy for making of resistors, because they have:
Temp. coefficient Resistivity
(a) Low Low
(b) High High
(c) High Low
(d) Low High
15 Resistances R1 and R2 are connected respectively in the left gap and right gap of a metre
bridge. If the balance point is located at 55 cm, the ratio R2/R1 is
(a) 4/5 (b) 5/4 (c) 9/11 (d) 11/9
16 In a potentiometer arrangement; a cell of emf 1.25 V gives a balance point at 35.0 cm length
of the wire. If the cell is replaced by another cell and the balance point shifts to 63.0 cm,
what is the emf of the second cell?
(a) 1.00 V (b)1.25 V (c)2.00 V (d)2.25 V
17 Massesofthreewiresofcopperareintheratioof1:3:5andtheirlengthsareintheratioof 5 : 3 : 1.
The ratio of their electrical resistances are
(a) 1 : 3 : 5 (b) 5 : 3 : 1 (c)1 : 15 : 125 (d)125 : 15 : 1
18 S I unit of resistivity is
(a) Ohm (b) mho (c) ohm-m (d) mho-m-1
19 Resistances 3 ฮฉ and 6 ฮฉ are connected across the left gap and right gap respectively of a
metre bridge. When a 6 ฮฉ resistance is connected in series with the 3 ฮฉ resistance in the
left gap, the shift in the balance point is
(a) 25 cm (b) 22 cm (c) 26.67 cm (d) 29.67 cm
20 Two cells when connected in series are balanced on 8m on a potentiometer. If the cells
are connected with polarities of one of the cell is reversed, they balance on 2m. The
ratio of e.m.f.'s of the two cellsis
(a)3:5 (b)5 :3 (c)3: 4 (d)4 :3
21 A wire of 10 ฮฉ resistance is stretched to thrice its original length. Its new
resistance will be
(a) 90 ฮฉ (b) 80 ฮฉ (c) 70 ฮฉ (d) 60 ฮฉ
22 A cell of internal resistance 3 ohm and emf 10 volt is connected to a uniform wire of length
500 cm and resistance 3 ohm. The potential gradient in the wire is
(a) 30mV/cm (b) 10 mV/cm (c) 20mV/cm (d)4 mV/cm
23 Which of the following characteristics of electrons determines the current in a
conductor?
(a) Drift velocity alone
(b)Thermal velocity alone.
(c)Both drift velocity and drift velocity
(d)Neither drift nor thermal velocity
24 Which of the following statements are true with regard to resistance?
(a)Resistance is directly proportional to a length of the wire
(b)Resistance is directly proportional to an area of cross section of the wire
(c)Resistance is inversely proportional to the length of the wire
(d)Resistance is inversely proportional to the resistivity of the wire
25 What is the value of current if a 50C charge flows in a conductor over a period of 5
seconds?
(a)5A (b)10A (c)15A (d) 20A
26 For a cell of e.m.f. 2 V, a balance is obtained for 50 cm of the potentiometer wire. If the
cell is shunted by a 2 ฮฉ resistor and the balance is obtained across 40 cm of the wire,
then the internal resistance of the cell is
(a) 1 ฮฉ (b) 0.5 ฮฉ
(c) 1.2 ฮฉ (d) 2.5 ฮฉ
27 With rise in temperature, relaxation time in metals
(a)Decreases (b)Increases
(c)Remains same (d)First increase then decrease
28 Two bulbs of 500 W and 200 W rated at 250 V will have resistance ratio as
(a) 4:25 (b) 25:4 (c) 2:5 (d) 5:2
29 In the circuit shown in figure E1 = 7V, E2 = 7V R1 = R2 = 1 ฮฉ and R3 = 3 ฮฉ respectively. The
current through the resistance R3 is
(a) 2 A
(b) 3.5 A
(c) 1.75 A
(d) 2.5 A
30 In a Whetstoneโs bridge, all the four arms have equal resistance R. If resistance of the
galvanometer arm is also R, then equivalent resistance of the combination is
(a)4 R (b) 3 R (c) 2 R (d) 1 R
31 The current in the given circuit will be ________ .
(a) 1A (b) 0.1A (c) 0.2 A (d) 10A
32 A resistance R is to be measured using a meter bridge, a student chooses the standard
resistance S to be 100 ฮฉ He finds the null point at l1 = 2.9 cm. He is told to attempt to
improve the accuracy. Which of the following is a useful way?
(a) He should measure l1, more accurately
(b) He should change S to 1000 ฮฉ and repeat the experiment
(c) He should change S to 3 ฮฉ and repeat the experiment
(d) He should have given up hope of a more accurate measurement with a meter bridge
33 Two cells of emfs approximately 5 V and 10 V are to be accurately compared using a
potentiometer of length 400 cm.
(a) The battery that runs the potentiometer should have voltage of 8 V.
(b) The battery of potentiometer can have a voltage of 15 V and R adjusted so that the
potential drop across the wire slightly exceeds 10 V.
(c) The first portion of 50 cm of wire itself should have a potential drop of 10 V.
(d) Potentiometer is usually used for comparing resistances and not voltages.
34 A metal rod of length 10 cm and a rectangular cross-section of 1 cm x 1/2 cm is connected to
a battery across opposite faces. The resistance will be
(a) maximum when the battery is connected across 1 cm x 1/2 cm faces
(b) maximum when the battery is connected across 10 cm x 1 cm faces
(c) maximum when the battery is connected across 10 cm x 1/2 cm faces
(d) same irrespective of the three faces
35 Kirchhoffโs junction rule is a reflection of
(a) conservation of current density vector.
(b) conservation of charge.
(c) the fact that the momentum with which a charged particle approaches a junction is
unchanged (as a vector) as the charged particle leaves the junction.
(d) the fact that there is no accumulation of charges at a junction.
36 Temperature dependence of resistivity ฯ(T) of semiconductors, insulators and metals is
significantly based on the following factors:
(a) number of charge carriers can change with temperature T.
(b) time interval between two successive collisions can depend on T.
(c) length of material can be a function of T.
(d) mass of carriers is a function of T.
37 In a meter bridge, the point D is a neutral point (figure).
(a) The meter bridge can have no other neutral. A point for this set of resistances.
(b) When the jockey contacts a point on meter wire left of D, current flows to B from the
wire
(c) When the jockey contacts a point on the meter wire to the right of D, current flows from
B to the wire through galvanometer
(d) When R is increased, the neutral point shifts to left
38 For measurement of potential difference, a potentiometer is preferred over voltmeter
because
(a) potentiometer is more sensitive than voltmeter.
(b) the resistance of potentiometer is less than voltmeter.
(c) potentiometer is cheaper than voltmeter.
(d) potentiometer does not take current from the circuit.
39 When there is an electric current through a conducting wire along its length, then an electric
field must exist
(a) outside the wire but normal to it.
(b) outside the wire but parallel to it.
(c) inside the wire but parallel to it.
(d) inside the wire but normal to it.
40 An electric heater is connected to the voltage supply. After few seconds, current gets its
steady value then its initial current will be
(a) equal to its steady current
(b) slightly higher than its steady current
(c) slightly less than its steady current
(d) zero
41 In a Wheatstone bridge if the battery and galvanometer are interchanged then the deflection
in galvanometer will
(a) change in previous direction
(b) not change
(c) change in opposite direction
(d) none of these.
42 In a potentiometer of 10 wires, the balance point is obtained on the 7th wire. To shift the
balance point to 9th wire, we should
(a) decrease resistance in the main circuit.
(b) increase resistance in the main circuit.
(c) decrease resistance in series with the cell whose emf is to be measured.
(d) increase resistance in series with the cell whose emf is to be determined.
43 AB is a wire of potentiometer with the increase in the value of resistance R, the shift in the
balance point J will be
(a) towards B
(b) towards A
(c) remains constant
(d) first towards B then back towards A
44 Consider a simple circuit shown in figure stands for a variable resistance Rโ. Rโ can vary from
R0 to infinity, r is internal resistance of the battery (r << R << R0). [NCERT Exemplar]
(a) Potential drop across AB is not constant as R0 is varied.
(b Current through R0 is nearly a constant as R0 is varied.
(c) Current I depends sensitively on R0.
(d) IโฅVr+R always.
45 n the circuit shown, potential difference between X and Y is ________ and across 40 ฮฉ is
________ .
(a) 120V, 0V
(b) 60V, 2V
(c) 30V, 4V
(d) None of these
ANSWERS(Multiple Choice Questions):
Q.No. Answer Q.No. Answer
1 b 26 b
2 a 27 a
3 a 28 c
4 b 29 a
5 c 30 d
6 c 31 c
7 a 32 c
8 b 33 b
9 b 34 a
10 b 35 b
11 b 36 a,b
12 d 37 a,c
13 a 38 d
14 a 39 c
15 d 40 b
16 d 41 b
17 d 42 d
18 d 43 a
19 c 44 d
20 b 45 a
21 a
22 b
23 c
24 a
25 b
ASSERTION AND REASON BASED QUESTIONS: Two statements are given-one labeled Assertion (A) and the other labeled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below. a) Both A and R are true and R is the correct explanation of A b) Both A and R are true but R is NOT the correct explanation of A c) A is true but R is false d) A is false and R is also false
1. Assertion (A): The dimensional formula for product of resistance and conductance is same as
for dielectric constant.
Reason(R): Both have dimension for time constant.
2. Assertion (A): A wire carrying an electric current has no electric field around it.
Reason(R): rate of flow of electron is one direction is equal to the rate of flow of protons in opposite direction.
3. Assertion(A): The binding of an insulated wire increase the resistance of wire
Reason(R): Drift velocity of electron in bent wire decrease.
4. Assertion (A): The EMF of the driver cell in the potentiometer experiment should be greater
than the EMF of the cell to be determined.
Reason(R): The fall of potential across the potentiometer wire should not be less than the EMF of the cell to be determined.
5. Assertion(A).The value of temperature coefficient of resistance of positive for metals
Reason(R): The temperature coefficient of resistance for insulator is always positive
6. Assertion (A).In a meter bridge experiment null point for an unknown resistance is put
inside an enclosure maintained at a higher temperature. The null point can be obtained at
the same point as before by discharging the value of standard resistance.
Reason(R): Resistance of metal increase with increase in temperature.
7. Assertion (A).There is no current in metals in the absence of electric field.
Reason(R): Motion of free electron is randomly.
8. Assertion (A).In a simple battery circuit the point of lowest potential is positive terminal of
the battery.
Reason(R): The current flows towards the point of the higher potential as it flows in such a circuit from the negative to positive terminal.
9. Assertion (A). If a wire is stretched to increase its length X times then its resistance also
increases.
Reason(R): Resistance of conductor is directly depend upon the length of conductor.
10. Assertion (A). A potentiometer of longer length is used for accurate measurement.
Reason(R): The potential gradient for a potentiometer of longer length with a given source of EMF becomes small.
11. Assertion (A). When the Cell is in the open circuit there is no force on a test charge inside
the electrolyte of the cell.
Reason(R): There is no field inside the cell when the cell is in the open circuit. 12. Assertion (A). if the potential difference between two point is zero and resistance between
those point is zero current may flow between the points
Reason(R): Kirchhoff 1st law is based on conservation of charge
13. Assertion (A). The constant potential difference is applied across a conductor if temperature
of conductor is increase, drift speed of electron will decrease
Reason(R): resistivity increase with increase in temperature 14. Assertion (A). A potentiometer is preferred over a volt meter of the measurement of emf of
a cell
Reason(R): A potentiometer is preferred as it does not draw any current from the cell
ANSWERS(Assertion and Reason): 1 C 5 C 9 D 13 B
2 C 6 D 10 A 14 A
3 D 7 A 11 C
4 A 8 D 12 B
Explanation of Answers(A & R): 1. c) Resistance x conductance = R * 1/R = [M0L0T0] 2. c)There is no net charge on the wire 3. d) both are false 4. a) 5. c) ฮฑ is positive for metal and negative for insulator 6. d) same null point can be obtained by increase in standard resistance 7.a) 8.d) current flow from higher potential to lower potential 9.d) resistance of a wire becomes x2 times 10.a) 11.c) 12.b) 13. b) 14. a)
CASE STUDY BASED QUESTIONS:
Read the source given below and answer any four out of the following questions:
1. Potentiometer: The potentiometer consists of a long resistive wire (L) and a battery of known EMF,
'V' whose voltage is known as driver cell voltage. Assume a primary circuit arrangement by connecting
the two ends of L to the battery terminals. One end of the primary circuit is connected to the cell
whose EMF 'E' is to be measured and the other end is connected to galvanometer G. This circuit is
assumed to be a secondary circuit.
(i) How can we increase the sensitivity of a potentiometer?
(a) Increasing the potential gradient
(b) Decreasing the potential gradient
(c) Decreasing the length of potentiometer wire
(d) Increasing resistance put in parallel
(ii) If l1 and l2 are the balancing lengths of the potentiometer wire for the cells of EMFs ฮต1 and ฮต2 , then
(a)ฮต1+ ฮต2= l1 + l2
(b) ฮต1/ ฮต2= l1/l2
(c) ฮต1* ฮต2 =l1*l2
(d) None of these
iii) Example of a potentiometer is
(a) Mobile
(b)Modem
(c) Joystick
(d) All of these
(iv) The emf of a cell is always greater than its terminal voltage. Why?
(a) Because there is some potential drop across the cell due to its small internal resistance
(b) Because there is some potential drop across the cell due to its large internal resistance
(c) Because there is some potential drop across the cell due to its low current
(d) Because there is some potential drop across the cell due to its high current
(v) Why is a ten wire potentiometer more sensitive than a four-wire one?
(a) Small potential gradient
(b) Large potential gradient
(c) Large length
(d) None of these
2. Factors Affecting Resistance: According to Ohm's law, the current flowing through a conductor is
directly proportional to the potential difference across the ends of the conductor i .e., I ฮฑ V ,so V/I=
R, where R is resistance of the conductor. Electrical resistance of a conductor is the obstruction posed
by the conductor to the flow of electric current through it. It depends upon length, area of cross-
section, nature of material and temperature of the conductor. We can write, R or R = p =, where p is
electrical resistivity of the material of the conductor.
(i) Dimensions of electric resistance is
(a) [ML2T-2A-2] (b) [ML2T-3A-2] (c) [M-1L-2T-1A] (d) [M-1L2T2A-1]
(ii) If 1 ยตA current flows through a conductor when potential difference of 2 volt is applied across its
ends, then the resistance of the conductor is
(a) 2x 106 ฮฉ (b) 3 x 105 ฮฉ (c) 1.5 x 105 ฮฉ (d) 5 x 107 ฮฉ
(iii) Specific resistance of a wire depends upon
(a) Length (b) cross-sectional area (c) mass (d) none of these
(iv) The slope of the graph between potential difference and current through a conductor is
(a) A straight line (b) curve
(c) First curve then straight line (d) first straight line then curve
(v) The resistivity of the material of a wire 1.0 m long, 0.4 mm in diameter and having a resistance of
2.0 ohm is
(a) 1.57 x 10-6 ฮฉ m (b) 5.25 x 10-7 ฮฉ m (c) 7.12 x 10-5 ฮฉ m (d) 2.55 x 10-7 ฮฉ m
3.Kirchhoff's Rules:
In 1942, a German physicist Kirchhoff extended Ohm's law to complicated circuits and gave two laws,
which enable us to determine current in any part of such a circuit. According to
Kirchhoff's first rule, the algebraic sum of the currents meeting at a junction x
in a closed electric circuit is zero. The current flowing in a conductor towards
the junction is taken as positive and the current flowing away from the junction is taken as negative.
According to Kirchhoff's second rule, in a closed loop, the algebraic sum of the emf's and algebraic
sum of the products of current and resistance in the various arms of the loop is zero. While traversing
a loop, if negative pole of the cell is encountered first, then its emf is negative, otherwise positive.
(i) Kirchhoff's Ist law follows
(a) Law of conservation of energy (b) Law of conservation of charge
(c)Law of conservation of momentum (d) Newton's third law of motion
(ii) The value of current I in the given circuit is
(a) 4.5A
(b) 3.7 A
(c) 2.0 A
(d) 2.5A
(iii) Kirchhoff's loop law is based on
(a) Law of conservation of momentum of electron
(b)Law of conservation of charge and energy
(c) Law of conservation of energy
(d) None of these.
(iv) Point out the right statements about the validity of Kirchhoff's Junction rule.
(a) The current flowing towards the junction is taken as positive.
(b) The currents flowing away from the junction are taken as negative.
(c) Bending or reorienting the wire does not change the validity of Kirchhoff's Junction rule.
(d) All of the above
(v) Potential difference between A and B in the circuit shown here is B
(a) 4V
(b) 5.6 V
(c) 2.8 V
(d) 6 V
4. Wheatstone Bridge and its Applications:
WHEATSTONE bridge is an arrangement of four resistances P, Q, R and S connected as shown in the
figure.
Their values are so adjusted that the galvanometer G shows no deflection. The bridge is then said to
be balanced when this condition is achieved happens. In the setup shown here, the points B and D
are at the same potential and it can be shown that P/Q=R/S. This is called the balancing condition. If
any three resistances are known, the fourth can be found .The practical form of Wheatstone bridge is
slide Wire Bridge or Meter Bridge. Using this the unknown resistance S= (100-I)/l*R, where l is the
balancing length of the Meter bridge.
(i) In a Wheatstone bridge circuit, P = 5ฮฉ, Q = 6ฮฉ, R = 10ฮฉ and S= 5ฮฉ. What is the value of additional
resistance to be used in series with S, so that the bridge is balanced?
(a) 9ฮฉ (b) 7ฮฉ (c) 10ฮฉ (d) 5 ฮฉ
(ii) A Wheatstone bridge consisting of four arms of resistances P, Q, R, S is most sensitive when
(a) All the resistances are equal
(b) All the resistances are unequal
(c) The resistances P and Q are equal but R >> P and S >>Q
(d) The resistances P and Q are equal but R<< P and S << Q
(iii) When a metal conductor connected to left gap of a meter bridge is heated, the balancing point
(a) Shifts towards right (b) shifts towards left
(c) Remains unchanged (d) remains at zero.
(iv) The percentage error in measuring resistance with a meter bridge can be minimized by adjusting
the Balancing Point close to
(a) 0 (b) 20 cm (c) 50 cm (d) 80 cm
(v) In a meter bridge experiment, the ratio of left gap resistance to right gap resistance is 2: 3. The
balance point from left i
(a) 20 cm (b) 50 cm (c) 40 cm (d) 60 cm
5. Potentiometer: An Ideal Voltmeter:
Potentiometer is an apparatus used for measuring the emf of a cell or potential difference between
two points in an electrical circuit accurately. It is also used to determine the internal resistance of a
primary cell. The potentiometer is L based on the principle that, if V is the potential difference across
any portion of the wire of length โlโ and resistance R, then V directly prop. to l or V = kl where k is the
potential gradient. Thus, potential difference across any portion of potentiometer wire is directly
proportional to length of the wire of that portion. The potentiometer wire must be uniform. The
resistance of potentiometer wire should be high.
(i) Which one of the following is true about potentiometer?
(a) Its sensitivity is low.
(b) It measures the emf of a cell very accurately.
(c) It is based on deflection method.
(d) It takes current from the circuit.
(ii) A current of 1.0 mA is flowing through a potentiometer wire of length 4 cm and of resistance 4ฮฉ
The potential gradient of the potentiometer wire is
(a) 10-3 Vm -1 (b) 10-5 Vm-2 (c) 2x 10-3 Vm-1 (d) 4x10-3 Vm-1
(iii) Sensitivity of a potentiometer can be increased by
(a) Decreasing potential gradient along the wire
(b)Increasing potential gradient along the wire
(c) Decreasing current through the wire
(d)Iincreasing current through the wire
(iv) A potentiometer is an accurate and versatile device to make electrical measurements of EMF
because the method involves
(a) potential gradients
(b) a condition of no current flow through the galvanometer
(c) a combination of cells, galvanometer and resistances
(d) cells
(v) In a potentiometer experiment, the balancing length is 8 m, when the two cells E, and E, are joined
in series.When the two cells are connected in opposition the balancing length is 4 m. The ratio of the
e. m. f. of two cells (E/ E) is
(a) 1: 2 (b) 2: 1 (c) 1: 3 (d) 3: 1
ANSWERS(Case Study Questions):
Q.1 Q.2 Q.3 Q.4 Q.5
ANS.i b b a b b
ANS.ii d a c a a
ANS.iii c d c a a
ANS.iv a a d c b
ANS v a d b c d
CHAPTER 4
MOVING CHARGES & MAGNETISM
GIST OF LESSON:
1. Biot-Savart Law The magnetic field B due to a current element dl carrying a steady current I at a point, at distance r from the current element is
๐๐ต =๐0๐ผ๐๐๐๐๐๐
4๐๐2 ฮผ0=4ฯ x 10
-7 Tm/A
*Direction of dB can be found by using Maxwellโs Right hand thumb rule.]
2. Applications : (i) Magnetic field at a centre of a current carrying circular coil B= ฮผ0I/2a (ii) Magnetic field at a point on the axis of current carrying coil.
๐ต =๐0 ๐๐ผ๐2
2(๐2+๐ฅ2)32
N=no. of turns in the coil
3. Ampereโs circuital law:The line integral of magnetic field B around any closed path in vacuum is equal to ๐0 time the total current enclosed by the path โฎ B.dl= ฮผ0I
4. Applications i) Magnetic field due to straight infinitely long current carrying straight conductor. B= ฮผ0I/2ฯr ii) Magnetic field due to a straight solenoid carrying current B= ฮผ0nI
n= no. of turns per unit length iii) Magnetic field due to toroidal solenoid carrying current. B= ฮผ0NI/2ฯr
N= Total no. of turns.
5. Force on a moving charge (i) In magnetic field F=q(V x B) (ii) In magnetic and electric field(Lorentz force) F=qxE+(ฮฝ x B) (ii) Cyclotron frequency or magnetic resonance frequency ฮฝ=qB/2ฯm, T=2ฯm/Bq (iii) Maximum velocity of charged particle. Vm=Bqr/m
6. Force on a current carrying conductor in uniform F= (Il x B) l=length of conductor Direction of force can be found out using Flemingโs left hand rule.
7. Force per unit length between parallel infinitely long current carrying straight conductors.
๐น/๐ =๐0๐ผ1๐ผ2
2๐๐
(a) If currents are in same direction the wires will attract each other. (b) If currents are in opposite directions they will repel each other.
8. Torque experienced by a current loop in a uniform B. ฯ = NIBA Sinฮธ ฯ=m X B Where m=NIA
9. Motion of a charge in a magnetic field (a) Perpendicular magnetic field F=q(vxB),F=qvBSin90=qvB (circular path) (b) Parallel or antiparallel field F=qvBSin0 (or) qvBSin180=0(Straight-line path)
10. Moving coil galvanometer It is a sensitive instrument used for detecting small electric Currents. Principle: When a current carrying coil is placed in a magnetic field, it experiences a
torque. I ฮฑ ฮธ and I = K ฮธ where, K= NAB / C Current sensitivity, I s= ฮธ / I=NBA/K voltage sensitivity, Vs= ฮธ /V=NBA/KR
Changing N -> Current sensitivity changes but Voltage Sensitivity does not change 11. (a) Conversion of galvanometer into ammeter
A small resistance S is connected in parallel to the galvanometer coil S=IgG/I-Ig RA=GS/G+S
(b) Conversion of galvanometer into a voltmeter. A high resistance R is connected in series with the galvanometer coil. R=V/Ig-G Rv=G+R
using
CHAPTER 4
MOVING CHARGES & MAGNETISM
MULTIPLE CHOICE QUESTIONS:
1. A wire of length L carries a current of I ampere on bending it into a circle, the value of its magnetic
moment will be:-
(a) IL2 (b) IL2/2 (c) IL2/ (d) IL2/4
2. Unit of magnetic flux density is :-
(a) Tesla (b) Weber/metre2
(c) Newton/ampere-metre (d) All of the above
3. A charged particle is moving with velocity v under the magnetic field B. The force acting on the
particle will be maximum if:-
(a) v and B are in same direction
(b) v and B are in opposite direction
(c) v and B are perpendicular
(d) None
4. The radius of circular loop is r and a current i is flowing in it. The equivalent magnetic moment will
be:-
(a) ir (b) 2ฯr
(c) iฯr2 (d) i/r2
5. A magnetic field of 5.0 ร 10โ4 T just perpendicular to the electric field of 15 kV/m in their effect an
electron beam passes undeflected and perpendicular to both of them. The speed of the electrons
is:-
(a) 75 m/s (b) 3 ร 104 m/s
(c) 7.5 ร 104 m/s (d) 3 ร 107 m/s
6. There are two straight long wires, insulated from each other, along x and y axis carrying equal
currents as shown in figure. AB and CD are lines in xy plane and at 45ยฐ with the axes. The magnetic
field of the system is zero at points on the line :-
(a) AB (b) OB but not on OA
(c) CD (d) OC but not on OD
7. An electron, moving in a circular orbit of radius 'R' with a period 'T'. The equivalent magnetic dipole
moment of circular orbit is:-
(a) 2eR/T (b) eR/T
(c) eR2T (d) R2e/T
8. A coil of one loop is made by a wire of length L and there after a coil of two loops is made by same
wire. The ratio of magnetic field at the centre of coils respectively:-
(a) 1 : 4 (b) 1 : 1
(c) 1 : 8 (d) 4 : 1
9. Two long parallel wires are at a distance of 1m. If both of them carry 1A of current in same direction.
The magnetic force of attraction on unit length of each wire will be:-
(a) 2 ร 10โ7 N/m (b) 4 ร 10โ7 N/m
(c) 8 ร 10โ7 N/m (d) 10โ7 N/m
10. Two identically charged particles A and B initially at rest, are accelerated by a common potential
difference V. They enters into a uniform transverse magnetic field B and describe a circular path of
radii r1 and r2 respectively then their mass ratio is:-
(a) (r1/r2)2 (b) (r2/r1)2 (c) (r1/r2) (d) (r2/r1)
11. A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled
and the number of turns per cm is halved, the new value of the magnetic field is:-
(a) B/2 (b) B (c) 2B (d) 4B
12. A charged particle moves through a magnetic field in a direction perpendicular to it. Then the:-
(a) Speed of the particle remains unchanged
(b) Direction of motion of particle remains unchanged
(c) Acceleration of particle remains unchanged
(d) Velocity of particle remains unchanged.
13. A closely wound flat circular coil of 25 turns of wire has diameter of 10 cm and carries a current of
4 ampere. Determine the magnetic flux density at the centre of the coil:-
(a) 1.679 ร 10โ5 T (b) 2.028 ร 10โ4 T
(c) 1.257 ร 10โ3 T (d) 1.512 ร 10โ6 T
14. A proton and an ฮฑ-particle moving with the same velocity and enter into a uniform magnetic field
which is acting normal to the plane of their motion. The ratio of the radii of the circular paths
described by the proton and a-particle respectively:-
(a) 1 : 2 (b) 1 : 4 (c) 1 : 16 (d) 4 : 1
15. Two parallel beams of positrons moving in the same direction will:-
(a) Repels to each other
(b) Will not interact with each other
(c) Attracts to each other
(d) Be deflected normal to the plane containing the two beams.
16. An electron is moving around a proton in an orbit of radius 1ร and produces 16 Wb/m2 of magnetic
field at the centre, then find the angular velocity of electron :-
(a) 20 X 1016 rad/sec
(b) 10 X 1016 rad/sec
(c) 5/2 x 1016 rad/sec
(d) 5/4 X 1016 rad/sec
17. Current I is flowing in a conducting circular loop of radius R. It is kept in a magnetic field B which is
perpendicular to the plane of circular loop, the magnetic force acting on the loop is :-
(a) IRB (b) 2IRB
(c) Zero (d) IRB
18. In the shown figure magnetic field at point A will be :-
(a) (b) (c) (d) Zero
19. If the permeability of iron piece is 3 ร 10โ3 Wb/A-m and intensity of magnetizing field of iron piece
is 120 A/m, then what is the magnetic induction of iron piece:-
(a) 0.36 Wb/m2 (b) 5 ร 10โ3 Wb/m2
(c) 40 Wb/m2 (d) 2.5 ร 10โ4 Wb/m2
20. A long solenoid with 20 turns per cm is made to produce a magnetic field of 20 mT inside the
solenoid. The necessary current will nearly be:-
(a) 8.0 ampere (b) 4.0 ampere
(c) 2.0 ampere (d) 1.0 ampere
0
4
I 0
4
I
R
0
4
I
R
21. A current is flowing in a circular coil of radius R and the magnetic field at its centre is Bo. It what
distance from the centre on the axis of the coil, the magnetic field will be Bo/8:-
(a) 3 R (b) 3 R (c) 2R (d) 8R
22. Wire in the form of a right angle ABC, with AB=3cm and BC = 4cm, carries a current of 10A. There is
a uniform magnetic field of 5T perpendicular to the plane of the wire. The force on the wire will be:-
(a) 1.5N (b) 2.0N (c) 2.5N (d) 3.5N
23. A rectangular coil 20 cm ร 20cm, has 100 turns and carries a current of 1A. It is placed in a uniform
magnetic field 0.5T with the direction of magnetic field parallel to the plane of the coil. The
magnitude of the torque required to hold this coil in this position is:-
(a) zero (b) 200N-m
(c) 2N-m (d) 10N-m
24. A straight wire carries a current vertically upwards. A point P lies to the east of it at a small distance
and another point Q lies to the west at the same distance. The magnetic field at P is (consider earth
field):-
(a) Greater than at Q
(b) Same as at Q
(c) Less than at Q
(d) Greater or less than at Q, depending upon the strength of current
25. A circular coil of radius 20 cm and 20 turns of wire is mounted vertically with its plane in magnetic
meridian. A small magnetic needle is placed at the centre of the coil and it is deflected through 45ยฐ,
when a current is passed through the coil. When horizontal component of earth's field is
0.34 ร 10โ4 T, the current in coil is:-
(a) 0.6 A (b) 6A (c) 6 ร 10โ3 A (d) 0.06 A
26. A current loop of area 0.01m2 and carrying a current of 10A is held perpendicular to a magnetic
field of 0.1T, the torque in Nโm acting on the loop is :-
(a) 0 (b) 0.001 (c) 0.01 (d) 1.1
27. In a region constant uniform electric and magnetic field is present. Both field are parallel. In this
region a charge released from rest, then path of particle is:-
(a) Circle (b) Helical
(c) Straight line (d) Ellipse
28. A current carrying coil is placed in a constant uniform magnetic field B. Torque is maximum on this
coil when plane of coil is:-
(a) Perpendicular to B (b) parallel to B
(c) at 45ยฐ to B (d) at 60ยฐ to B
29. 2A current is flowing in a circular loop of radius 1m. Magnitude of magnetic field at the centre of
circular loop will be:-
(a) 0/2 (b) 20 (c) 0 (d) 0/4
30. A particle of mass m, charge Q and kinetic energy T enters a transverse uniform magnetic field of
induction. After 3 seconds the kinetic energy of the particle will be:-
(a) T (b) 4 T (c) 3T (d) 2T
31. A long straight wire of radius 'a' carries a steady current i. The current is uniformly distributed across
its cross section. The ratio of the magnetic field at a/2 and 2a distances from the axis of the wire is:
(a) 4 (b) 1 (c) 1/2 (d) 1/4
32. A horizontal overhead powerline is at a height of 4m from the ground and carries a current of 100
A from east to west. The magnetic field directly below it on the ground is:-
(a) 2.5 ร 10-7 T, southward (b) 5 ร 10-6 T, northward
(c) 5 ร10-6 T, southward (d) 2.5 ร10-7 T, northward
33. A current I flows along the length of an infinitely long, straight, thin walled pipe, then:-
(a) the magnetic field is different at different points inside the pipe
(b) the magnetic field at any point inside the pipe is zero
(c) the magnetic field at all points inside the pipe is the same, but not zero
(d) the magnetic field is zero only on the axis of the pipe
34. A and B are two concentric circular loops carrying current i1 and i2 as shown in
figure. If ratio of their radii is 1:2 and ratio of the flux densities at the centre O due
to A and B is 1:3 then the ratio of current will be :-
(a) 1/2 (b) 1/3
(c) 1/4 (d) 1/6
35. A magnetic field
(a) Always exerts a force on a charged particle
(b) Never exerts a force on a charged particle
(c) Exerts a force, if the charged particle is moving across the magnetic field lines
(d) Exerts a force, if the charged particle is moving along the magnetic field lines
36. A current of 10 A is flowing in a wire of length 1.5 m. A force of 15 N acts on it when it is placed
in a uniform magnetic field of 2 T. The angle between the magnetic field and the direction of the
current is
(a) 30ยฐ
(b) 45ยฐ
(c) 60ยฐ
(d) 90ยฐ
37. Biot-Savart law indicates that the moving electrons with velocity (v) produce a magnetic field B
such that
(a) B parallel to v
(b) B is perpendicular to v
(c) it obeys inverse cube law
(d) it is along the line joining electron and point of observation
38. If we double the radius of a coil keeping the current through it unchanged, then the magnetic
field at any point at a large distance from the centre becomes approximately
(a) double
(b) three times
(c) four times
(d) one-fourth
39. A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle 3/2
radian at its centre. The magnetic field B at the centre is
(a) ๐0 ๐
๐
(b) ๐0 ๐
2๐
(c) 2๐0 ๐
๐
(d) 3๐0 ๐
8๐
40. A positively charged particle moving due east enters a region of uniform magnetic field directed
vertically upward. The particle will
(a) get deflected in vertically upward direction
(b) move in circular path with an increased speed
(c) move in circular path with a decreased speed
(d) move in a circular path with uniform speed.
41. The radius of the circular path of an electron moving in magnetic field perpendicular to its path
is equal to
(a) ๐ต๐
๐๐ฃ
(b) ๐๐
๐ต
(c) ๐๐ฃ
๐๐ต
(d) ๐ต
๐๐ฃ
42. A uniform electric field and a uniform magnetic field are acting along the same direction in a
certain region. If an electron is projected along the direction of the fields with a certain velocity,
then
(a) its velocity will decrease
(b) its velocity will increase
(c) it will turn towards right of direction of motion
(d) it will turn towards left of direction of motion.
43. If a current is passed in a spring, it
(a) gets compressed
(b) gets expanded
(c) oscillates
(d) remains unchanged
44. A galvanometer acting as ammeter will have
(a) high resistance in parallel
(b) high resistance in series
(c) low resistance in parallel
(d) low resistance in series
45. If resistance of a galvanometer is 6 ฮฉ and it can measure a maximum current of 2 A. Then
required shunt resistance to convert it into an ammeter reading up to 6 A, will be
(a) 2 ฮฉ
(b) 3 ฮฉ
(c) 4 ฮฉ
(d) 5 ฮฉ
46. A galvanometer can be changed into voltmeter by providing
(a) low resistance in series
(b) low resistance in parallel
(c) high resistance in series
(d) high resistance in parallel
47. If the number of turns in a moving coil galvanometer is increased, its current sensitivity
(a) increases
(b) remains same
(c) decreases
(d) may increase or decrease
48. The magnetic field due to a straight conductor of uniform cross-section of radius a and carrying a
steady current is represented by
49. A charged particle moves through a magnetic field perpendicular to its direction. Then
(a) kinetic energy changes but the momentum is constant
(b) the momentum changes but the kinetic energy is constant
(c) both momentum and kinetic energy of the particle are not constant
(d) both momentum and kinetic energy of the particle are constant.
ANSWERS(Multiple Choice Questions):
Q.NO. ANS Q.NO. ANS Q.NO. ANS Q.NO. ANS Q.NO. ANS
1 D 11 B 21 A 31 B 41 C
2 D 12 A 22 C 32 C 42 A
3 C 13 C 23 C 33 B 43 A
4 C 14 A 24 A 34 D 44 C
5 D 15 A 25 A 35 B 45 B
6 A 16 A 26 A 36 A 46 C
7 D 17 C 27 C 37 A 47 A
8 A 18 B 28 B 38 C 48 A
9 A 19 A 29 C 39 D 49 B
10 A 20 A 30 A 40 D โฆโฆ. โฆโฆ.
ASSERTION AND REASONING QUESTIONS:
For these questions two statements are given-one labeled Assertion (A) and the other labeled
Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as
given below.
a. Both A and R are true and R is the correct explanation of A
b. Both A and R are true but R is NOT the correct explanation of A
c. A is true but R is false
d. A is false and R is also false.
1. Assertion: Free electron always keep on moving in a conductor even then no magnetic force act
on them in magnetic field unless a current is passed through it.
Reason: The average velocity of free electron is zero.
2. Assertion: A circular loop carrying current lies in XY plane with its center at origin
having a magnetic flux in Z-axis direction.
Reason: Magnetic flux direction is independent of the direction of current in the
conductor.
3. Assertion: The energy of charged particle moving in a uniform magnetic field does not
change.
Reason: Work done by magnetic field on the charge is zero.
4. Assertion: If an electron, while coming vertically from outer space, enters the earth's
magnetic field, it is deflected towards west.
Reason: Electron has negative charge.
5. Assertion: A direct current flows through a metallic rod, produced magnetic field
only outside the rod.
Reason: There is no flow of charge carriers inside the rod.
6. Assertion: Magnetic field interacts with a moving charge and not with a stationary
charge.
Reason: A moving charge produces a magnetic field.
7. Assertion: The magnetic field at the ends of a very long current carrying solenoid is half
of that at the center.
Reason: If the solenoid is sufficiently long, the field within it is uniform.
8. Assertion: If a charged particle is moving on a circular path in a perpendicular
magnetic field, the momentum of the particle is not changing.
Reason: Velocity of the particle in not changing in the magnetic field.
9. Assertion: If two long wires, hanging freely are connected to a battery in series, they
come closer to each other.
Reason: Force of attraction acts between the two wires carrying current.
10. Assertion: A current I flows along the length of an infinitely long straight and thin
walled pipe. Then the magnetic field at any point inside the pipe is zero.
Reason: โฎ . ๐๐ = ๐0๐ผ.
ANSWERS(Assertion & Reason Question):
Q.No. 1 2 3 4 5 6 7 8 9 10
ANS a c a b d a b d d a
Explanation of Answers ( A and R) :
1. a. In the absence of the electric current, the free electrons in a conductor are in a state of
random motion, like molecules in a gas. Their average velocity is zero. i.e. they do not have any
net velocity in a direction. As a result, there is no net magnetic force on the free electrons in the
magnetic field. On passing the current, the free electrons
acquire drift velocity in a definite direction, hence magnetic force acts on them,
unless the field has no perpendicular component.
2. c. The direction of magnetic field due to current carrying conductor can be found by applying
right hand thumb rule or right hand palm rule. When electric current is passed through a circular
conductor, the magnetic field lines near the center of the conductor are almost straight lines.
Magnetic flux direction is determined only by the direction of current.
3. a. The force on a charged particle moving in a uniform magnetic field always acts in direction
perpendicular to the direction of motion of the charge. As work done by magnetic field on the
charge is zero, [๐ = ๐น๐ cos ๐], so the energy of the charged particle does not change.
4. b. We know that the direction of the earthโs magnetic field is toward north and the velocity of
electron is vertically downward. Applying Flemingโs left hand rule, the direction of force is
towards west. Therefore, an electron coming from outer space will be deflected toward west.
5. d. In the case of metallic rod, the charge carriers flow through whole of the cross section.
Therefore, the magnetic field exists both inside as well as outside. However magnetic field inside
the rod will go on decreasing as we go towards the axis.
6. a. A moving charge experiences a force in magnetic field. It is because of interaction of
two magnetic fields, one which is produced due to the motion of charge and other in which
charge is moving.
7. b. For a solenoid . ๐ต๐๐๐ =1
2๐ต๐๐. Also for a long solenoid, magnetic field is uniform within it but
this reason is not explaining the assertion.
8. d. When a charged particle is moving on a circular path in a magnetic field, the magnitude of
velocity does not change but direction of velocity is changing every moment. Hence velocity is
changing, so momentum mv is also changing.
9. d. When two long parallel wires, are connected to a battery in series. They carry currents in
opposite directions, hence they repel each other.
10. a. Here, both Assertion and Reason are correct and reason is the correct explanation of
assertion.
CASE STUDY BASED QUESTIONS:
1. Motion of Charged Particle Inside Magnetic Field :A charged particle moving in a magnetic field
experiences a force that is proportional to the strength of the magnetic field, the component of the
velocity that is perpendicular to the magnetic field and the charge of the particle. This force is given by
= ๐( ร ) , where q is the electric charge of the particle, is the instantaneous velocity ofthe
particle, and is the magnetic field (in tesla).
The direction of force is determined by the rules of cross product of two vectors.
Force is perpendicular to both velocity and magnetic field. Its direction is same as ร if q is positive
and opposite of ร if q is negative.
The force is always perpendicular to both the velocity of the particle and the magnetic field that created
it. Because the magnetic force is always perpendicular to the motion, the magnetic field can do no work
on an isolated charge. The direction of force on a moving charge particle can also be found using
Flemingโs Left Hand Rule as shown in figure below.
(i) When a magnetic field is applied on a stationary electron, it
(a) remains stationary
(b) spins about its own axis
(c) moves in the direction of the field
(d) moves perpendicular to the direction of the field.
(ii) A proton is projected with a uniform velocity along the axis of a current carrying solenoid,
then
(a) the proton will be accelerated along the axis
(b) the path of proton will be circular about the axis
(c) the proton moves along helical path
(d) the proton will continue to move with velocity v along the axis.
(iii) A charged particle experiences magnetic force in the presence of magnetic field. Which of the
following statement is correct?
(a) The particle is stationary and magnetic field is perpendicular.
(b) The particle is moving and magnetic field is perpendicular to the velocity.
(c) The particle is stationary and magnetic field is parallel.
(d) The particle is moving and magnetic field is parallel to velocity.
(iv) A charge q moves with a velocity 2 m/s along x-axis in a uniform magnetic field = (๐ + 2๐ +
3), then charge will experience a force
(a) in y-z plane
(b) along -y axis
(c) along +z axis
(d) along โz axis
(v) A beam of positively charged particles moving along +x axis, experience a force in +y direction
due to a magnetic field. The direction of magnetic field is
(a) In x-y plane
(b) Along +z axis
(c) Along โz axis
(d) Along +x axis
2. HELICAL MOTION OF CHARGED PARTICLES : A charged particle of mass m and charge q, entering
a region of magnetic field with an initial velocity making an angle ฮธ with . Let this velocity
have a component ๐๐(= ๐ ๐๐จ๐ฌ ๐) parallel to the magnetic field and a component๐๐ (=
๐ ๐ฌ๐ข๐ง๐) normal (perpendicular) to it. There is no force on a charged particle in the direction of
the field. Hence the particle continues to travel with the velocity๐๐ parallel to the field. The
normal component ๐๐of the particle results in a Lorentz force๐(๐๐ ร ๐ฉ )which is perpendicular
to both ๐๐ and ๐ฉ .The particle thus has a tendency to perform a circular motion in a plane
perpendicular to the magnetic field. When this is coupled with the velocity parallel to the field,
the resulting trajectory will be a helix along the magnetic field line, as shown in Figure below.
The radius of the helical path is given by ๐ =๐ ๐๐
๐๐ฉ=
๐๐๐ฌ๐ข๐ง๐
๐๐ฉ (By the fact that required centripetal
force is provided by Lorentz force).The distance moved along the magnetic field during the
period of one rotation is called pitch (๐ = ๐ฃ๐๐, where ๐ is time taken by particle to complete
one rotation). Since the Lorentz force is normal to the velocity of each point, the field does no
work on the particle and the magnitude of velocity remains the same.
(i) Two charged particles A and B having the same charge, mass and speed enter into a
magnetic field in such a way that the initial path of A makes an angle of 30ยฐ and that of B
makes an angle of 90ยฐ with the field. Then the trajectory of
(a) B will have smaller radius of curvature than that of A
(b) both will have the same curvature
(c) A will have smaller radius of curvature than that of B
(d) both will move along the direction of their original velocities.
(ii) An electron having momentum 3.2 x 10-23 kg m/s enters a region of uniform magnetic field
of 0.2 T. The magnetic field vector makes an angle of 30ยฐ with the initial velocity vector of
the electron. The radius of the helical path of the electron in the field will be
(a) 1 mm
(b) 2 mm
(c) 20 mm
(d) 0.5 mm
(iii) A neutron enters a region of uniform magnetic field 0.15 T with a velocity making an angle
30ยฐ with the magnetic field vector. The path of the neutron will be
(a) Circular
(b) Helical
(c) Straight line
(d) Parabolic
(iv) The magnetic field in a certain region of space is given by = ๐๐ ร ๐๐โ๐ ๐ป . A proton is
shot into the field with velocity ๐ = (๐ ร ๐๐๐ + ๐ ร ๐๐๐๐) ๐/๐. The proton follows a
helical path in the field. The distance moved by proton in the x-direction during the period
of one rotation in the yz-plane will be
(a) 0.312m
(b) 0.209m
(c) 0.450m
(d) 0.157m
(v) A negatively charged particle having velocity ๐ enters a region of uniform magnetic field at
an angle 30ยฐ with the direction of magnetic field. Then its kinetic energy
(a) Increase
(b) Decrease
(c) Remains same
(d) First increases and then decreases
3. A VELOCITY SELECTOR: A velocity selector is a region in which there is a uniform electric field and a
uniform magnetic field. The fields are perpendicular to one another, and perpendicular to the initial
velocity of the charged particles that are passing through the region. The force exerted on a charged
particle having charge q by the electric field is given by:๐น = ๐ . The magnitude of the force exerted
by the magnetic field is ๐น = ๐๐ฃ๐ต, as long as the velocity๐ฃ is perpendicular to the magnetic field .
The idea is that, if the two forces are equal and opposite, the net force is zero, and the particle
passes through the region without changing direction. With the magnetic force being speed
dependent, however, any charges traveling faster or slower than the ones that go straight through
will be deflected one way or another out of the beam.
(i) Assuming the particle in the figure is positively charged, what are the directions of the forces due
to the electric field and to the magnetic field?
(a) The force due to the electric field is directed up (toward the top of the page); the force due to
the magnetic field is directed down (toward the bottom of the page).
(b) The force due to the electric field is directed down (toward the bottom of the page); the force
due to the magnetic field is directed up (toward the top of the page).
(c) The force due to the electric field is directed out of the plane of the paper; the force due to the
magnetic field is directed into the plane of the paper.
(d) The force due to the electric field is directed into the plane of the paper; the force due to the
magnetic field is directed out of the plane of the paper.
(ii) Suppose a particle with twice the velocity of the particle in the figure enters the velocity selector.
The path of this particle will curve
(a) upward (toward the top of the page)
(b) downward (toward the bottom of the page)
(c) out of the plane of the paper
(d) into the plane of the paper
(iii) If the electric field has a magnitude of 480 N/C and the magnetic field has a magnitude of 0.16T,
what speed must the particles have to pass through the selector undeflected?
(a) 2500 m/s
(b) 2700 m/s
(c) 3000 m/s
(d) 3200 m/s
(iv) A beam of neutrons is passed through the velocity selector, then
(a) All the neutrons will pass without any deflection
(b) Only the neutrons having a particular value of velocity will pass without any deflection
(c) Neutrons will be deflected in the direction of electric field
(d) All the neutrons will be deflected from their path
(v) A beam of electrons is moving with a constant velocity 40m/s in a region having uniform electric
field and uniform magnetic field perpendicular to each other and also perpendicular to the of
velocity of electrons. The magnitude of electric field is 20 N/C. The magnitude of magnetic field
is (in tesla)
(a) 2 T
(b) 1 T
(c) 0.5 T
(d) 1.5 T
4. Mass Spectrometer: The mass spectrometer is an instrument which can measure the masses and
relative concentrations of atoms and molecules. It makes use of the basic magnetic force on a moving
charged particle. The process begins with an ion source, a device like an electron gun. The ion source
gives ions their charge(q), accelerates them to some velocity ๐ฃ, and directs a beam of them into the
next stage of the spectrometer. This next region is a velocity selector that only allows particles with a
particular value of ๐ฃ to get through undeflected. The velocity selector has both an electric field and a
magnetic field, perpendicular to one another and also to velocity of ions. . In the final region, there is
only a uniform magnetic field perpendicular to the velocity of ions and so the charged particles move in
circular arcs with radii proportional to particle mass.
๐ =๐๐
๐๐ฉ
(i) Velocity selector works on the principle
(a) Electric and magnetic forces are in same direction
(b) Electric and magnetic forces are equal and opposite to each other
(c) Electric force is more than magnetic force
(d) Electric force is less than magnetic force
(ii) Which of the following concept is used in mass spectroscopy?
(a) Charged particles are evenly deflected in a magnetic field
(b) Particles of lower mass are deflected in a magnetic field with a greater radius of curvature
(c) Particles of greater mass are deflected in a magnetic field with a greater radius of curvature
(d) None of the above
(iii) The ratio of radius of semi-circular path of two ions having same charge in mass spectrometer is
๐1
๐2=
3
4. What is the ratio of their masses?
(a) ๐1
๐2=
3
4
(b) ๐1
๐2=
1
2
(c) ๐1
๐2=
3
5
(d) ๐1
๐2=
4
3
(iv) Which of the following will trace a circular trajectory with largest radius?
(a) Proton
(b) Electron
(c) alpha-particle
(d) A particle with charge twice and mass thrice that of electron.
(v) The radius of curvature of the ion's path depends on the ratio of m/q. (m is the mass and q is the
charge of the ion). Which of the following ions will bend the most (have lesser radius of
curvature)?
(a) Ion A with m = 20 and q = +1
(b) Ion B with m = 10 and q = +1
(c) Ion C with m = 20 and q = +2
(d) Ion D with m = 10 and q = +2
5. Moving coil galvanometer: Moving coil galvanometer is an electromagnetic device that can
measure small values of current. It consists of permanent cylindrically cut magnets, coil, soft iron
core, pivoted spring, non-metallic frame, scale, and pointer. The magnetic field in moving coil
galvanometer is radial in nature it means the magnetic field always lies in the plane of coil which
makes the torque acting on the coil maximum. When the current is passed through the coil a
torque acts on the coil. Due to this torque the coil rotates and with the coil spring also rotates.
This rotation in the coil generates a restoring torque in the spring. The restoring torque is given
by ๐โ , where โ is the deflection in coil and ๐ is torsional constant of spring. In equilibrium
condition torque in the coil due to current is equal to the restoring torque in the spring.
(i) A moving coil galvanometer is an instrument which
(a) is used to measure emf
(b) is used to measure potential difference
(c) is used to measure resistance
(d) is a deflection instrument which gives a deflection when a current flows through its
coil
(ii) To make the field radial in a moving coil galvanometer
(a) number of turns of coil is kept small
(b) poles are cylindrically cut
(c) soft iron core is used
(d) both b and c
(iii) In a moving coil galvanometer, having a coil of N-turns of area A and carrying current I is
placed in a radial field of strength B. The torque acting on the coil is
(a) NA2BI
(b) NABI2
(c) NABI
(d) N2ABI
(iv) The deflection in a moving coil galvanometer is
(a) directly proportional to torsional constant of spring
(b) directly proportional to the number of turns in the coil
(c) inversely proportional to the area of the coil
(d) inversely proportional to the current in the coil
(v) Moving coil galvanometer can be used to measure alternating current
(a) True
(b) False
ANSWERS(Case Study Based Questions):
Q.1 Q.2 Q.3 Q.4 Q.5
ANS.i A C A B D
ANS.ii D D B C D
ANS.iii B C C A C
ANS.iv A B A C B
ANS v C C C D B
CHAPTER 5
MAGNETISM & MATTER
GIST OF LESSON:
Magnetic Line of Force
It is the path along which a unit north pole would, if it is tends to free to do so.
Representation of uniform magnetic field
-------------------------> o o o o X X X X
-------------------------> o o o o X X X X
-------------------------> o o o o X X X X
Current loop as a magnetic dipole
(i).Dipole moment of current loop m=nIA
(ii).Dipole moment of revolving electron m=evr/2
Gauss law for magnetism
The net magnetic flux through a closed surface is zero.
Dipole in a unifrom magnetic field
ฮถ = mBSin ๊
I d2 ๊/dt2 = - mBSin ๊
d2 ๊/dt2 = (mB ๊)/I ( this equation represent simple harmonic motion)
ฯ2= (mB)/I
T=2๐ฑโ(๐ฐ/๐๐ฉ)
Magnetic element of Earth magnetic field:
1) Magnetic declination
The angle between the geographic meridian and magnetic meridian at a place.
2) Angle of dip
The angle between the direction of total intensity of earthโs magnetic field and its
horizontal component.
Angle of dip at equator ฮด = 00
Angle of dip at poles ฮด = 900
3) Horizontal component of earthโs magnetic field
Horizontal component of earth magnetic field BH = B Cosฮด
Horizontal component of earth magnetic field BV = B Sinฮด
It is the component of total intensity of earthโs magnetic field along the horizontal.
Tanฮด= Bv/BH and B = โ( Bv)2 +(BH)2
CHAPTER 5
MAGNETISM AND MATTER
MULTIPLE CHOICE QUESTIONS:
1. Magnetic moment (or magnetic dipole moment) of a current carrying coil is given by
(a) m = INA
(b) m = I/A
(c) m = NA
(d) m = NI/A
2. Magnetic field at the centre of a circular loop of area A is B. the magnetic moment of the
loop will be
(a) ๐ต๐ด2
๐๐๐
(b) ๐ต๐ด3/2
๐๐๐
(c) ๐ต๐ด3/2
๐๐ ๐ ๐/๐
(d) 2๐ต๐ด3/2
๐๐ ๐ ๐/๐
3. For an atom shown in the figure, the direction of magnetic moment related to revolving
electron is,
(a) Vertically upwards
(b) Vertically downwards
(c) along the velocity of electron
(d) none of these
4. In a hydrogen atom, an electron revolves around the nucleus in an orbit of radius r with
velocity v, the current corresponding to the revolving electron is
(a) I = ๐๐
2 ๐ ๐ (b) I =
๐๐
2 ๐
(c) I = ๐๐ฃ
2 ๐ ๐ (d) I =
๐๐ฃ
๐ ๐
5. Bohr magneton(ยตB) is a unit of
(a) Magnetic dipole moment
(b) Charge of electron
(c) Angular momentum
(d) Magnetic flux density
6. Magnitude of angular magnetic moment associated with a revolving electron in a hydrogen
atom will be
(a) ฮผl = ๐
2๐๐
(b) ฮผl = โ๐๐2
2๐๐
(c) ฮผl = โ๐
4๐๐
(d) ฮผl = โ๐๐
2๐๐
7. The gyro magnetic ratio of an revolving electron is,
(a) ๐
๐
(b) ๐
2๐๐
(c) 8.8 ร 1010 C kg-1
(d) all of the above
8. Magnetic field lines show the direction (at every point) along which a small magnetised needle
aligns. Do the magnetic field lines also represent the lines of force on a moving charge at every
point?
(a) No
(b) yes
(c) Neither (a) nor (b)
(d) given information is not sufficient
9. The resemblance of magnetic field lines for a bar magnet and a solenoid suggest that
(a) a bar magnet may be thought of as a large number of circulating currents in analogy with a
solenoid
(b) cutting a bar magnet in half is like cutting a solenoid
(c) both (a) and (b)
(d) neither (a) nor (b)
10. Cutting a bar magnet in half is like cutting a solenoid, such that we get two smaller solenoids
with
(a) weaker magnetic properties
(b) strong magnetic properties
(c) constant magnetic properties
(d) both (a) and (b)
11. The strength of the earth's magnetic field varies from place to place on the earthโs surface, its
value being of the order of
(a) 105 T
(b) 10-6 T
(c) 10-5 T
(d) 108 T
12. The magnetic field is now thought to arise due to electrical currents produced by convective
motion of metallic fluids (consisting mostly of molten iron and nickel) in the outer core of the
earth. This is known as the
(a) dynamo effect
(b) Tindal effect
(c) both (a) and (b)
(d) Neither (a) nor (b)
13. The pole near the geographic North-pole of the Earth is called theโฆโฆโฆ.magnetic pole and the
pole near the geographic south pole is called theโฆโฆโฆ...magnetic pole.
(a) South-North
(b) South- East
(c) North-East
(d) North- South
14. The vertical plane containing the longitude circle and the axis of rotation of earth is called
the
(a) geographic meridian
(b) magnetic meridian
(c) magnetic declination
(d) magnetic inclination
15. One can defineโฆโฆ of a place as the vertical plane which passes through the imaginary line
joining the magnetic North and South poles.
(a) geographic meridian
(b) magnetic meridian
(c) magnetic declination
(d) magnetic inclination
16. Which of the following elements need to describe Earthโs magnetic field at a point on the
surface of earth?
(a) Angle of declination D
(b) Angle of Dip
(c) Horizontal component of Earthโs magnetic field
(d) all of the above
17. If a magnetic needle is perfectly balanced about a horizontal axis, so that it can swing in a
plane of the magnetic meridian, the needle would make an angle with horizontal. This is known
as the
(a) angle of dip
(b) angle of inclination
(c) angle of declination
(d) Both (a) and (b)
18. The angle of dip at a certain place where the horizontal and vertical components of earthโs
magnetic field are equal is
(a) 30o
(b) 70o
(c) 50o
(d) 45o
19. The primary origin of magnetism lies in
(a) atomic currents
(b) intrinsic spin of electrons
(c) Pauli exclusion principle
(d) both (a) and (b)
20. At a certain place, the horizontal component of the Earthโs magnetic field is Bo and the angle
of dip is 60o. The total intensity of the field at that place will be
(a) Bo
(b) 2Bo
(c) โ2Bo
(d) 1.5 Bo
21. The magnetism of magnet is due to
(a) Earth
(b) Cosmic rays
(c) Due to pressure of big magnet inside the earth
(d) Spin motion of electrons
22. The vertical component of earth magnetic field is zero at
(a) Magnetic poles
(b) Magnetic equator
(c) Geographic poles
(d) Geographic equator
23. Angle on the horizontal plane between magnetic north and true north is
(a) Magnetic declination
(b) Electric declination
(c) Magnetic inclination
(d) Electric inclination
24. A small bar magnet of moment M is placed in a uniform field B. If magnet makes an angle
of 30ยฐ with field. The torque acting on the magnet is:-
(a) MB (b) MB/2 (c) MB/3 (d) MB/4
25. A magnetic needle suspended horizontally by a silk fibre, oscillates in the horizontal plane
because of the restoring torque originating mainly from:-
(a) The torsion of the silk fibre
(b) The force of gravity
(c) The horizontal component of earth's magnetic field
(d) All the above factors
26. The period of oscillation of a magnet in vibration magnetometer is 2 sec. The period of
oscillation of a magnet whose magnetic moment is four times that of the first magnet is
(a) 1 sec (b) 4 sec (c) 8 sec (d) 0.5 sec
27. At certain place the angle of dip is 30ยฐ and the horizontal component of earth magnetic field
is 0.50 Gauss. The earth's total magnetic field (in Gauss) is:-
(a) 1/4 (b) 1 (c) 1/3 (d) ยฝ
28. The angle of dip at the magnetic equator is:-
(a) 0ยฐ (b) 45ยฐ (c) 30ยฐ (d) 90ยฐ
29. At Geo-magnetic poles, the angle of dip is:-
(a) 45ยฐ (b) 30ยฐ (c) zero (d) 90ยฐ
30. The time period of a freely suspended magnet is 4 sec. If it is broken perpendicular to its
length into two equal parts and one part is suspended in the same way, then its time period
in seconds will be :-
(a) 4 (b) 2 (c) 0.5 (d) 0.25
31. At magnetic North Pole of the earth the value of horizontal component BH and angle of dip
q is:-
(a) BH = 0, q = 45ยฐ (b) BH = 90, q = 0ยฐ
(c) BH = 0, q = 90ยฐ (d) BH = 45, q = 45ยฐ
32. A magnet of magnetic moment M is rotating through 360ยฐ with respect to the magnetic
field B, the work done will be :-
(a) MB (b) 2MB (c) 2MB (d) Zero
33. The work done in rotating a magnet of magnetic moment M by an angle of 90ยฐ from the
external magnetic field direction is 'n' times the corresponding work done to turn it
through an angle of 60ยฐ where 'n' is :-
(a) 1/2 (b) 2 (c) 1/4 (d) 1
ANSWERS(MULTIPLE CHOICE QUESTIONS):
Q. ANS Q ANS Q ANS Q ANS Q ANS Q ANS Q ANS
1 a 6 d 11 c 16 d 21 d 26 a 31 c
2 d 7 d 12 a 17 d 22 b 27 c 32 d
3 b 8 a 13 d 18 d 23 a 28 a 33 b
4 c 9 c 14 a 19 d 24 d 29 d
5 a 10 b 15 b 20 b 25 c 30 b
ASSERTION & REASON QUESTIONS:
Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given
below:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false
1. Assertion (A): Magnetic moment of an atom is due to both the orbital motion and spin motion
of every electron.
Reason (R): A charged particle produces a magnetic field.
2. Assertion (A): The ends of a magnet suspended freely point out always along north south.
Reason (R): Earth behaves as a huge magnet.
3. Assertion (A): Magnetic moment is measured in joule/tesla or amp m2.
Reason (R): Joule/tesla is equivalent to amp m2.
4. Assertion (A): The true geographic north direction is found by using a compass needle.
Reason (R): The magnetic meridian of the earth is along the axis of rotation of the earth.
5. Assertion (A) : The magnetic poles of earth do not coincide with the geographic poles.
Reason (R) : The discrepancy between the orientation of compass and true north-south
direction is known as magnetic declination.
6.Assertion (A): the magnetic moment of an electron revolving around the nucleus decreases
with increasing principal quantum number (n).
Reason (R): magnetic moment of revolving electron is inversely proportional to the principal
quantum number (n).
7. Assertion (A) : When the radius of a circular loop carrying current is doubled, its magnetic
moment becomes four times.
Reason (R): magnetic moment depends on area of the loop.
8. Assertion (A): The earthโs magnetic field is due to iron present in its core.
Reason (R): At a low temperature magnet losses its magnetic property or magnetism.
9.Assertion (A): A compass needle when placed on magnetic north pole of the earth rotates in
vertical direction.
Reason (R): The earthโs has only horizontal component of its magnetic field at north poles.
10. Assertion (A): Earthโs magnetic field doesnโt affect the working of moving coil
galvanometer.
Reason (R): The earthโs magnetic field is quite weak as compared to magnetic field produced
in the moving coil galvanometer.
ANSWERS(Assertion & Reason):
CASE STUDY BASED QUESTIONS:
1. Components of Earthโs Magnetic Field:
The earthโs magnetic field at a point on its surface is usually characterised by three quantities:
(a) declination (b) inclination or dip and (c) horizontal component of the field. These are known
as the elements of the earthโs magnetic field. At a place, angle between geographic meridian and
magnetic meridian is defined as magnetic declination, whereas angle made by the earthโs
magnetic field with the horizontal in magnetic meridian is known as magnetic dip.
Q. 1 2 3 4 5 6 7 8 9 10
ANS c a a d a d a c d a
(i) In a certain place, the horizontal component of the magnetic field is 1/3 times the vertical
component. The angle of dip at this place is
(a) zero
(b) ฯ/3
(c) ฯ/2
(d) ฯ/6
(ii) The angle between the true geographic north and the north shown by a compass needle is
called as
(a) inclination
(b) magnetic declination
(c) angle of meridian
(d) magnetic pole.
(iii) The angles of dip at the poles and the equator respectively are
(a) 30ยฐ, 60ยฐ
(b) 0ยฐ, 90ยฐ
(c) 45ยฐ, 90ยฐ
(d) 90ยฐ, 0ยฐ
(iv) A compass needle which is allowed to move in a horizontal plane is taken to a
geomagnetic pole. It
(a) will become rigid showing no movement
(b) will stay in any position
(c) will stay in the north-south direction only
(d) will stay in the east-west direction only.
(v) Select the correct statement from the following.
(a) The magnetic dip is zero at the centre of the earth.
(b) Magnetic dip decreases as we move away from the equator towards the magnetic pole.
(c) Magnetic dip increases as we move away from the equator towards the magnetic pole.
(d) Magnetic dip does not vary from place to place.
2. Earthโs Magnetic Field:
The magnetic field lines of the earth resemble that of a hypothetical magnetic dipole located at
the centre of the earth. The axis of the dipole is presently tilted by approximately 11.3ยฐ with
respect to the axis of rotation of the earth.
The pole near the geographic North Pole of the earth is called the North magnetic pole and the
pole near the geographic South Pole is called South magnetic pole.
(i) The strength of the earthโs magnetic field varies from place to place on the earthโs surface,
its value being of the order of
(a) 105 T
(b) 10โ6 T
(c) 10โ5 T
(d) 108 T
(ii) A bar magnet is placed North-South with its North-pole due North. The points of zero
magnetic field will be in which direction from the centre of the magnet?
(a) North-South
(b) East-West
(c) North-East and South-West
(d) None of these.
(iii) The value of angle of dip is zero at the magnetic equator because
(a) V and H are equal
(b) the values of V and H zero
(c) the value of V is zero
(d) the value of H is zero.
(iv) The angle of dip at a certain place, where the horizontal and vertical components of the
earthโs magnetic field are equal, is
(a) 30ยฐ
(b) 90ยฐ
(c) 60ยฐ
(d) 45ยฐ
(v) At a place, the angle of dip is 30ยฐ. If horizontal component of earthโs magnetic field is H,
then the total intensity of magnetic field will be
(a) H /2
(b) 2/โ3 H
(c) H/3
(d) 2H
3. Gaussโs law of Magnetism:
By analogy to coulombโs law of electrostatics, we can write Gaussโs law of magnetism as
โฎ ๐. ๐๐ฌ = ยต0 minside where ส B.ds is the magnetic flux and minside is the net pole strength inside
the closed surface.
We do not have an isolated magnetic pole in nature. At least none has been found to exist till
date. The smallest unit of source of magnetic field is a magnetic dipole where the net magnetic
pole is zero. Hence, the net magnetic pole enclosed by any closed surface is always zero.
Correspondingly, the flux of the magnetic field through any closed surface is zero.
(i).. Consider the two idealized systems.
(I) A parallel plate capacitor with large plates and small separation and
(II) A long solenoid of length L>>R , radius of cross section.
In (I) E is ideally treated as a constant between plates and zero outside. In(II) magnetic field is
constant inside the solenoid and zero outside. Thse idealised assumptions, however,
contradict fundamental laws as
(a) case (I) contradicts Gaussโs law for electric fields
(b) case (II) contradicts gaussโs law for magnetic fields.
(c) case(I) agrees with ส E.dl = 0.
(d) case (II) contradicts ส H.dl = Ien.
(ii) The net magnetic flux through any closed surface, kept in a magnetic field is
(a) Zero (b) ยต0/4ฯ (c) 4 ฯยต0 (d) 4 ยต0/ฯ
(iii) A closed surface S encloses a magnetic dipole of magnetic moment 2ml. The magnetic flux
emerging from the surface is.
(a) ยต0m (b) Zero (c) 2 ยต0m (d) 2m/ ยต0
(iv) Which of the following is not a consequence of Gaussโs law?
(a) The magnetic poles always exists as unlike pairs of equal strength.
(b) If several magnetic lines of force enter in a closed surface, then an equal number of lines of
force must leave that surface.
(c) There are abundant sources of sinks of the magnetic field inside a closed surface.
(d) Isolated magnetic poles do not exist.
(v) The surface integral of a magnetic field over a surface
(a) is proportional to mass enclosed (b) is proportional to change enclosed
(c) is Zero (d) equal to its magnetic flux through that surface.
4. Dipole:
In electromagnetism, there are two kinds of dipoles:
An electric dipole deals with the separation of the positive and negative charges found in
any electromagnetic system. A simple example of this system is a pair of electric charges of
equal magnitude but opposite sign separated by some typically small distance.
A magnetic dipole is the closed circulation of an electric current system. A simple example is a
single loop of wire with constant current through it. A bar magnet is an example of a magnet
with a permanent magnetic dipole moment.
Dipoles, whether electric or magnetic, can be characterized by their dipole moment, a vector
quantity. For the simple electric dipole, the electric dipole moment points from the negative
charge towards the positive charge, and have a magnitude equal to the strength of each charge
times the separation between the charges
For the magnetic (dipole) current loop, the magnetic dipole moment points through the loop
(according to the right hand grip rule), with a magnitude equal to the current in the loop times the
area of the loop.
(i) The SI unit of magnetic dipole moment is
(a,) N-m (b) J-T (c) A-m2 (d) A/m2
(ii) The direction of Magnetic dipole moment is
(a) From South Pole of the magnet to North pole
(b) From North Pole of the magnet to South pole
(c) From South pole to any arbitrary direction
(d) From North Pole to any arbitrary direction
(iii) The magnetic dipole moment of a current carrying Loop is
(a) M = NIA (b) M = I/A (c) M= NA (d) M = NI/A
(iv) The Direction of magnetic dipole moment is decide by
(a) Left Hand screw rule (b) Right hand screw rule
(c ) Gaussโs law (b) Ampereโs Circuital law
(v) Magnetic field at any axial point of dipole is given by
(a) ยต0/4ฯ . 4M/r3 (b) ยต0/4ฯ . M/2r3 (c) ยต0/4ฯ . M/r3 (d) ยต0/4ฯ . 2 M/r3
5. Magnetic Moment and Magnetic Field :
Observe the following figures
(i) (ii) (iii)
(iv) (v)
(i) If the magnet 1 has a magnetic moment 3 times that of magnet 2,are pivoted so that it is free
to rotate in the horizontal plane. In equilibrium what angle will the magnet 1 subtend with the
magnetic meridian?
(a) tanโ1(1/2) (b) tanโ1(1/3) (c) tanโ1(1) (d) 00
(ii) In figure 2 in equilibrium position. The ratio of distance d1 and d2 will be
(a) (2tanฮธ)1/3 (b) (2tanฮธ)โ1/3 (c) (2cotฮธ)1/3 (d) (2cotฮธ)โ1/3
(iii) In figure 3 The magnitude of the magnetic field at a distance d from the centre on the
bisector of the right angle will be
(a) ยต0/4ฯ . M/d3 (b) ยต0/4ฯ . M โ2 /d3 (c) ยต0/4ฯ . 2โ2 M/d3 (d) ยต0/4ฯ.2 M/d3
(iv) In figure 4 two identical bar magnets with a length 10 cm and weight 50 gm-weight are
arranged freely with their like poles facing in a inverted vertical glass tube. The upper magnet
hangs in the air above the lower one so that the distance between the nearest poles of the magnet
is 3mm. Pole strength of the poles of each magnet will be
(a) 6.64 amp - m ( b) 2 amp-m (c ) 10.25 amp-m (d) 0 amp-m
(v) In figure 5 A small coil C with N = 200 turns is mounted on one end of a balance beam and
introduced between the poles of an electromagnet as shown in figure. The cross sectional area of
coil is A= 1.0 cm2, length of arm OA of the balance beam is l=30cm. When there is no current in
the coil the balance is in equilibrium. On passing a current I = 22 mA through the coil the
equilibrium is restored by putting the additional counter weight of mass ฮm=60mg on the balance
pan. Find the magnetic induction at the spot where coil is located.
(a) 0.4T (b) 0.3T (c) 0.2T (d) 0.1T
Solution: (i) - For equilibrium of the system torques on M1 and M2 due to BH must counter
balance each other i.e. M1รBH=M2รBH. If q is the angle between M1 and BH will be (90โฮธ); so
M1BHsinฮธ=M2BHsin(90โฮธ) โtanฮธ=M2/M1=M/3M=1/3 โฮธ=tanโ1(1/3)
(ii) In equilibrium B1=B2tanฮธ
โฮผ0/4ฯ.2Md13=ฮผ0/4ฯ.Md23tanฮธ โd1d2=(2cotฮธ)1/3
(iii) Resultant magnetic moment of the two magnets is Mnet=โM2+M2โโโโโโโโ= M โ2
Imagine a short magnet lying along OP with magnetic moment equal to Mโ2. Thus point P lies on
the axial line of the magnet. โดMagnitude of magnetic field at P is given by B=ฮผ0/4ฯ.2Mโ2/d3
(iv) The weight of upper magnet should be balanced by the repulsion between the two
magnet
โด ฮผ04ฯ.m2/r2=50gmโwt โ10โ7รm2/(9ร10โ6)=50ร10โ3ร9.8
โm=6.64ampรm
(v) On passing current through the coil, it acts as a magnetic dipole. Torque acting on magnetic
dipole is counter balanced by the moment of additional weight about position O. Torque acting
on a magnetic dipole ฯ=M B sinฮธ=(NIA)Bsin90o=NIAB Again ฯ=Force x Lever arm =ฮmg รl
โNIAB=ฮmg l โB=ฮmg l/NIA=60ร10โ3ร9.8ร30ร10โ2 /200ร22ร10โ3ร1ร10โ4 = 0.4 T
ANSWERS(Case Study Questions):
ANS.(i) ANS.(ii) ANS.(iii) ANS.(iv) ANS.(v)
Q.1 b b d a c
Q.2 c b c d b
Q.3 b a b c d
Q.4 c a a b d
Q.5 b c c a a
CHAPTER 6
ELECTROMAGNETIC INDUCTION
GIST OF LESSON: 1. Magnetic Flux: The magnetic flux linked with any surface is equal to total number of
magnetic lines of force passing normally through it. It is a scalar quantity.
2. The phenomenon of generation of current or emf by changing the magnetic flux is known as Electromagnetic Induction EMI. 3. Faradayโs Law of Electromagnetic Induction First Law: Whenever magnetic flux linked with the closed loop or circuit changes, an emf induces in the loop or circuit which lasts so long as change in flux continuous. Second Law : The induced emf in a closed loop or circuit is directly proportional to the rate of change of magnetic flux linked with the closed loop or circuit
where, N = number of turns in loop. Negative sign indicates the Lenzโs law. 4. Lenzโs Law The direction of induced emf or induced current is such that it always opposes the cause that produce it. NOTE: Lenzโs law is a consequence of the law of conservation of energy. 5. If N is the number of turns and R is the resistance of a coil. The magnetic flux linked with its each turn changes by dะค in short time interval dt, then induced current flowing through the coil is
6. If induced current is produced in a coil rotated in a uniform magnetic field, then
7. Motional Emf : The potential difference induced in a conductor of length l moving with velocity v, in a direction perpendicular to magnetic field B is given by
8. Flemingโs Right Hand Rule : If the thumb, forefinger and middle finger of right hand are stretched mutually perpendicular to each other such that the forefinger points the direction
of magnetic field, thumb points towards the direction of magnetic force, then middle finger points towards the direction of induced current in the conductor.
9. The induced emf developed between two ends of conductor of length l rotating about one end with angular velocity ฯ in a direction perpendicular to magnetic field is given by,
10. The induced emf can be produced in a coil by (i) putting the coil/loop/circuit in varying magnetic field. (ii) changing the area A of the coil inside the magnetic field, (iii) changing the angle 0 between B and A. 11. Rotation of rectangular coil in a uniform magnetic Field:
Magnetic flux linked with coil
= BANcos
= BANcost
a) Induced emf in thecoil
E = (๐ร/๐๐ก)
= BANwsinwt
= E0sinwt
b) Induced current in the coil. I = E/R
= ๐ธ0๐ ๐๐๐ค๐ก
๐
c) Both Emf and current induced in the coil are alternating. 12. Self Induction and Self inductance:
a) The phenomenon in which an induced emf is produced by changing the current in a
coil is called self induction.
โ ๐ผ I or โ = L I
Or L = โ
๐ผ
Now ๐ธ = โ๐ฟ๐๐ผ
๐๐ก
๐ฟ = โ๐ธ
๐๐ผ๐๐ก
where L is a constant, called self inductance or coefficient of self โ induction.
b) Self inductance of a solenoid.
๐ฟ = ๐0๐2๐ด
๐ , where symbols have their usual meanings.
CHAPTER 6
ELECTROMAGNETIC INDUCTION
MULTIPLE CHOICE QUESTIONS:
1. In the given figure current from A to B in the straight wire is increasing. The direction of the induced current in the loop is
(a) clockwise. (b) anticlockwise. (c) straight line. (d) No current is induced.
2. In a coil of self-induction 5 H, the rate of change of current is 2 As-1. Then emf induced in the coil is (a) 10 V (b) -10 V (c) 5 V (d) -5 V
3. The magnetic flux linked with a coil of N turns of area of cross section A held with its plane parallel to the field B is
4. Two identical coaxial coils P and Q carrying equal amount of current in the same direction are brought nearer. The current in (a) P increases while in Q decreases (b) Q increases while in P decreases (c) both P and Q increases (d) both P and Q decreases
5. Faradayโs laws are consequence of the conservation of (a) charge (b) energy (c) magnetic field (d) both (b) and (c)
6. Direction of current induced in a wire moving in a magnetic field is found using (a) Flemingโs left hand rule (b) Flemingโs right hand rule (c) Ampereโs rule (d) Right hand screw rule
7. Which of the following statements is not correct? (a) Whenever the amount of magnetic flux linked with a circuit changes, an emf is induced in circuit. (b) The induced emf lasts so long as the change in magnetic flux continues. (c) The direction of induced emf is given by Lenzโs law. (d) Lenzโs law is a consequence of the law of conservation of momentum.
8. Lenzโs law is a consequence of the law of conservation of (a) charge (b) energy (c) induced emf (d) induced current
9. A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, the current will (a) increase (b) decrease (c) remain same (d) first increase then decrease
10. There is a uniform magnetic field directed perpendicular and into the plane of the paper. An irregular shaped conducting loop is slowly changing into a circular loop in the plane of the paper. Then (a) current is induced in the loop in the anti-clockwise direction. (b) current is induced in the loop in the clockwise direction. (c) ac is induced in the loop. (d) no current is induced in the loop.
11. In the given figure current from A to B in the straight wire is decreasing. The direction of induced current in the loop is A
(a) clockwise (b) anticlockwise (c) changing (d) nothing can be said
12. Which of the following does not use the application of eddy current? (a) Electric power meters (b) Induction furnace (c) LED lights (d) Magnetic brakes in trains
13. The north pole of a bar magnet is rapidly introduced into a solenoid at one end (say A). Which of the following statements correctly depicts the phenomenon taking place? (a) No induced emf is developed. (b) The end A of the solenoid behaves like a south pole. (c) The end A of the solenoid behaves like north pole. (d) The end A of the solenoid acquires positive potential.
14. A metal plate can be heated by (a) passing either a direct or alternating current through the plate. (b) placing in a time varying magnetic field. (c) placing in a space varying magnetic field, but does not vary with time. (d) both (a) and (b) are correct.
15. Identify the wrong statement. (a) Eddy currents are produced in a steady magnetic field. (b) Eddy currents can be minimized by using laminated core. (c) Induction furnace uses eddy current to produce heat. (d) Eddy current can be used to produce braking force in moving trains.
16. If number of turns in primary and secondary coils is increased to two times each, the mutual inductance (a) becomes 4 times (b) becomes 2 times (c) becomes A times (d) remains unchanged 4
17. When the rate of change of current is unity, the induced emf is equal to (a) thickness of coil (b) number of turns in coil (c) coefficient of self-inductance (d) total flux linked with coil
18. Two inductors of inductance. L each are connected in series with opposite? magnetic fluxes. The resultant inductance is (Ignore mutual inductance) (a) zero (b) L (c) 2L (d) 3L
19. A square of side L meters lies in the x-y plane in a region, where the magnetic field is given by B = B0 i + 3j + 4k) T, where Bo is constant. The magnitude of flux passing through the square is (a) 2BoLยฒ Wb. (b) 3BoLยฒ Wb. (c) 4BoLยฒ Wb. (d) โ29 BoLยฒ Wb.
20. A loop, made of straight edges has six comers at A(0, 0, 0), B(L, 0, 0) C(L, L, 0), D(0, L, 0), E(0, L, L) and F(0,0, L). A magnetic field B = Bo (i+k)T is present in the region. The flux passing through the loop ABCDEFA (in that order) is (a) BoLยฒ Wb. (b) 2BoLยฒ Wb. (c) โ2BoLยฒ Wb. (d) 4BoLยฒ Wb.
21. An e.m.f is produced in a coil, which is not connected to an external voltage source. This is not due to (a) the coil being in a time varying magnetic field. (b) the coil moving in a time varying magnetic field. (c) the coil moving in a constant magnetic field. (d) the coil is stationary in external spatially varying magnetic field, which does not change with time.
22. There are two coils A and B as shown in Figure. A current starts flowing in B as shown, when A is moved towards B and stops when A stops moving. The current in A is counterclockwise. B is kept stationary when A moves. We can infer that
(a) there is a constant current in the clockwise direction in A. (b) there is a varying current in A. (c) there is no current in A. (d) there is a constant current in the counterclockwise direction in A.
23. Same as question 4 except the coil A is made to rotate about a vertical axis (Figure). No current flows in B if A is at rest. The current in coil A, when the current in B (at t = 0) is counterclockwise and the coil A is as shown at this instant, t = 0, is
(a) constant current clockwise. (b) varying current clockwise. (c) varying current counterclockwise. (d) constant current counterclockwise.
24. A cylindrical bar magnet is rotated about its axis (Figure). A wire is connected from the axis
and is made to touch the cylindrical surface through a contact. Then (a) a direct current flows in the ammeter A. (b) no current flows through the ammeter A. (c) an alternating sinusoidal current flows through the ammeter A with a time period T = 2ฯฯ (d) a time varying non-sinusoidal current flows through the ammeter.
25. Eddy currents do not cause (a) damping (b) heating (c) sparking (d) loss of energy
26. Magnetic flux of 5 mwb is linked with a coil, when current of 1 mA flows through it, Self-induced will be a) 1 H b) 5 H c) 20 H d) 50 H
27. According to Faradayโs laws of electromagnetic induction, an emf is induced in a conductor whenever? a) The conductor is perpendicular to the magnetic field b) Lies in the magnetic field c) Cuts magnetic lines of flux d) Moves parallel to the magnetic field
28. Direction of induced current is determined by __________ a) Flemingโs left-hand rule b) Flemingโs right-hand rule c) Faradayโs law d) Right hand thumb rule
29. โThe direction of an induced e.m.f. is always such that it tends to set up a current opposing the motion or the change of flux responsible for inducing that e.m.f.โ, this is the statement for? a) Flemingโs left-hand rule b) Flemingโs right hand rule c) Faradayโs law d) Lenzโs law
30. According to Flemingโs right-hand rule, the thumb points towards? a) Current b) E.M.F. c) Motion of the conductor d) Magnetic flux
31. According to Flemingโs right-hand rule, the middle finger points towards? a) Current b) E.M.F. c) Motion of the conductor d) Magnetic flux
32. The relation between the direction of induced emf and the direction of motion of the conductor is? a) Parallel b) Equal c) Not related d) Perpendicular
33. According to _________________ induced emf is equal to rate of change of magnetic flux. a) Newtonโs law b) Lenz law c) Faradayโs law d) Coulombโs law
34. What is the principle of the transformer? a) Gauss law b) Coulombโs law c) Mutual induction d) Ampereโs law
35. As the number of turns in the coil increases, what happens to the inductance of the coil? a) Increases b) Decreases c) Remains the same d) Becomes zero
36. What happens to the self inductance of a coil when its length increase? a) Increases b) Decreases c) Remains the same d) Becomes zero
37. What happens to the inductance when the current in the coil becomes double its original value? a) Becomes half b) Becomes four times c) Becomes infinity d) remains same
38. If the current changes from 20A to 10A in 5 seconds and the value of inductance is 1H, calculate the emf induced. a) 8V b) 6V c) 4V d) 2V
39. The phenomenon due to which there is an induced current in one coil due to the current in a neighboring coil is? a) Eddy currents b) Self-induction c) Mutual induction d) Steady current
40. If the current in one coil becomes steady, back emf in the coil is? a) Zero b) Infinity c) Doubles d) Halves
ANSWERS(Multiple Choice Questions):
Q. 1 2 3 4 5 6 7 8 9 10 11 12 13
ANS a b d d b b d b b a b c c
Q. 14 15 16 17 18 19 20 21 22 23 24 25 26
ANS d a a c c c b d d b b c b
Q. 27 28 29 30 31 32 33 34 35 36 37 38 39
ANS c b d c a d c c a b d d c
Q. 40
ANS a
ASSERSION AND REASON QUESTIONS:
Directions: These questions consist of two statements, each printed as Assertion and Reason. While answering these questions, you are required to choose any one of the following four responses. (a) If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion. (b) If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion. (c) If the Assertion is correct but Reason is incorrect. (d) If both the Assertion and Reason are incorrect.
1. Assertion: Induced emf will always occur whenever there is change in magnetic flux. Reason : Current always induces whenever there is change in magnetic flux.
2. Assertion: Faradayโs laws are consequence of conservation of energy. Reason : Self inductance of a coil depends on current flowing through the coil.
3. Assertion : Only a change in magnetic flux will maintain an induced current in the coil. Reason : The presence of large magnetic flux through a coil maintain a current in the coil of the circuit is continuous. 4. Assertion: Lenzโs law violates the principle of conservation of energy. Reason: Induced emf always opposes the change in magnetic flux responsible for its production. 5. Assertion : In the phenomenon of mutual induction, self-induction of each of the coils
persists.
Reason : Self induction arises when strength of current in same coil changes. In mutual
induction, current is changing in both the individual coils.
6. Assertion : Acceleration of a magnet falling through a long solenoid decreases. Reason : The induced current produced in a circuit always flow in such direction that it opposes the change to the cause that produced it.
7. Assertion : Figure shows a horizontal solenoid connected to a battery and a switch. A copper ring is placed on a smooth surface, the axis of the ring being horizontal. As the switch is closed, the ring will move away from the solenoid.
Reason : Induced emf in the ring, e=-dฮฆ/dt
8. Assertion : An emf can be induced by moving a conductor in a magnetic field. Reason : An emf can be induced by changing the magnetic field.
9. Assertion : Figure shows a metallic conductor moving in magnetic field. The induced emf across its ends is zero.
Reason : The induced emf across the ends of a conductor is given by e = Bvโ sinฮธ.
10. Assertion : Eddy currents are produced in any metallic conductor when magnetic flux is changed around it. Reason : Electric potential determines the flow of charge.
ANSWERS (Assertion & Reason Questions):
Q. 1 2 3 4 5 6 7 8 9 10
ANS c c c a b a a b a b
CASED STUDY QUESTIONS:
1. Motional EMF : Conductor PQ of length L moving towards right with velocity V perpendicular
to magnetic field B directed into the plane of paper as the conductor pk moves it its free electrons
also move in the same direction and experience magnetic Lorentz force F=evB. By Fleming's left
hand rule electrons move from P to Q within the conductor the end P becomes positive and end
Q becomes negative. An electric field is set up in the conductor from P to Q this exerts a force
F=eE on the free electrons. The accumulation of charges at the two ends continues till these two
forces balance each other ie Fm=Fe or evB=eE or vB=E. Potential difference between the ends P
and Q .
is V=El=vBl. It is the magnetic force on the free electrons that maintains potential difference and
produces the EMF E=Blv. This MF is produced due to the motion of conductor it is called a
motional EMF.
(i) A conducting wire sits on smooth metal rails as shown in the figure a variable magnetic field points out the page the strength of this field is increased linearly from zero immediately after the field start to increase what will be the direction of the current in the wire and the direction of the wires motion
(ii) A 50 cm long bar ab is moved with a speed of 4 metre per second in a magnetic field
B=0.01 T as shown in the figure the EMF generated is a) 01V b) 0.02V c) 0.03 V
d) 0.04 V
(iii) An aeroplane having a wing span of 35 M flies due north with a speed of 90 metre per
second given B= 4 x10-โต T. The potential difference between the tips of the wings will be
a). 0.126V
b). 1.26V
c). 12.6V
d). 0.013V
(iv) If the vertical component of Earth's magnetic field be. 6x10-5Wbm-2, then what will be
induced potential difference between the rails of a meter-gauge when a train is running on
them with a speed of 36 km/h
(v) A wheel with 10 metallic spokes each 4.5 m long is rotated with a speed of 120 rev/min
in a plane normal to the horizontal component of Earth's magnetic field BH at a place. if BH =
0.4 G at the place. the magnitude of induced EMF between the axle and the rim of the wheel
is
2. Eddy Currents:
The motion of a copper plate is damped when it is allowed to oscillate between the magnetic
pole pieces. Magnetic flux associated with the plate keeps on changing as the plate moves in
and out of the region between the magnetic poles. The changing flux sets up induced currents
in the copper plates which flow along closed path in planes perpendicular to the magnetic
field the current looks like adress aur whirlpools in water. So they are known as eddy currents.
They also oppose the change in magnetic flux. Eddy currents develop heat at the cost of
kinetic energy of the plates as the plate slows down. This is called electromagnetic damping.
To reduce electromagnetic damping one can cut slots in the plate which reduces the possible
parts of Eddy currents considerably.
(i) A metallic pendulum oscillating in a uniform magnetic field directed perpendicular to the
plane of oscillation
a. slows down
b. Becomes faster
c. Unaffected
d. Oscillates with the changing frequency
(ii). A metallic cylinder is held vertically. A small bar magnet is dropped along its Axis will fall
with acceleration such that
a. a>g
b. a<g
c. a=g
d. a=0, velocity
(iii). A coil is suspended in a uniform magnetic field with the plane of the coil parallel to the
magnetic lines of force when a current is passed through the coil it starts oscillating, it is very
difficult to stop. But if an aluminium plate is placed near the coil is. This is due to
a. Development of air current when the plate is placed
b. Induced of electric charge on the plate
c. Shielding of magnetic lines of force as element aluminium is a paramagnetic material
d. Electromagnetic induction in the aluminium plate giving rise to electromagnetic damping
(iv). Eddy currents are produced when
a. A metal is kept in a steady magnetic field
b. A metal is kept in a varying magnetic field
c. A circular coil is placed in a magnetic field
d. A current is passed through a circular coil
(v). The core of a transformer is laminated so that
a. Rusting of iron core may be stopped
b. Ratio of voltage in primary and secondary coil may be increased
c. Rate of change of flux is increased
d. Energy losses due to Eddy currents may be reduced.
3. Self Induction:
When a current passing through a coil changes the magnetic flux linked with the coil changes.
As a result and EMF is induced in the coil. This phenomenon is called self induction.
At any instant the flux linked with that n number of turns of the coil is proportional to the
current I through the coil that is N directly proportional to I or and Nษธ =LI.
The proportionality constant L is called self inductance or simply inductance. Inductance is
the ratio of flux linkage to the current. It is equal to Nษธ/I lenz law the induced EMF opposes
the change of current so inductance L is measure of the inertia of the coil against the change
of current through it. In contrast to it a resistor r opposes the flow of current I through the
circuit. A solenoid made from a thick wire has a negligible resistance but a sufficiently large
inductance. Such an element is called an ideal inductor. Inductance of a coil depends upon
the geometry of the coil, number of turns in the coil and the permeability of the medium
inside the coil.
(i). What is the unit of self inductance of a coil?
(ii). If the number of turns per unit length of a coil of a solenoid is doubled, its self
inductance will be
a. remains constant
b. be doubled
c. be halved
d. be four times
(iii). If both the number of turns and core length of an inductor are doubled keeping other
factors constant self inductance will be
a. unaffected
b. doubled
c. halved
d. quadrupled
(iv). In a coil of self inductance 5 Henry, the rate of change of current is 2 amp per second.
The EMF induced in the coil is
a. -5V
b. 5V
c. -10V
d. 10V
(v). A Coil of 100 turns carries a current of 5 mA and creates a magnetic flux of 10-5 wb. The
inductance is
a. 0.2mH
b. 2.0 mH
c. 0.02mH
d. None of these
4. Eddy Currents:
Eddy Currents and their Effects Currents can be induced not only in conducting coils, but also in conducting sheets or blocks. Current is induced in solid metallic masses when the magnetic flux threading through them changes. Such currents flow in the form of irregularly shaped loops throughout the body of the metal. These currents look like eddies or whirlpools in water so they are known as eddy currents. Eddy currents have both undesirable effects and practically useful applications. For example, it causes unnecessary heating and wastage of power in electric motors, dynamos and in the cores of transformers.
(i) The working of speedometers of trains is based on
(a) wattles current
(b) eddy currents
(c) alternating current (d) pulsating currents
(ii) Identify the wrong statement.
(a) Eddy currents are produced in a steady magnetic field.
(b) Induction furnace uses eddy currents to produce heat.
(c) Eddy currents can be used to produce braking force in moving trains.
(d) Power meters work on the principle of eddy currents.
(iii) Which of the following is the best method to reduce eddy currents?
(a) Laminating core (b) Using thick wires (c) By reducing hysteresis loss
(d) None of these
(iv) The direction of eddy currents is given by
(a) Fleming's left hand rule (b) Biot-Savart law (c) Lenz's law (d) Ampere-circuital law
(v) Eddy currents can be used to heat localised tissues of the human body. This branch of medical
therapy is called
(a) Hyperthermia (b) Diathermy (c) Inductothermy (d) none of these.
ANSWERS(Case Study Questions):
ANS.(i) ANS.(ii) ANS.(iii) ANS.(iv) ANS.(v)
Q.1 c b a b d
Q.2 a b d b d
Q.3 d d b c c
Q.4 b a a c C
Solutions of Case Study Questions:
1(i)
1(ii)
1(iii)
1(iv)
1(v)
2(i)
2(ii)
2(iii)
2(iv)
2(v)
3(i)
3(ii)
3(iii)
3(iv)
3(v)
4(i) B
4(ii) A
4(iii) A
4(iv) C
4(v) C
CHAPTER 7
ALTERNATING CURRENT
GIST OF LESSON: An electric current whose magnitude changes continuously with time and changes its direction periodically, is called an alternating current.
The instantaneous value of alternating current at any instant of time t is given by
I = Io sin ฯt where, I0 = peak value of alternating current.
The variation of alternating current with time is shown in graph given below
Mean or average value of alternating current for first half cycle
Im = 2Io / ฯ = 0.637 Io Mean or average value of alternating current for next half cycle
Iโm = โ 2Io / ฯ = โ 0.637 Io Mean or average value of alternating current for one complete cycle = O.
Root mean square value of alternating current
Iv = Irms = Io / โ2 = 0.707 Io Where, Io = peak value of alternating current. Root mean square value of alternating voltage
Vrms = Vo / โ2 = 0.707 Io = 0.707 Vo
Reactance The opposition offered by an inductor or by a capacitor in the path of flow of alternating current is called reactance.
Reactance is of two types
(i) Inductive Reactance (XL) Inductive reactance is the resistance offered by an inductor. Inductive reactance (XL) = Lฯ = L2ฯf = L2ฯ / T Its unit is ohm. XL โ f For direct current, XL = 0 (f = 0)
(ii) Capacitive Reactance (Xc) Capacitive reactance is the resistance offered by an inductor Capacitive reactance,
Xc = 1 / Cฯ = 1 / C2ฯf = T / C 2ฯ Its unit is ohm Xc โ 1 / f For direct current, Xc = โ (f = 0)
Impedance The opposition offered by an AC circuit containing more than one out of three components L, C and R, is called impedance (Z) of the circuit.
Impedance of an AC circuit, Z = โR2 + (XL โ XC)2 Its SI unit is ohm.
Power in an AC Circuit The power is defined as the rate at which work is being in the circuit.
The average power in an AC circuit,
Pav = Vrms irms cos ฮธ = V / โ2 i / โ2 cos ฮธ = Vi / โ2 cos ฮธ
where, cos ฮธ = Resistance(R) / Impedance (Z) is called the power factor 0f AC circuit.
Current and Potential Relations Here, we will discuss current and potential relations for different AC circuits.
(i) Pure Resistive Circuit (R circuit)
(a) Alternating emf, E = Eo sin ฯt (b) Alternating current, I = Io sin ฯt (c) Alternating emf and alternating current both are in the same phase.
(d) Average power decay, (P) = Ev . Iv (e) Power factor, cos ฮธ = 1
(ii) Pure Inductive Circuit (L Circuit)
(a) Alternating emf, E = Eo sin ฯt (b) Alternating current, I = Io sin (ฯt โ ฯ / 2) (c) Alternating current lags behind alternating emf by ฯ / 2.
(d) Inductive reactance, XL = Lฯ = L2ฯf (e) Average power decay, (P) = 0
(f) Power factor, cos ฮธ = cos 90ยฐ = 0
(iii) Pure Capacitive Circuit
(a) Alternating emf, E = Eo sin ฯt (b) Alternating current, I = Io sin (ฯt + ฯ / 2) (c) Alternating current lags behind alternating emf by ฯ / 2.
(d) Inductive reactance, XL = Cฯ = C2ฯf (e) Average power decay, (P) = 0
(f) Power factor, cos ฮธ = cos 90ยฐ = 0
(iv) R โ C Circuit
E = Eo sin ฯt I = Eo / 2 sin (ฯt โ ฯ) Z = โR2 + (1 / ฯC)2 tan ฯ = โ 1 / ฯC / R
Current leading the voltage by ฯ
V2 = V2R = V2
C
(v) L โ C Circuit
(vi) L โ C โ R Circuit
(a) Alternating emf, E = Eo sin ฮฉt (b) Alternating current, I = Io sin (ฮฉt ยฑ ฮธ) (c) Alternating current lags leads behind alternating emf by ฯ.
(d) Resultant voltage, V = โV2R + (VL โ VC)2
(e) Impedance, Z = โR2 + (XL โ XC)2 (f) Power factor, cos ฮธ = R / Z = R / โโR2 + (XL โ XC)2 (g) Average power decay, (P)= EVIV cos ฮธ Resonance in AC Circuit The condition in which current is maximum or impedance is minimum in an AC circuit, is called resonance.
(i) Series Resonance Circuit
In this circuit components L, C and R are connected in series.
At resonance = XL = XC Resonance frequency f = 1 / 2ฯโLC
A series resonance circuit is also known as acception circuit.
(ii) Parallel Resonance Circuit
In this circuit L and C are connected in parallel with each other.
At resonance, XL = XC Impedance (Z) of the circuit is maximum.
Current in the circuit is minimum.
Wattless Current Average power is given by
Pav = Erms = Irms cos ฮธ Here the Irms cos ฯ contributes for power dissipation. Therefore, it is called wattless current. Transformer It is a device which can change a low voltage of high current into a high voltage of low current and vice-versa.
Its working is based on mutual induction.
There are two types of transformers.
(i) Step-up Transformers It converts a low voltage of high current into a high voltage of low current.
In this transformer,
Ns > NP, Es > EP and IP > IS (ii) Step-down Transformer It converts a high voltage of low current into a low voltage of high current. In this transformer,
NP > NS, EP > ES and IP < IS Transformation Ratio Transformation ratio,
K = NS / NP = ES / EP = IP / IS For step-up transformer, K > 1
For step-down transformer, K < 1
Energy Losses in a Transformer The main energy losses in a transformer are given below
1. Iron loss
2. Copper loss
3. Flux loss
4. Hysteresis loss
5. Humming loss
Important Points Transformer does not operate on direct current. It operates only on alternating voltages at input as well as at
output.
Transformer does not amplify power as vacuum tube.
Transformer, a device based on mutual induction converts magnetic energy into electrical energy.
Efficiency, ฮท = Output power / Input power
Generally efficiency ranges from 70% to 90%.
CHAPTER 7
ALTERNATING CURRENT
MULTIPLE CHOICE QUESTIONS:
1. In A.C. circuit having only capacitor, the current
(a) Lags behind the voltage by 900 in phase
(b) Leads the voltage by 900 in phase
(c) Leads the voltage by 1800 in phase
(d) Lags behind the voltage by 1800 in phase
2. The ratio of peak value and r.m.s. value of an alternating current is
(a) 1 (b) 1
2
(c) โ2 (d) 1
โ2
3. The maximum value of a.c. voltage in a circuit is 770V. Its r.m.s. Value is
(a) 70.7 V b) 100 V
(c) 500 V d) 704 V
4. In a pure inductive circuit, the current
(a) Leads the e.m.f. by 900
(b) Lags behind the e.m.f. by 900
(c) Sometimes leads and sometime legs behind the e.m.f.
(d) Is in phase with the e.m.f.
5. Voltage and current in an ac circuit are given by
๐ = 5 sin(100๐๐ก โ๐
6), ๐ผ = 4 sin (100๐๐ก +
๐
6)
(a) Voltage leads the current by 300
(b) Current leads the voltage by 300
(c) Current leads the voltage by 600
(d) Voltage leads the current by 600
6. An inductor L of reactance XL is connected in series with a bulb B to an ac source as shown in the figure.
How does the brightness of the bulb change when Number of turns of the inductor is increased?
(a) Increases (b) Decreases (c) Remains same (d) none of these
7. The instantaneous current in an ac circuit is I=2.0 sin314t, what is its frequency?
(a) 100 Hz (b) 60 Hz (c) 50 Hz (d) 2ฯ
8. An A.C source is connected to a resistive circuit. Which of the following is true?
(a) Current leads the voltage and both are in same phase
(b) Current lags behind the voltage and both are in same phase
(c) Current and voltage are in same phase
(d) Any of the above may be true depending upon the value of resistance
9. What is the effective value of current?
(a) RMS current (b) Average current (c) Instantaneous current (d) Total current
10. In a sinusoidal wave, average current is always _______ rms current.
(a) Greater than (b) Less than (c) Equal to (d) Not related
11. Using an A.C. voltmeter, the potential difference in the electrical line in a house is read to be 234 volts.
If the line frequency is known to be 50 cycles per second, the equation for the line voltage is
(a) V = 165 sin(100ฯt) (b) V = 331 sin(100ฯt)
(c) V = 234 sin(100ฯt) (d) V = 440 sin(100ฯt)
12. What are the dimensions of impedance?
(a) ML2T-3I-2 (b) M-1L-2T-3I2
(c) ML3T-3I-2 (d) M-1L-3T3I2
13. A voltage across a pure inductor is represented in figure.
Which one of the following curves in the figure will represent the current?
14. The reactance of a capacitor C is X. If both the frequency and capacitance be doubled, then new
reactance will be
(a) 2X (b)X
(c) 4X (d)๐
4
15. An Inductor may store energy in
(a) Its electric field (b)Its coil
(c)Its magnetic field (d) Both in electric and magnetic fields.
16. For high frequency, capacitor offers
(a)More reactance (b) Zero reactance
(c) Less reactance (d) None of these.
17. Choose the correct statement.
(a) The capacitor can conduct in a dc circuit but not an inductor
(b) In dc circuit the inductor can conduct but not a capacitor
(c) In dc circuit both the inductor and capacitor cannot conduct
(d) The inductor has infinite resistance in a dc circuit
18. If a capacitor is connected across a source of AC voltage then
(a) voltage and current are in same phase.
(b) voltage and current are out of phase.
(c) voltage leads current by 90 degree phase angle.
(d) Current leads voltage by 90 degree phase angle.
19. What is power factor of an ac circuit:
(a) cosฯ
(b) tanฯ
(c) cotฯ
(d) sinฯ
20. If the value of C in a series RLC circuit is decreased, the resonant frequency
(a)Is not affected
(b) Increases
(c)Is reduced to zero
(d)Decreases
21. In a series RLC circuit that is operating above the resonant frequency, the current
(a) Lags the applied voltage
(b) Leads the applied voltage
(c) Is in phase with the applied voltage
(d) zero
22. The impedance at the resonant frequency of a series RLC circuit with L = 20 mH C = 0.02 ฮผ F and R = 90
ฮฉ is
(a)0 ฮฉ (b) 90 ฮฉ
(c) 20 ฮฉ (d) 40 ฮฉ
23. A 24 ฮฉ resistor, an inductor with a reactance of 120 ฮฉ, and a capacitor with a reactance of 120 ฮฉ are in
series across a 60 V source. The circuit is at resonance. The voltage across the inductor is
(a) 60 V (b) 660 V
(c) 30 V (d) 300 V
24. How many types of power can be defined in an AC circuit?
(a) 3 (b) 2
(c) 1 (d) 5
25. Which among the following varies in both magnitude and sign over a cycle?
(a) Apparent power (b) Effective power
(c) Instantaneous power (d) Average power
26. What is the power factor for a series LCR circuit at resonance?
(a) Infinity (b) -1
(c) 0 (d) 1
27. In A.C generator increasing the no. of turns in the coil
(a) Decreases the Electromotive force (EMF)
(b) Electromotive force (EMF) remains same
(c) Increases the Electromotive force (EMF)
(d) Electromotive force (EMF) becomes zero
28. The metal detectors installed at airports and other places for security purpose are based on the principle
of
(a) Potential difference (b) Electromagnetic difference
(c) Electromagnetic induction (d) Potential energy
29. In alternative current generator in India, AC current reverses its direction
(a) 10 times per second (b) 20 times per second
(c) 60 times per second (d) 50 times per second
30. The direction of induced Emf or current is indicated by
(a) Flemingโs left-hand rule (b) Flemingโs right-hand rule
(c) Faradayโs law of electromagnetic induction (d) None of these
31. An iron core transformer with a turns ratio of 8 : 1 has 120 V applied across the primary. The voltage
across the secondary is
(a) 15 V (b) 120 V (c) 180 V (d) 960 V
32. Transformer works on the principle of:
(a) Convertor (b) Inverter
(c) Mutual induction (d) Self-induction
33. Which of the following effects is not shown in alternating current ?
(a) Chemical effect (b) Magnetic effect
(c) Heating current (d) All of these
34. The figure shows variation of R, XL and XC with frequency f in a series LCR circuit. Then for what
frequency point, the circuit is inductive.
(a) A (b) B
(c) C (d) A and B
35. The core of a transformer is laminated, so as to
(a) Make it light weight (b) Make it robust and strong
(c) Increase the secondary voltage (d) Reduce energy loss due to eddy current
36. In a transformer, the no. of turns of primary and secondary coil are 500 and 400 respectively. If 220
V is supplied to the primary coil, then ratio of currents in primary and secondary coils is
(a) 4:5 (b) 5:4 (c) 5:9 (d) 9:5
37. In an LC oscillator, the frequency of oscillator is โฆโฆโฆโฆโฆ. L or C.
(a)Proportional to square of
(b)Directly proportional to
(c)Independent of the values of
(d)Inversely proportional to square root of
38. EMF generated in an alternator depends on which of the following factors?
(a) Number of turns in the coil
(b)Speed of the rotating field
(c)Magnetic field strength
(d)All of these
ANSWERS(Multiple Choice Questions):
Q. NO. ANSWER Q. NO. ANSWER Q. NO. ANSWER Q. NO. ANSWER
1 B 11 A 21 A 31 A
2 C 12 A 22 B 32 C
3 C 13 D 23 C 33 A
4 B 14 D 24 A 34 C
5 C 15 C 25 C 35 D
6 B 16 C 26 D 36 A
7 C 17 B 27 C 37 D
8 C 18 D 28 C 38 D
9 A 19 A 29 D
10 B 20 C 30 B
ASSERTION & REASON QUESTIONS:
Directions.
In each of the following questions 2 statements are given. One is assertion and the other is reason.
Examine the statements carefully mark the correct answer as
(a) If both assertion and Reason are true and reason is the correct explanation of assertion.
(b) If both assertion and Reason are true and but reason is not the correct explanation of assertion.
(c) If assertion is true but reason is false.
(d) If both assertion and reason is false.
1. Assertion(A): - A capacitor of suitable capacitance can be used in a circuit in place of the choke coil.
Reason(R): - A capacitor blocks DC and allow AC only.
2. Assertion(A): -The sum of the instantaneous current values over one complete cycle is zero, and the
average current is zero.
Reason(R): - The applied voltage and the current varies sinusoidally and has corresponding positive and
negative values during each cycle.
3. Assertion(A): -The inductive reactance limits the current in a purely inductive circuit in the same way as
the resistance limits the current in a purely resistive circuit.
Reason(R): - The inductive reactance is directly proportional to the inductance and to the frequency of
the current.
4. Assertion(A): Transformers are used only in alternating current source not in direct current.
Reason(R) : Only a.c. can be stepped up or down by means of transformers.
5. Assertion(A): An important application of electromagnetic induction is ac generator.
Reason(R): The direction of current changes periodically and therefore the current is called alternating
current.
6. Assertion(A): In a series LCR circuit at resonance condition, power consumed by the circuit is maximum.
Reason(R): At resonance, the effective resistance of the circuit is maximum.
7. Assertion (A): We use a thick wire in the secondary coil of a step down transformer to reduce the
production of heat.
Reason (R): When the plane of the armature is parallel to the line of force of magnetic field, the
magnitude of induced e.m.f. is maximum
8. Assertion (A): Soft iron is used as a core of transformer.
Reason (R): Area of hysteresis loop for soft iron is small.
9. Assertion (A): Capacitor serves as a block for D.C. and offers an easy path to A.C.
Reason (R): Capacitive reactance is inversely proportional to frequency.
10. Assertion (A): In the phenomenon of mutual induction self-induction of each of coils persists
Reason(R)- Self-induction arises when strength of current in same coil change in the mutual induction,
current is changing in both the individual
ANSWERS(Assertion & Reason Questions):
Q.No. 1 2 3 4 5 6 7 8 9 10
ANS b a a a a c b a a b
CASE STUDY QUESTIONS:
1. Transformer:
A transformer is an electrical device which is used for changing the a.c. voltages. It is based on the
phenomenon of mutual induction i.e. whenever the amount of magnetic flux linked with a coil changes, an
e.m.f. is induced in the neighboring coil. For an ideal transformer, the resistances of the primary and
secondary windings are negligible
It can be shown that Es/Ep=Is/Ip=Ns/Np=K
For a step-up transformer Ns>Np: Es>Ep: K>1 ((Is<Ip)
For a step-down transformer Ns<Np: Es<Ep: K<1
The above relations are on the assumptions that efficacy of transformer is 100%
Infact efficiency= out power/input power=Es Is/Ep Ip
(i) Which of the following quantity remains constant in an ideal transformer?
(a) Current (b) Voltage
(c) Power (d) All of these
(ii) Transformer is used to
(a) Convert ac to dc voltage (b) Convert dc voltage into ac
(c) Obtain desired dc power (d) Obtain desired ac voltage and current
(iii) The number of turns in primary coil of a transformer is 20 and the number of turns in a secondary
is 10. If the voltage across the primary is 220V ac what is the voltage across the secondary?
(a) 100 V (b) 120 V
(c) 110 V (d) 220 V
(iv) In a transformer the number of primary turns is four times that of the secondary turns. Its primary
is connected to an a.c. source of voltage V. Then
(a) Current through its secondary is about four times that of the current through its primary.
(b) Voltage across its secondary is about four times that of the voltage across its primary.
(c) Voltage across its secondary is about two times that of the voltage across its primary.
(d) Voltage across its secondary is about ?& times that of the voltage across its primary.
(v) A transformer is used to light 100 W-110 V lamp from 220 V mains. If the mains current is 0.5 A, the
efficiency of the transformer is
(a) 95% (b) 99% (c) 90% (d) 96%
2. Power Associated with LCR Circuit:
In an a.c. circuit, values of voltage and current change every instant. Therefore, power of an a.c. circuit
at any instant is the product of instantaneous voltage (E) and instantaneous current (I). The average
power supplied to a pure resistance R over a complete cycle of a.c. is P=Ev Iv. When circuit is inductive,
average power per cycle is EvIv Cosฯ
In an a.c. circuit, 600 mH inductor and a 50 pf capacitor are connected in series with 10 ohm resistance.
The a.c. supply to the circuit is 230 V, 60 Hz.
(i) The average power transferred per cycle to resistance is
(a) 10.42 W (b) 15.25 W (c) 17.42 W (d) 13.45 W
(ii) The average power transferred per cycle to capacitor is
(a) zero (b) 10.42 W (c) 17.42 W (d) 15W
(iii) The average power transferred per cycle to inductor is
(a) 25 W (b) 17.42 W (c) 16.52 W (d) zero
(iv) The total power transferred per cycle by all the three circuit elements is
(a) 17.42 W (b) 10.45 W (c) 12.45 W (d) zero
(v) The electrical energy spend in running the circuit for one hour is
(a) 7.5 x 105 Joule (b) 10 x 103 Joule (c) 9.4 x 103 Joule (d) 6.2 x 104 Joule
3. AC Voltage applied to a capacitor:
Let a source of alternating e.m.f ๐ธ = ๐ธ0sin (๐ค๐ก) be connected to a capacitor of capacitance C. If I is
the instantaneous value of current in the circuit at instant t, then ๐ผ = ๐ค๐ ๐ธ0 sin (๐ค๐ก +๐
2). The capacitive
reactance limits the amplitude of current in a purely capacitive circuit and It is given by ๐๐ถ = 1
๐๐ถ.
(i) What is the unit of capacitive reactance?
(a) Farad (b) Ampere (c) ohm (d) ohm-1
(ii) The capacitive reactance of a 5 ยตF capacitor for a frequency of 106 Hz is
(a) 0.032 ฮฉ (b)2.52 ฮฉ
(c) 1.25 ฮฉ (d) 4.51 V
(iii) In a capacitive circuit, resistance to the flow of current is offered by
(a) Resistor (b) capacitor
(c)Inductor (d) frequency
(iv) In a capacitive circuit, by what value of phase angle does alternating current leads the e.m.f.?
(a) 450 (b) 900 (c) 750 (d) 600
(v) One microfarad capacitor is joined to a 200V, 50 Hz alternator. The r.m.s. current through capacitor
is
(a) 6.28 ร 10-2 A (b) 7.5 ร 10-4 A
(c) 10.52 ร 10-2 A (d) 15.25 ร 10-2 A
4. Step Down Transformer in the Transmission of Electric Power:
Step down transformers is used to decrease or step-down voltages. These are used when voltage need to
be lowered for use in homes and factories.
A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric
plant generating power at 440 V. The resistance of the two-wire line carrying power is 0.5ฮฉ per km. The
town gets power from the line through a 4000-220 V step-down transformer at a sub-station in the town.
(i) The value of total resistance of the wires is
(a) 25 ฮฉ (b) 30 ฮฉ
(c) 35 ฮฉ (d) 15 ฮฉ
(ii) The line power loss in the form of heat is
(a) 550 KW (b) 650 kW
(c) 600 kW (d) 700 kW
(iii) How much power must the plant supply, assuming there is negligible power loss due to leakage?
(a) 600 KW (b) 1600 KW
(c) 500 kW (d) 1400 KW
(iv) The voltage drop in the power line is
(a) 1700 V (b) 3000 V
(c) 2000 V (d) 2800 V
(v) The total Value of voltage transmitted from the plant is
(a) 500 V (b) 4000 V
(c) 3000 V (d) 7000 V
5. AC Voltage applied to an Inductor:
Let a source of alternating e.m.f ๐ธ = ๐ธ0sin (๐ค๐ก) be connected to a capacitor of capacitance C. If I is he
instantaneous value of current in the circuit at instant t, then ๐ผ = ๐ค๐ ๐ธ0 sin (๐ค๐ก โ๐
2). The inductive
reactance limits the amplitude of current in a purely capacitive circuit and it is given by ๐๐ฟ = ๐ค๐ฟ.
(i) A 100 Hz a.c. is flowing in a 14 mH coil. The reactance of the coil is
(a) 15 ฮฉ (b)7.5 ฮฉ
(c) 8.8 ฮฉ (d) 10 ฮฉ
(ii) In a pure inductive circuit, resistance to the flow of current is offered by
(a) Resistor (b) inductor
(c) Capacitor (d) resistor and inductor
(iii) In a inductive circuit, by what value of phase angle does alternating current legs behind e.m.f.?
(a) 450 (b) 900
(c) 1200 (d) 750
(iv) How much inductance should be connected to 200 V, 50 Hz a.c. supply so that a maximum current of
0.9 A flows through it?
(a) 5 H (b) 1 H
(c) 10 H (d) 4.5 H
(v) The maximum value of current when inductance of 2 H is connected to 150 volt, 50 Hz supply is
(a) 0.337 A (b) 0.721 A
(c) 1.521 A (d) 2.522 A
ANSWERS(Case Study Questions):
ANS.(i) ANS.(ii) ANS.(iii) ANS.(iv) ANS.(v)
Q.1 c d c a c
Q.2 c a d a d
Q.3 c a b b a
Q.4 d c d b d
Q.5 c b b b a
SAMPLE PAPER
&
ANSWER KEY
CLASS XII
PHYSICS(042)
2021-22
Sample Question Paper 2021-22 Term 1
Subject: Physics (042)
Time: 90 Minutes Max. Marks 35 General Instructions: 1. The Question Paper contains three sections. 2. Section A has 25 questions. Attempt any 20 questions. 3. Section B has 24 questions. Attempt any20 questions. 4. Section C has 6 questions. Attempt any 5 questions. 5. All questions carry equal marks. 6. There is no negative marking.
SECTION A
This section consists of 25 multiple choice questions with overall choice to
attempt any 20 questions. In case more than desirable numberof questions are
attempted, ONLY first 20 will be considered for evaluation.
Q1.Which of the following is NOT the property of equipotential surface?
(i) They do not cross each other.
(ii) The rate of change of potential with distance on them is zero.
(iii) For a uniform electric field they are concentric spheres.
(iv) They can be imaginary spheres.
Q2. Two point charges +8q and -2q are located at x=0 and x=L respectively. The point on x axis at which net electric field is zero due to these charges is-
(i) 8L
(ii) 4L
(iii) 2 L
(iv) L
Q3. An electric dipole of moment p is placed parallel to the uniform electric field. The amount of work done in rotating the dipole by 900 is-
(i) 2pE
(ii) pE
(iii) pE/2
(iv) Zero
Q4. Three capacitors 2ยตF, 3ยตF and 6ยตF are joined in series with each other. The equivalent capacitance is-
(i) 1/2ยตF
(ii) 1ยตF
(iii) 2ยตF
(iv) 11ยตF
Q5. Two point charges placed in a medium of dielectric constant 5 are at a distance r between them, experience an electrostatic force โFโ. The electrostatic force between them in vacuum at the same distance r will be-
(i) 5F
(ii) F
(iii) F/2
(iv) F/5
Q6. Which statement is true for Gauss law-
(i) All the charges whether inside or outside the gaussian surface contribute to the electric flux.
(ii) Electric flux depends upon the geometry of the gaussian surface.
(iii) Gauss theorem can be applied to non-uniform electric field.
(iv) The electric field over the gaussian surface remains continuous and uniform at every point.
Q7.A capacitor plates are charged by a battery with โVโ volts. After charging battery is disconnected and a dielectric slab with dielectric constant โKโ is inserted between its plates, the potential across the plates of a capacitor will become
(i) Zero
(ii) V/2
(iii) V/K
(iv) KV
Q8.The best instrument for accurate measurement of EMF of a cell is-
(i) Potentiometer
(ii) metre bridge
(iii) Voltmeter
(iv) ammeter and voltmeter
Q9.An electric current is passed through a circuit containing two wires of same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 3:2 and 2:3, then the ratio of the current passing through the wire will be
(i) 2:3
(ii) 3:2
(iii) 8:27
(iv) 27:8
Q10.By increasing the temperature, the specific resistance of a conductor and a semiconductor-
(i) increases for both.
(ii) decreases for both.
(iii) increases for a conductor and decreases for a semiconductor.
(iv) decreases for a conductor and increases for a semiconductor.
Q11.We use alloys for making standard resistors because they have
(i) low temperature coefficient of resistivity and high specific resistance
(ii) high temperature coefficient of resistivity and low specific resistance
(iii) low temperature coefficient of resistivity and low specific resistance
(iv) high temperature coefficient of resistivity and high specific resistance
Q12. A constant voltage is applied between the two ends of a uniform metallic wire, heat โHโ is developed in it. If another wire of the same material, double the radius and twice the length as compared to original wire is used then the heat developed in it will be-
(i) H/2
(ii) H
(iii) 2H
(iv) 4H
Q13.If the potential difference V applied across a conductor is increased to 2V with its temperature kept constant, free electrons in a conductor
(i) remain the same(ii) become half of its previous value(iii) be double of its initial value(iv) become zero.
Q14.The equivalent resistance
(i) 3 ohms
(ii) 5.5 ohms
(iii) 7.5 ohms
(iv) 9.5 ohms
Q15. The SI unit of magnetic field intensity is
(i) AmN-1 (ii) NA-1m-1
(iii) NA-2m-2
(iv) NA-1m-2
Q16.The coil of a moving coil galvanometer is wound over a metal frame in order to
(i) reduce hysteresis(ii) increase sensitivity
(iii) increase moment of inertia (iv) provide electromagnetic damping
Q17.Two wires of the same length are shaped into a square of side 'a' and a circle with radius 'r'. If they carry same current, the ratio of their magnetic moment is
(i) 2 : ฯ (ii) ฯ : 2 (iii) ฯ : 4 (iv) 4 : ฯ
potential difference V applied across a conductor is increased to 2V with its temperature kept constant, the drift velocity of the
in a conductor will -
emain the same. become half of its previous value. e double of its initial value.
quivalent resistance between A and B is-
. The SI unit of magnetic field intensity is
The coil of a moving coil galvanometer is wound over a metal
reduce hysteresis increase sensitivity increase moment of inertia provide electromagnetic damping
.Two wires of the same length are shaped into a square of side 'a' and a circle with radius 'r'. If they carry same current, the ratio of their
potential difference V applied across a conductor is increased the drift velocity of the
.Two wires of the same length are shaped into a square of side 'a' and a circle with radius 'r'. If they carry same current, the ratio of their
Q18. The horizontal component of earthโs magnetic field at a place is โ3 times the vertical component. The angle of dip at that place is (i) ฯ/6 (ii) ฯ/3
(iii) ฯ/4 (iv) 0
Q19. The small angle between magnetic axis and geographic axis at a place is-
(i) Magnetic meridian (ii) Geographic meridian (iii) Magnetic inclination (iv) Magnetic Declination
Q20.Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon the
(i) rate at which current change in the two coils (ii) relative position and orientation of the coils (iii) rate at which voltage induced across two coils (iv) currents in the two coils
Q21. A conducting square loop of side 'L' and resistance 'R' moves in its plane with the uniform velocity 'v' perpendicular to one of its sides. A magnetic induction 'B' constant in time and space pointing perpendicular and into the plane of the loop exists everywhere as shown in the figure. The current induced in the loop is
(i) BLv/R Clockwise
(ii) BLv/R Anticlockwise
(iii) 2BLv/R Anticlockwise
(iv)Zero
Q22. The magnetic flux linked with the coil (in Weber) is given by
theequation โ
ี = 5t2 + 3t + 16
The induced EMF in the coil at time, t=4 will be-
(i) -27 V
(ii) -43 V
(iii) -108 V
(iv) 210 V
Q23. Which of the following graphs represent the variation of current(I) with frequency (f) in an AC circuit containing a pure capacitor?
(i) (ii) (iii) (iv)
Q24. A 20 volt AC is applied to a circuit consisting of a resistance and a coil with negligible resistance. If the voltage across the resistance is 12 volt, the voltage across the coil is-
(i) 16 V
(ii) 10 V
(iii) 8 V
(iv) 6 V
Q25. The instantaneous values of emf and the current in a series ac circuit are-
E = Eo Sin ฯt and I= Io sin( ฯt+ฯ/3) respectively, then it is
(i) Necessarily a RL circuit
(ii) Necessarily a RC circuit
(iii)Necessarily a LCR circuit
(iv) Can be RC or LCR circuit
SECTION B
This section consists of 24 multiple choice questions with overall choice to
attempt any 20 questions. In case more than desirable number of questions
are attempted, ONLY first 20 will be considered for evaluation.
Q26. A cylinder of radius r and length l is placed in an uniform electric field parallel to the axis of the cylinder. The total flux for the surface of the cylinder is given by-
(i) zero
(ii) ฯ r2
(iii) E ฯ r2
(iv) )2 Eฯ r2
Q27. Two parallel large thin metal sheets have equal surface densities
26.4x10-12 C/m2of opposite signs. The electric field between these sheets is-
(i) 1.5N/C
(ii) 1.5 x 10-16 N/C
(iii) 3 x 10-10N/C
(iv) 3N/C
Q28. Consider an uncharged conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,
(i) negative and uniformly distributed over the surface of sphere
(ii) positive and uniformly distributed over the surface of sphere
(iii) negative and appears at a point the surface of sphere closest to point charge.
(iv) Zero
Q29. Three Charges 2q, -q and -q lie at vertices of a triangle. The value of E and V at centroid of triangle will be-
(i) E#0 and V#0
(ii) E=0 and V=0
(iii) E#0 and V=0
(iv) E=0 and V#0
Q30. Two parallel plate capacitors X and Y, have the same area of plates and same separation between plates. X has air and Y with dielectric of constant 2 , between its plates. They are connected in series to a battery of 12 V. The ratio of electrostatic energy stored in X and Y is-
(i) 4:1
(ii) 1:4
(iii) 2:1
(iv) 1:2
Q31.Which among the following, is not a cause for power loss in a transformer-
(i) Eddy currents are produced in the soft iron core of a transformer. (ii) Electric Flux sharing is not properly done in primary and secondary
coils.
(iii) Humming sound produed in the tranformers due to magnetostriction. (iv) Primary coil is made up of a very thick copper wire.
Q32.An alternating voltage source of variable angular frequency โwโ and fixed amplitude โVโ is connected in series with a capacitance C and electric bulb of resistance R(inductance zero). When โwโ is increased-
(i) The bulb glows dimmer. (ii) The bulb glows brighter. (iii) Net impedance of the circuit remains unchanged. (iv) Total impedance of the circuit increases.
Q33. A solid spherical conductor has charge +Q and radius R. It is surrounded by a solid spherical shell with charge -Q, innerradius 2R, and outer radius 3R. Which of the following statements is true?
(i)The electric potential has a maximum magnitude at C and the electric field has a maximum magnitude at A
(ii) The electric potential has a maximum magnitude at D and the electric field has a maximum magnitude at B.
(iii) The electric potential at A is zero and the electric field has a maximum magnitude at D.
(iv). Both the electric potential and electric field achieve a maximum magnitude at B.
Q34. A battery is connected to the conductor of non-uniform cross section area. The quantities or quantity which remains constant is-
(i) electric field only
(ii) drift speed and electric field
(iii)electric field and current
(iv) current only
Q35. Three resistors having values R battery. Suppose R1 carries a current of 2.0 A, R ohms, and R3 dissipates 6.0 watts of power. Then the voltage across R is-
(i) 1V
(ii) 2V
(iii) 3V
(iv) 4V
Q36.A straight line plot showing the terminal potential difference (V) of a cell as a function of current (I) drawn from it, is internal resistance of the cell would be then
(i) 2.8 ohms
(ii) 1.4 ohms
(iii) 1.2 ohms
(iv) zero
Q37. A 10 m long wire of uniform cross a potentiometer. The wire is connected in series with a battery of 5 V along with an external resistance of 480 balanced at 6.0 m length of the wire
(i) 1.2 V
(ii) 1.02 V
(iii) 0.2 V
. Three resistors having values R1, R2, and R3 are connected in series to a carries a current of 2.0 A, R2 has a resistance of 3.0
dissipates 6.0 watts of power. Then the voltage across R
Q36.A straight line plot showing the terminal potential difference (V) of a cell as a function of current (I) drawn from it, is shown in the figure. The internal resistance of the cell would be then-
A 10 m long wire of uniform cross-section and 20 ฮฉ resistance is used in a potentiometer. The wire is connected in series with a battery of 5 V along with an external resistance of 480 ฮฉ. If an unknown emf E is balanced at 6.0 m length of the wire, then the value of unknown emf is
are connected in series to a has a resistance of 3.0
dissipates 6.0 watts of power. Then the voltage across R3
Q36.A straight line plot showing the terminal potential difference (V) of a cell shown in the figure. The
resistance is used in a potentiometer. The wire is connected in series with a battery of 5 V
. If an unknown emf E is , then the value of unknown emf is-
(iv) 0.12 V
Q38.The current sensitivity of a galvanometer increases by 20%. If its resistance also increases by 25%, the voltage sensitivity will
(i ) decrease by 1%
(ii) increased by 5%
(iii) increased by 10%
(iv ) decrease by 4%
Q39. Three infinitely long parallel straight current carrying wires A, B and C are kept at equal distance from each other as shown in the figure . The wire C experiences net force F .The net force on wire C, when the current in wire A is reversed will be
(i) Zero
(ii) F/2
(iii) F
(iv) 2F
Q40. In a hydrogen atom the electron moves in an orbit of radius 0.5 Ao
making 10 revolutions per second, the magnetic moment associated with the orbital motion of the electron will be
(i) 2.512 x 10-38 Am2
(ii) 1.256 x 10-38 Am2
(iii) 0.628 X10-38 Am2
(iv) zero
Q41. An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 800, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10-3s. Ignoring the variation in magnetic field near the ends of the solenoid, the average back emf induced across the ends of the open switch in the circuit would be
(i) zero
(ii)3.125 volts
(iii) 6.54 volts
(iv) 16.74 volts
Q42. A sinusoidal voltage of peak value 283 V and frequency 50 Hz is applied to a series LCR circuit in which R = 3 ฮฉ, L = 25.48 mH, and C = 796 ยตF, then the power dissipated at the resonant condition will be-
(i)39.70 kW
(ii) 26.70 kW
(iii)13.35 kW
(iv)Zero
Q43. A circular loop of radius 0.3cm lies parallel to much bigger circular of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with the bigger loop is
(i) 3.3 X 10-11weber
(ii) 6 X 10-11weber
(iii) 6.6 X 10-9weber
(iv) 9.1 X 10-11weber
Q44.If both the number of turns and core length of an inductor is doubled keeping other factorsconstant, then its self-inductance will be-
(i) Unaffected (ii) doubled
(iii) halved
(iv) quadrupled
45. Given below are two statements labelled as Assertion (A) and Reason (R)
Assertion (A): To increase the range of an ammeter, we must connect
a suitable high resistance in series to it.
Reason (R): The ammeter with increased range should have high resistance.
Select the most appropriate answer from the options given below:
(i) Both A and R are true and R is the correct explanation of A
(ii) Both A and R are true but R is not the correct explanation of A.
(iii)A is true but R is false.
(iv) A is false and R is also false.
46. Given below are two statements labelled as Assertion (A) and Reason (R)
Assertion (A): An electron has a high potential energy when it is at a location associated with a more negative value of potential, and a low potential energy when at a location associated with a more positive potential.
Reason (R):Electrons move from a region of higher potential to region of lower potential.
Select the most appropriate answer from the options given below:
(i) Both A and R are true and R is the correct explanation of A
(ii) Both A and R are true but R is not the correct explanation of A.
(iii)A is true but R is false.
(iv) A is false and R is also false.
47. Given below are two statements labelled as Assertion (A) and Reason (R)
Assertion(A): A magnetic needle free to rotate in a vertical plane, orients itself (with its axis) vertical at the poles of the earth.
Reason (R): At the poles of the earth the horizontal component of earthโs magnetic field will be zero.
Select the most appropriate answer from the options given below:
(i) Both A and R are true and R is the correct explanation of A
(ii) Both A and R are true but R is not the correct explanation of A.
(iii)A is true but R is false.
(iv) A is false and R is also false.
48. Given below are two statements labelled as Assertion (A) and Reason (R)
Assertion(A): A proton and an electron, with same momenta, enter in a magnetic field in a direction at right angles to the lines of the force. The radius of the paths followed by them will be same.
Reason(R): Electron has less mass than the proton.
Select the most appropriate answer from the options given below:
(i) Both A and R are true and R is the correct explanation of A
(ii) Both A and R are true but R is not the correct explanation of A.
(iii)A is true but R is false.
(iv) A is false and R is also false.
49. Given below are two statements labelled as Assertion (A) and Reason (R)
Assertion (A):On Increasing the current sensitivity of a galvanometer by increasing the number of turns, may not necessarily increase its voltage sensitivity.
Reason(R ): The resistance of the coil of the galvanometer increases on increasing the number of turns.
Select the most appropriate answer from the options given below:
(i) Both A and R are true and R is the correct explanation of A
(ii) Both A and R are true but R is not the correct explanation of A.
(iii)A is true but R is false.
(iv) A is false and R is also false.
SECTION C
This section consists of 6 multiple choice questions with an overall choice to attempt any 5. In case more than desirable number of questions are attempted, ONLY first 5 will be considered for evaluation.
Q50. A small object with charge q and weight mg is attached to one end of a string of length โLโ attached to a stationary support. The system is placed in a uniform horizontal electric field โEโ, as shown in the accompanying figure. In the presence of the field, the string makes a constant angle ฮธ with the vertical. The sign and magnitude of q-
(i) positive with magnitude mg/E
(ii) positive with magnitude (mg/E)tanฮธ
(iii) negative with magnitude mg/E tanฮธ
(iv) positive with magnitude E tanฮธ/mg
Q51.A free electron and a free proton are placed between two oppositely charged parallel plates. Both are closer to the positive plate than the negative plate.
Which of the following statements is true?
I. The force on the proton is greater than the force on the electron.
II. The potential energy of the proton is greater than that of the electron.
III. The potential energy of the proton and the electron is the same.
(i) I only
(ii) II only
(iii) III and I only
(iv)II and I only
Case study : Read the following paragraph and answers the questions:
The large-scale transmission and distribution of electrical energy over long distances is done with the use of transformers. The voltage output of the generator is stepped-up. It is then transmitted over long distances to an area sub-station near the consumers. There the voltage is stepped down. It is further stepped down at distributing sub-stations and utility poles before a power supply of 240 V reaches our homes.
Q52. Which of the following statement is true?
(i) Energy is created when a transformer steps up the voltage
(ii) A transformer is designed to convert an AC voltage to DC voltage
(iii) Stepโup transformer increases the power for transmission
(iv) Stepโdown transformer decreases the AC voltage
Q53. If the secondary coil has a greater number of turns than the primary,
(i) the voltage is stepped-up (Vs >Vp ) and arrangement is called a step-up transformer
(ii) the voltage is stepped-down (Vs <Vp ) and arrangement is called a step- down transformer
(iii) the current is stepped-up (Is >Ip ) and arrangement is called a step-up transformer
(iv) the current is stepped-down (Is <Ip ) and arrangement is called a step- down transformer
Q54. We need to step-up the voltage for power transmission, so that
(i) the current is reduced and consequently, the I2R loss is cut down
(ii) the voltage is increased , the power losses are also increased
(iii) the power is increased before transmission is done
(iv) the voltage is decreased so V2/R losses are reduced
Q55. A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The number of turns in the secondary in order to get output power at 230 V are
(i) 4
(ii) 40
(iii) 400
(iv) 4000
Physics
Marking Scheme
For SQP โ 45
XII โ I Term
Q.1 Which of the_____________________
Ans. 1 (iii)
As all other statements are correct. In uniform electric field equipotential surfaces are never
concentric spheres but are planes to Electric field lines.
Q.2 Two Point charges_____________________
Ans. 2 (iii)
Let P is the observation point at a distance r from -2q
and at (L+r) from +8q.
Given Now, Net EFI at P = 0
1E = EFI (Electric Field Intensity) at P due to +8q
2E = EFI (Electric Field Intensity) at P due to -2q
1 2E = E
2 2
k(8q) k(2q)
(L r) r
2 2
4 1
(L r) (r)
4r2 = (L+r)2
2r = L+r
r = L
P is at x = L + L = 2L from origin
Correct Option is (iii) 2L
Q3. An electric______________________
Ans. 2 (ii)
W = pE (cos1 โ cos2)
1 = 0
2 = 90
W = pE (cos 0 - cos 90)
= pE (1 โ 0) = pE
Q4. Three Capacitors______________
Ans.4. (ii)
series 1 2 3
series
1
F
1 1 1
C C C C
1 1 1 1
C 2 3 6
3+2+1 6
6 6
Cseries 1
Q5. Two Point Charges___________________
Ans.5. (i)
Q2
r K = 5 1 2
2
1 Q QF
4 ok r
Q2 Force in the charges in the air is
1 2
2
1 Q QF
4 o r
= K F
= 5 F
Q6. Which statement is true________________
Ans.6. (iv)
All other statements except (iv) are in correct
The electric field over the Gaussian surface remains continuous and uniform at every point.
Q7. A capacitor plates
Ans.7. (iii)
C
+ โ
+ โ
+ โ
Battery is disconnected`สน
Ck
+ โ
+ โ
+โ
Q = Charge remains context
Cสน = K C
Qสน = Cสน Vสน
Q = Cสน Vสน
Q = K C Vสน
Vสน= ๐
๐พ ๐ถ=
๐
๐พ
Q.8. The best instrument for_________________
Ans.8. (i)
Potentiometer
Q9. An electric current___________________
Ans.9. (iii) 8:27
R1
+ -
R2
l : = 3 : 2
r r 2 3
I I ?
1 2 l
: = :
: =
1 2
1 2
1
2
11
2
22
2
lR
r
lR
r
2 21 1 2 1 2
2 22 2 1 2 1
2 3
3
1 1 2
2 2 1
R l r l r =
R l r l r
3 3 (3) 27 = =
2 2 (2) 8
I V / R R = = 8 / 27
I V / R R
Q.10. By increasing the temperature___________________
Ans. 10. (iii) Specific resistance of a conductor increases and for a semiconductor decreases with
increase in temperature because for a conductor, a temperature.
coefficient of resistivity = + ve
and for a semiconductor, = -ve
Q.11. We use alloys___________________
Ans. 11 (i) Alloys have low temperature coefficient of resistivity and high specific resistance. If
= low , the value of โRโ with temperature will not change much and specific resistance is high
then required length of the wire will be less.
Q.12. A constant Voltage___________________
Ans. 12. (iii)
2
2 2
2 2
1
2
2
2
2
l 2lR R
A (2r)
l 2lR = R
r 4r
V VH t & H t
R R
V = constant
H V R t
H R V t
R l 2 r =
R r l
H 2 =
H 1
H 2H
Correct
option is (iii)
Q.13. If the potential diff____________________
Ans.13. We know
deE
Vml
V =e
ml
If temperature is kept constant, relaxation time - will remain constant, and e, m are also constants.
d
d
V V
V 2V
Correct option is (ii)
Q.14. The equivalent resistance _________________
Ans. 14. (iii)
Redrawing the circuit, we get
B
3 8
30
6
1
1
2 1
2
2
2
3 & 6 are in parallel.
3 6 18 R 2
3 6 9
Now R and 8 in series
R = R + 8 = 2 + 8 = 10
Now R and 30 in parallel
R 30 10 30 Rep =
R 30 10 30
300 30 15 =
40 4 2
= 7.5 (iii) correct option
Q.15. The SI unit of magnetic field intensity is ______________
Ans.15. We know
1 1
FB
Il sin
NSI Unit of B = NA m
Am
Correct option is (ii)
Q16. The coil of _____________________
Ans. (iv) Correct Option
The coil of a moving coil galvanometer is wound over metallic frame to provide electromagnetic
damping so it becomes dead beat galvanometer.
Q.17. Two wires of__________________
Ans.17. Correct option (iii)
lA
lB
aa
Square r Circle
Area of a Square
1
2
2
2
a
Also here l = 4a
l a =
4
l Area =
16
l A =
16
Area of a Circle
2
2
2
2
r
Also here, 2 r l
l r =
2
l Now Area =
2
l A =
4
Now Magnetic moment = I A
M1 = IA, & M2 = I A2
Since I (current) is same in both
21 1
22 2
1 2
M A l 4 =
M A 16 l 4
M M = : 4
Correct option is (iii)
Q.18. The horizontal comp________________
Ans.18. Correct option (i)
Target law Bv = BH tan
V
H
H v
0
Btan =
B
Given B = 3 B
Bv 1tan =
3 Bv 3
= 30 or radians.6
Q.19. The small___________________
Ans. 19. Correct option is Magnetic declination or Angle of declination. It is the small angle
between geographic axis & magnetic axis.
Q.20. Two coils___________________
Ans.20. Correct option is (ii)
Mutual inductance of a pair of two coils depends on the relative position and orientation of two
coils, other statements are incorrect.
Q.21. A conducting__________________
Ans. 21. Correct option is (iv)
Current induced is I = lel
R
d
Now lel = dt
But there is no change of flux with time, as B, A & all remain constant with time.
No current is induced
Q22. The magnetic flux___________
Ans.22. 2
2
t=4
5t 3t 16
de
dt
d 5t 3t 16
dt
10t + 3
e = 10(4)+3 = 43V
e = -43Volts
Correct option is (ii)
Q23 Which of the following_______________
Ans.23. Correct option is (iii)
C
VI in Pure Capacitor
X
V = V 2 fc
1
2 fc
I f
other parameters kept cosntant
Q24. A 20 Volt AC________________
Ans.24. Correct option is (i)
VR VL
R
R
L
L
eff
eff
2 2R L
2 2 2 2eff eff
2 2L
2 2 2L
V = Effective Voltage across R
V I R
V = Effective Voltage across L
V I L
Net V = V V
= I R I L
20 = (12) V
(20) (12) V
2L
L
400 = 144 + V
V = 400 144 = 256 16 Volts
Q25. The instantaneous_________________
Ans. 25.
0
0
E = E sin t
I = I sin t + 3
Correct option is (iv)
as I can lead the Voltage in RC and LCR circuit, so it can be RC or LCR circuit.
(iv) is correct option.
fStraight line paragraph
Section - B
Q26.
r
l
Q27. Two Parallel______________________
Ans. 27. (iv) Correct option.
++
E
12
2
0 0
0 0
12
12
CSurface Charge density, = 26.4 10
m
E = + 2 2
2 = =
2
26.4 10 N =
8.85 10 C
N = 3
C
Correct option is (iv)
Q28. Consider__________________
Ans.28.
-Q
+Q
+
Equal and Opposite charges appear on the nearby conductor due to
induction, but still net charge on the conductor is zero. Correct option (iv)
Correct option is (i)
Since โve electric flux
= + ve flux electric flux enclosed with a cylinder
here
Total Electric
Flux = 0.
Q29. Three Charges_________________
Ans.29.
r
-q E1-q
E2rE2 Gr
Q30. Two parallel______________
Ans.30.
k=2
12V
A = Samed = Same
Q = Same in Series
0 0x y
2 2
x y
x y
x y x
y x x
A 2 AC = C =
d d
Q QU = U =
2C 2C
U C 2C 2 = =
U C C 1
Correct Option is (iii)
Q31. Which among_________________
Ans.31. Correct statement is option (iv) as Primary coil made of Thick Coper wire has very less
R. Therefore negligible power loss. Rest all options are reasons for power losses in a transformer.
Q32. An alternating Voltage_______________
Ans.32.
B C
V
Net E F I at G O
Net Potential at G,
K2Q KQV =
r r
KQ -
r
= 0
Correct option is (iii)
c c1 1
X i.e. X2 fc c
I Brightness of the bulb will .
Correct option is (ii)
Q.33. A solid Sphere______________
Ans.33. Correct option is (4)
As all other statements seem incorrect in context with the given figure.
Q. 34. A battery is connected โฆ..
Ans. Correct option is (iv).
Rest all quantities change with area of cross-section of a conductor.
Q. 35. Three resistorsโฆโฆ
Ans. + โ
R1 R2 R3
Given
I = 2 A, R2 = 3 ฮฉ, P3 = 6 W
Power across R3 = V3I
6 W = I2 R3
6
4 = R3 =
3
2 = 1.5 ฮฉ
V3 = I R3 = 2 (1.5) = 3 V
Correct option is (iii).
Q. 36. A straight lineโฆโฆ
Ans. I = O, V = E, E = 5.6 V
r = 5.6
2.82.0
E
I
Correct option is (i).
Q. 37. A 10 m long potentiometer โฆ..
Ans. Let PQ is a potentiometer wore of length 10m,
I = 5 5
480 20 500
E
R R
= 1
0.01 A100
VPQ = I RPQ = 0.01 ร 20
= 0.2 V
If 10 m potentiometer wire balances 0.2 V
Then 1 m potentiometer wire balances 0.2
10 V
Then 6 m potentiometer wire balances 0.2
610
V
= 1.2
0.12 V10
Correct option is (iv).
Q. 38. The current sensitivityโฆโฆ
Ans. Given, gI = 20
100g gI I
= 120
1.2100
g gI I
R = 25 125
100 100 R R R
= 1.25 R
gV = ?
gV = 1.2
1.25
g gI I
R R
= 120 25
125 25g gV V
% change = 100
g g
g
V V
V
=
24
25100
g g
g
V V
V
= (24 25)
10025
= 1
10025
= 4%
Decrease by 4%. Correct option is (iv).
Q. 39. Three infinitely long parallel โฆ..
Ans.
F1
r r
F2
2I I
F2
I
A B C
Let F1 is force per unit, length between A & C
1. . i e F = 0 2
4 2
I I
r
And F2 is force per unit, length between B & C
2F = 0
4
I I
r
Now net force on โCโ is per unit length
1 2F F = 2
(1 1)4
I
r
= 2
02
4
IF
r (given)
Now Fig.
B C
I
2I
F1
1
r r
F2
1F2
1
I
F1
1
b
1F = Repulsive force between A & C
= 2
0 2
4 2
I
r
2 2 = F F = A reactive force between B & C
Net force on โCโ 1 2 F F = 0
1F = 2
F = 22
4 2
I
r
Net Force on โCโ is zero.
Correct option is (i).
Q. 40. In a H-atom โฆโฆ.
Ans. R = 0.5 Aยฐ
= 10 rps = 10 ร 2 rad/s
= 10 Hz
M = I A = e r2
= 1.6 ร 10โ19 ร 10 ร 3.14 ร 0.5 ร 0.5 ร 10โ10 ร 10โ10
= 1.256 ร 10โ38 Am2
Ans. (ii).
Q. 41. An air-cored solenoid โฆ..
Ans. Magnetic field inside a solenoid
B = 0N
Il
'
Flux linked with โNโ turns
Initial flux 1 = N B A = 0N
N I Al
= 2
0N
I Al
= 7 44 10 800 800 2.5 2.5 10
0.30
= 16.74 ร 10โ 3 Wb
Final flux 2 = 0
Average back emf | e | = d
dt =
3
3
16.74 10 0
10
= 16.74 V
Correct option is (ii).
Q. 42. Vo = 283 V, f = 50 Hz
R = 3 ฮฉ, L = 25.48 mH
C = 796 F
P |at resonance = ?
Power dissipated P = I2 R
I = 0 1 283
32 2
I
= 66.7 A
P = I2 R
= (66.7)2 3
= 13.35 kW
Correct option is (iii).
Q. 43. A circular loop โฆ..
Ans. Let flux linked with smaller loop is 1 and with bigger loop is 2.
Fig.
1 R1
I1
2
Given R2 = 0.2 m
R1 = 0.003 m
x = 15 cm = 0.15 m
Now 1 = B2 A1
= 2
20 2 212 2 3/ 2
2
2
4 ( )
R IR
R x
M = 2 2
01 2 12 2 3/ 2
2 2
2
4 ( )
R R
I R x
Now 2 = M I1
= 2 2
0 2 112 2 3/ 2
2
2.
4 ( )
R RI
R x
= 9.1 ร 10โ11 Weber
Correct answer is (iv).
Q. 44. If both the no. of turnsโฆ..
Ans. L = 2
0N
Al
L = 2
0
(2 )
2
NA
l
= 2
02 2 N
A Ll
Correct answer is (ii). Doubted.
Q.45. Given below___________________
To increase the range
Ans. 45. Correct option is (iv) as both statements are false. To increase the range of an ammeter, suitable
low R (or shunt) should be connected in parallel to it. The ammeter with increased range has low
resistance.
Q.46. An electron____________________
Ans.46. Correct option is (iii)
Statements correct but reason is wrong because electrons move from a region of low potential to high
potential.
Q. 47. A magnetic needle โฆโฆ..
Ans. The given statement is correct and reason is the correct explanation of the above statement. At
poles, magnetic needle orients itself vertically because horizontal components of earthโs field is zero
there. (correct option is (i))
Q. 48. A proton and an electron, โฆโฆ.
Ans. we know ๐๐ฃ2
๐= ๐ต๐๐ฃ๐ ๐๐ ๐ = ๐ต๐๐ฃ ๐๐๐ ๐
Centripetal force = magnetic Lorentz force
sin๐ = sin90๐ = 1 (โ between & = 90ยฐ)
๐๐ฃ2
๐= ๐ต๐๐ฃ
๐๐ฃ
๐= ๐ต๐
๐ = ๐๐ฃ
๐ต๐=
๐
๐ต๐=
๐๐๐๐๐๐ ๐๐๐๐๐๐ก๐ข๐
๐ต๐
Since ๐ = ๐
๐ต๐
Given p, B are same
Also q for proton & electron is same except its sign
Radius is same. So statement is correct but
reason is not the correct explanation of the given assertion.
correct option is (ii)
Q. 49. On increasingโฆโฆโฆโฆ..
Ans. 49. When we increase current sensitivity by increasing no. of turns, then resistance of coil also
increases. So increasing current sensitivity does not necessarily imply that voltage sensitivity will
increase because ๐๐ = ๐ผ๐
๐
โด if ๐ผ๐ โ & ๐ โ by different amounts, then ๐๐ may increase or decrease.
Correct option is (i).
Q.50. A small objectโฆโฆโฆ
Ans. 50. Ans is (ii)
F๐ = ๐๐ ๐ก๐๐๐
๐๐ธ = ๐๐ ๐ก๐๐๐
๐ = (๐๐
๐ธ) tan ๐
tan ๐ = ๐น๐
๐๐
Tq
E
qE
Correct ans. is (ii)
Q. 51. A free electronโฆโฆโฆโฆ
Ans. 51. Correct ans. (ii) i.e. II only
โต ๐น๐ = ๐น๐ โต ๐น = ๐๐ธ
๐ธ = ๐ ๐๐๐
โ๐โ = ๐ ๐๐๐
Now, ๐๐ = ๐ ๐(๐)
(๐. ๐)๐ > (๐. ๐)๐
Q. 52. Correct ans is (iv) i.e. step down transformer decreases the ac voltage.
Q.53. correct ans is (i)
i.e. ๐๐
๐๐=
๐ธ๐
๐ธ๐
i.e. if no. of turns in secondary coil are more than no. of turns in primary, then voltage is increased or
stepped up in secondary, so called step up transformer.
Q.54 Correct ans. is (i).
i.e. current is reduced if voltage is stepped โ up so corresponding ๐ผ2๐ losses are cut down.
Q. 55. Correct ans is (iii)
Given ๐ธ๐ = 2300๐
๐ธ๐ = 230๐
๐๐ = 4000
๐๐ = ?
๐ธ๐
๐ธ๐=
๐๐
๐๐
2300
230=
4000
๐ฅ
๐ฅ = 400 = ๐๐ = No of turns in secondary coil