topper’s package physics - xii unit emi & ac circuits · 2020. 8. 8. · (a) b v d 0 0 (b) 2...

Topper’s Package Physics - XII Permutation and CombinationsEMI & AC CIRCUIT

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1. FARADAY’S LAW & MAGNETIC FLUX & LENSLAW1. An electron moves along the line AB which lies

in the same plane as a circular loop ofconducting wire as shown in the diagram. Whatwill be the direction of current induced, if any,in the loop

(a) no current will be induced(b) the current will be clockwise(c) the current will be anticlockwise(d) the current will change direction as theelectron passed by

2. A square shaped coil of side 10 cm and numberof turns 500 is placed perpendicular to magneticflux lines, which is changing at the rate of 1.0tesla/sec. The e.m.f. induced in the coil is(a) 0.1 V (b) 0.5 V(c) 1.0 V (d) 5.0 V

3. Figure represents an area A = 0.5 m2. situateedin a uniform magnetic field B = 2.0, weber/m2

and making an angle of 60º with respect to themanetic field , the value of the magnetic fluxthrough the area A would be equal to

(a) 2.0 weber (b) 3 weber

(c)32

weber (d) 0.5 weber

4. An induced e.m.f. is produced when a magnetis plunged into a coil. The strength of theinduced e.m.f. is independent of(a) the strength of the magnet(b) number of turns in the coil(c) the resistivity of the wire of the coil(d) speed with which the magnet is moved

5. A cylindrical magnet is placed near a circularcoil. The magnet is rotated about its own axis

as shown in figure. The induced current in thecoil is

(a) zero(b) in clockwise direction(c) in anti-clockwise direction(d) directly proportional to the speed of rotation

6. The flux linked with a coil at any instant t isgiven by 10t 2 – 50 t + 250 . The induced emfat t = 2 sec, is(a) 190 V (b) – 190 V(c) – 10 V (d) 10 V

7. A metallic square loop ABCD is moving in itsown plane with velocity v in a uniform magneticfield perpendicular to its plane as shown in thefigure. Electric field is induced

(a) in AD, but not in BC(b) in BC, but not in AD(c) neither in AD nor in BC(d) in both AD and BC

8. Some magnetic flux is changed from a coil ofresistance of 10 ohm. As a result an inducedcurrent is developed in it, which varies withtime as shown in figure. The magnitude ofchange in flux, through the coil in webers, is

(a) 2 (b) 4(c) 6 (d) 8

EMI & AC CIRCUITS Unit 5


63

9. Dimensions of magnetic fluxelectric flux are electric flux

(a) [LT –1] (b) [TL–1](c) [L3T 2A–2] (d) [ M 0L0T0 ]

10. A coil having n turns and resistance R isconnected with a galvonometer of resistance4R . This combination is moved in time tsecond from a magnetic frield W1 weber to W2weber. The induced current in the circuit is

(a) 2 1W W

5Rnt

(b) 2 1n W W5Rnt

(c) 2 1W W

Rnt

(d) 2 1n W W

Rt

11. As shown in the figure, P and Q are two coaxialconducting loops separated by some distance.When the switch S is closed, a clockwise currentIp flows in P (as seen by E) and an induced currentIQ1 flows in Q. The switch remains closed for along time. When S is opened, a current IQ2 flowsin Q. Then the directions of IQ1 and IQ2 (as seenby E) are

(a) Respectively clockwise and anticlockwise(b) Both clockwise(c) Both anticlockwise(d) Respectively anticlockwise and clockwise

12. A square coil ABCD is lying in x-y plane with itscentre at origin. A long straight wire passingthrough origin carries a current i = 2t innegative z-direction. The induced current in thecoil is

(a) clockwise (b) anticlockwise(c) alternating (d) zero

13. The magnetic field in a region is given by

0xB B ka

. A square loop of side d is placed

with its edges along the x and y axis. The loop ismoved with a constant velocity 0

ˆv v i . The emf

induced in the loop is

(a) 0 0B v d (b)2

0 0B v d2a

(c)3

0 02

B v da (d)

20 0B v da

14. If a coil of 40 turns and area 4 cm2 is suddenlyremoved from a magnetic field, it is observedthat a charge of 2 × 10–4 C flows into the coil, ifresistance of the coil is 80 , the magnetic fluxdensity in Wb m–2 is(a) 0.5 (b) 1(c) 1.5 (d) 2

15. Two similar circular co-axial loops carry equalcurrents in the same direction. If the loops bebrought nearer, the currents in loops(a) decreases(b) increases(c) remains same(d) different in each loop

16. A magnetic flux through a stationary loop witha reistance R varies during the time interval as at( – t) . What is the amount of heatgenerated in the loop during that time?

(a)2 3a

4R

(b)2 3a

3R

(c)2 3a

6R

(d)2 3a

2R

17. A long solenoid S has n turns per metre, withdiameter a. At the center of this coil, we placea smaller coil of N turns and diameter b (b < a).If the current in the the solenoid increaseslinearly with time, then the emf will be inducedin the smaller coil. Which of the following is thecorrect graph showing verse t if currentvaries as a function of mt2 + C?


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(a) (b)

(c) (d)

18. A magnetic field B is confined to region r < aand points out of the paper (the z-axis), r = 0being the centre of the circular region.A chargedring (charge = q) of radius b(b > a) and mass mlies in the x-y plane with its centre at the origin.The ring is free to rotate and is at rest. Themagnetic field is brought to zero in time t .The angular velocity of the ring after the fieldvanishes, is

(a)2qBa

2mb (b) 2

qBa2mb

(b)2

2

2mbqBa (d)

2

2

qBa2mb

19. The variation of induced emf ( ) with time (t)in a coil if a short bar magnet is mvoed alongits axis with with a constant velocity is bestrepresented as

(a) (b)

(c) d)

2. MOTIONAL & ROTATIONAL EMF20. An aeroplane is moving north horizontally with

a speed of 200 m/s at a place where the verticalcomponent of the earth’s magnetic field is0.5 × 10–4 T . What is the induced e.m.f. set up

between the tips of the wings if they are 10 mapart?(a) 0.01 V (b) 0.1 V(c) 1V (d) 10 V

21. Figure shows a square loop of side 0.5 m andresistance 10 . The magnetic field has amagnitude B = 1.0T . The work done in pullingthe loop out of the field slowly and uniformly in2.0 s is

(a) 3.125 10–3 J (b) 6.25 10–4 J(c) 1.25 10–2 J (d) 5.0 10–4 J

22. Two identical conductors P and Q are placed ontwo frictionless rails R and S in a uniformmagnetic field directed into the plane. If P ismoved in the direction shown in figure with aconstant speed then rod Q

(a) will be attracted towards P(b) will be repelled away from P(c) will remain stationary(d) may be repelled or attracted towards P

23. A conducting rod PQ of length L 1.0 m is movingwith a uniform speed v = 2.0 m/s in a uniformmagnetic field B = 4.0 T . A capacitor of capacityC 10 µF is connected as shown in figure. Then

(a) qA = +80 µC and qB = –80 µC(b) qA = –80 µC and qB = +80 µC(c) qA = 0 = qB(d) charge stored in the capacitor increases

exponentially with time24. A square coil ACDE with its plane vertical is

released from rest in a horizontal uniformmagnetic field B

of length 2L . The accelerationof the coil is


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(a) less than g for all the time till the loopcrosses the magnetic field completely

(b) less than g when it enters the field andgreater than g when it comes out of thefield

(c) g all the time(d) less than g when it enters and comes out

of the field but equal to g when it is withinthe field

25. An equilateral triangular loop DC having someresistance is pulled with a constant velocity vout of a uniform magnetic field directed into thepaper. At time t = 0 , side DC of the loop is atedge of the magnetic field. The induced current(i) versus time (t) graph will be as

(a) (b)

(c) (d)

26. Two conducting rings P and Q of radius r and 3rmove in opposite directions with velocities 2vand v respectively on a conducting surface S.There is a uniform magnetic field of magnitudeB perpendicular to the plane of the rings. Thepotential difference between the highest pointsof the two rings is

(a) zero (b) 2 Brv(c) 6 Brv (d) 10 Brv

27. Two concentric and coplanar circular coils haveradii a and b (>> a) as shown in figure.Resistance of the inner coil is R. Current inthe outer coil is increased from 0 to i, then thetotal charge circulating the inner coil is

(a)2

0µ ia2Rb (b)

0µ iab2R

(c)2

0µ i b2a R

(d) 0µ ib

2 R

28. A long conducting wire AH is moved over aconducting triangular wire CDE with a constantvelocity v in a uniform magnetic field B

directedinto the paper. Resistance per unit length ofeach wire is . Then

(a) a constant clockwise induced current willflow in closed loop

(b) an increasing anticlockwise inducedcurrent will flow in the closed loop

(c) a decreasing anticlockwise inducedcurrent will flow in the closed loop

(d) a constant anticlockwise induced currentwill flow in the closed loop

29. A horizontal wire is free to slide on the verticalrails of a conducting frame as shown in figure.The wire has a mass m and length L. Resistanceof the circuit is R. If a uniform magnetic field Bis directed perpendicular to the frame, theterminal speed of the wire as it falls under theforce of gravity is


66

(a)mgRBl

(b)mglBR

(c)2 2B l

mgR (d) 2 2

mgRB l

30. A connecting rod PQ of mas slides withoutfriction over two long conducting rails separatedby a distance l. At the left end, the rails areinterconnected by a resistance R. Thearrangement is located in a uniform magneticfield perpendicular to the plane of the loop. Atthe moment t = 0, the rod is given a initialvelcoity V0. Find the distance covered by the roduntil it comes to a stand still. Assumeresistance of the rod and the rod is neglected.

(a) 02 2

mv BSR l

(b) 02

mv RSBl

(c) 02 2

mv RSB l

(d) None

31. A sliding rod AB of resistance R is shown in thefigure. Here magnetic field B is constant and isout ouf the paper. Parallel wires have noresistance and wires hav no resistance and therod is moving with constant velocity v. Thecurrent in the sliding rod AB when switch S isclosed at tiem t = 0 is

)

(a) t/CvBd eR

(b) t/RCvBd eR

(c) RtCvBd eR (d) t/RCvBd e

R

32. A rod of lenght l roates with a uniform angularvelocity about an axis passing through itsmiddle point but normal to its length in auniform magnetic field of induction B with itsdirection parallel to the axis of rotation. Theinduced emf betwen the two ends of the rod is

(a)2Bl2

(b) zero

(c)2Bl

8

(d) 22Bl

33. A wheel with 20 metallic spokes each of length0.8 m long is roated with a speed of 120revolution per minute in a plane normal to thehorizontal component of earth magnetic field Hat a place. If H = 0.4 × 10–4 T at the place, theninduced emf between the axle and the rim ofthe wheel is(a) 2.3 × 10–4 V (b) 3.1 × 10–4 V(c) 2.9 × 10–4 V (d) 1.61 × 10–4 V

34. A rod AB of length l moves with a uniform velocityv parallel to a long straight wire carrying acurrent i, the end A remaining at a distance rfrom the wire. Calculate the emf induced acrossthe rod.

(a) 0µ iv r le lnr

(b) 0µ vi r le ln3 r

(c) 0µ vi r le lnr

(d) 0µ vi r le ln2 r

35. A long straight wire carrying a current i and a -shaped condutor with sliding connector arelocated in the same plane as shown. Theconnecotor of length 1 and reistance R slides tothe right with a constant velocity V. Find thecurrent induced in the loop as a function ofseparation r between the connector and straightwire. Assume resistance of -shaped conductorand the self inductance of the loop are negligible.

(a)0µ ivlrR (b)

0µ ivl2 rR

(c)2

0µ v l i2 rR (d) None


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3. EDDY CURRENT36. A uniform but time-varying magnetic field B (t)

exists in a circular region of radius a and isdirected into the plane of the paper, as shown.The magnitude of the induced electric field atpoint P at a distance r from the centre of thecircular region.

(a) is zero

(b) decreases as 1r

(c) increases as r

(d) decreases as 2

1r

37. Which of the follwing does not use theapplication of eddy current?(a) Electric power meters(b) Induction furnace(c) LED - lights(d) Magnetic brakes in trains

38. Induction furnace make use of(a) self induction (b) mutual induction(c) eddy current (d) none of these

39. The north pole of a bar magnet is moved towardsa coil along the axis passing through the centreof the coil and perpendicular to the plane of thecoil. The direction of the induced current in thecoil when viewed in the direction of the motionof the magnet is(a) clockwise(b) anti-clockwise(c) no current in the coil(d) either clockwise or anti-clockwise

4. INDUCTANCE40. Three pure inductances are connected as

shown in figure. The equivalent inductance ofthe circuit is

(a) 2.75 H (b) 2.25 H(c) 2.00 H (d) 1.75 H

41. If the circuit shown in the following figure E =10 volts, R1 = 2 ohms, R2 = 3 ohms, R3 = 6 ohmsand L = 5 henry. The current i1 just afterpressing the switch S is

(a) 10/4 amp (b) 10/5 amp(c) 10/12 amp (d) 10/6 amp

42. A coil of wire of a certain radius has 600 turnsand a self-inductance of 108 mH. The selfinductance of a second similar coil of 500 turnswill be(a) 74 mH (b) 75 mH(c) 76 mH (d) 77 mH

43. The average e.m.f. induced in a coil in whichthe current changes from 2A to 4A in 0.05seconds is 8V. What is the self inductance ofthe coil?(a) 0.1 H (b) 0.2 H(c) 0.4 H (d) 0.8 H

44. What is energy stored in a 50 mH inductorcarrying a current of 4A?(a) 0.4 J (b) 0.2 J(c) 0.1 J (d) 0.05 J

45. Two pure inductors each of inductance L areconnected in parallel but well separated fromeach other. The equivalent inductance of thecombination is

(a)L4

(b)L2

(c) 2L (d) 4L

46. The equivalent inductance of the networkshown in figure is

(a) 1.296 H (b) 9.126 H(c) 6.219 H (d) 2.619 H


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47. The current through an inductor of 1 H is givenby i = 3t sint . The voltage across the inductor of1 H is(a) 3sin t + 3cos t (b) 3cos t + t sin t(c) 3sint + 3t cos t (d) 3t cos t + sint

48. Dimension of self inductance are

(a) [ MLT – 2 A–2 ] (b) [ ML2T–1 A–2 ]

(c) [ ML2T –2A –2 ] (d) [ ML2T –2 A–1]

49. A sinusoidal a.c. current flows in an inductoras shown in figure. The p.d. across the inductoris maximum at the instant indicated on thegraph by the point(a) S

(b) Q

(c) R

(d) T50. When the current through a solenoid increases

at a constant rate, the induced current(a) is a constant and is in the direction of the

inducing current(b) is a constant and is opposite to the

direction of the inducing current(c) increases with time and is in the direction

of the inducing current(d) increases with time and is opposite to the

direction of the inducing current

51. A small squar loop of wire on side l is placedinside a large square loop of wire of side L ( L >> l ). The loops are coplanar and their centrescoincide. The mutual inductance of the systemis proportional to

(a)lL

(b)2lL

(c)Ll

(d)2Ll

52. Two solenoids A and B have same area of cross-section. The ratio of length of two is 1 : 2 andthe ratio of number of turns is 2 : 1. Find theratio of self inductance of A to that of B

(a)18 (b) 8

(c) 1/2 (d)14

53. Two coils P and Q are placed in a circuit suchthat a current changes by 3 ampere in coil Pwhen the change of magnetic flux in coil Q is

1.2 weber. The value of mutual inductance ofthe coil is(a) 0.2 henry (b) 0.6 henry(c) 3.6 henry (d) 0.4 henry

54. A coil is wound on a transformer of rectangularcross-section. If all the linear dimensions of thetransformer are increased to a factor 2 andnumber of turns per unit length of the coilremain the same, the self inductance increaseby a factor of(a) 16 (b) 12(c) 8 (d) 4

55. A current of 2 A is increasing at a rate of 4 A /sec through a coil of inductance 2H . The energystored in the inductor per unit time in giveninstant is(a) 2 J /sec (b) 1 J /sec(c) 16 J /sec (d) 4 J /sec

56. A coil of wire having finite inductance andresistance has a conducting ring placed coaxillywithin it. The coil is connected to a battery attime t = 0, so that a time - dependent currentI1(t) starts flowing through the coil. If I2(t) is thecurrent induced in the ring and B(t) is themagnetic field at the axis of the coil due to I1(t),then as a function of time (t > 0), the productI2(t )B (t)(a) increases with time(b) decreases with time(c) Does not vary with time(d) Passes through a maximum

57. The circular coils can be arranged in any of thethree situations shown in the figure. Theirmutual inductance will be

(a) Maximum in situation (A)(b) Maximum situation (B)(c) Maximum in situation (C)(d) The same in all situations

58. The network section shown in figure is part ofa complete circuit. When a current of 5 A isflowing from ‘A’ to ‘B’ and decreasing at the rateof 103 Amp./sec, find the potential differencebetween points A and B.


69

(a) 15 V (b) 10 V(c) 5 V (d) 25 V

59. In a inductor of self-inductane L = 2 mH, currentchanges with time according to relation, I = t2

e–1. At what tiem emf is zero?(a) 4 s (b) 3 s(c) 2s (d) 1 s

60. A small circular loop of wire of radius a is locatedat the centre of a much larger circular wire loopof radius b. The two loops are in the same plane.The outer loop of radius b carries an alternatingcurrent 0I I cos( t) . The emf induced in thesmaller inner loop is nearly.

(a) 2

0 0µ I a· cos t2 b

(b)

20 0µ I b cos ta

(c) 2

0 0µ I a· sin t2 b

(d)

2

0 0aµ I sin tb

61. When current in a coil changes from 5A to 2Ain 0.1 s, an average voltage of 50 V is produced.The selfinductance of the coil is(a) 0.67 H (b) 1.67 H(c) 3 H (d) 6 H

5. LR CIRCUITS (GROWTH & DECAY)62. A coil of inductance 300 mH and resistance 2

is connected to a source of voltage 2 V. Thecurrent reaches half of its steady state value in(a) 0.15 sec (b) 0.3 sec(c) 0.05 sec (d) 0.1 sec

63. A coil of inductance 0.20 H is connected inseries with a switch and cell of e.m.f 1.6 V. Thetotal resistance of the circuit is 4.0 . Theinitial rate of growth of current, when switch isclosed, is

(a) 0.050 A/sec (b) 0.13 A/sec(c) 4.0 A/sec (d) 8.0 A/sec

64. A series LR circuit is connected to a voltage withV(t) = 0V sin t . After very large time, current

I(t) behaves as 0LtR

(a)

t = t0

l(t)

(t)

(b)

l(t)

t –tn

t

(c)

l(t)

t –tn

t

(d)

l(t)

t –tn

t

65. A conducting metal circular- wire loop of radiusr is placed perpendicular to a magnetic field

which varies with time as t

0B B e , where B0

and are constants, at time t = 0. If theresistance of the loop is R then the heatgenerated in the loop after a long time t is

(a)2 4 4

0r B2 R

(b)2 4 2

0r B2 R

(c)2 4 2

0r B R

(d)2 4 2

0r BR

66. In a given circuit, the initial current throughthe inductor at t = 0 is I0. After time t = L/R, theswitch is quickly shifted to position ‘2’. Plot agraph showing the variation of current with thetime.

(a) (b)


70

(c) (d)

6. MEAN & RMS VALUE67. The rate of heating of a 10A alternating current

is the same as the rate of heating of a directcurrent of(a) 10 2 A (b) 10 A

(c) 10/ 2 A (d) 5 A

68. The electric current in a circuit is given by i =3t . Here, t is in second and i in ampere. Therms current for the period t = 0 to t =1 s is(a) 3 A (b) 9 A(c) 3 A (d) 3 3 A

69. In a.c. circuit, the rms value ofn current, Irmsis related tot the peak current, I0 by the relation.

(a) rms 01I I

(b) rms 01I I2

(c) rms 0I 2I (d) rms 0I I

70. A fuse wire is having 5 ampere current rating.What is the peak value of current it can have(a) 0.7074 A (b) 7.07(c) 0.0707 A (d) 7.707 A.

71. The peak value of AC voltage on a 220 V mainsis(a) 240 2V (b) 230 2V

(c) 220 2V (d) 200 2V

7. AC CIRCUITS & POWER72. A bulb and a capacitor are in series with an a.c.

source. On increasing frequency how will glowof the bulb change?(a) the glow decreases(b) the glow increases(c) the glow remain the same(d) the bulb quenches

73. An alternating current of frequency f is flowingin a circuit containing only a choke coil L. If V0and I0 represent peak values of the voltage and

the current respectively, the average powergiven by the source to the choke is equal to

(a) 0 01 V I2 (b) 2

01 I 2 f L2

(c) 0 (d) 01 V 2 f L2

74. An applied voltage signal consists of asuperposition of a d.c. voltage and an a.c. voltageof high frequency. If the circuit consists of aninductor and a capacitor in series, then(a) dc signal will appear across C and ac signal

across L(b) dc signal and ac signal will appear only

across C(c) dc and ac signals will appear only across L(d) dc signal will appear across L and ac signal

across C75. An a.c. circuit contains 4 ohmic resistance

in series with an inductance coil of reactance5 . The impedance of the circuit is

(a) 41 (b) 43

(c) 31 (d) 39

76. In an a.c. circuit V and I are given by V = 100

sin (100 t) volts. I = 100 sin 100t mA3

.

The power dissipated in the circuit is(a) 104 watt (b) 1250 watt(c) 2500 watt (d) 5 watt

77. An inductive circuit contains a resistance of10 ohms and an inductance of 2 henry. If ana.c. voltage of 120 volt and frequency of 60 Hz isapplied to this circuit, the current in the circuitwould be nearly(a) 0.32 amp (b) 0.16 amp(c) 0.48 amp (d) 0.8 amp

78. Power is transmitted from a power house onhigh voltage a.c. as(a) the rate of transmission is faster in high

voltage(b) it is more economical due to less power

wasted(c) power cannot be generated at low voltage(d) a precaution against theft of transmission

lines


71

79. A resistor R, an inductor L, a capacitor C andammeter A1 , A2 , A3 and A4 are connected to anoscillator in the circuit shown in figure. Whenthe frequency of the oscillator is increased, thenat resonant frequency, the reading of ammeterA4 is same as that of

(a) A1 (b) A2(c) A3 (d) A1 , A2 and A3

80. The phase difference between the alternating

current and emf is 2 . Which of the following

cannot be the constitutent of the circuit ?(a) L, C (b) L alone(c) C alone (d) R, L

81. An ac source is 120 V – 60 Hz. The value ofvoltage after 1/720 second from the start, is(a) 60 Volt (b) 40 Volt(c) 60 2 Volt (d) 40 2 Volt

82. In the given LCR series circuit, the qualityfactor of the circuit is

(a) 1 (b) 4(c) 8 (d) 1/8

83. Two alternating voltage generators produce emfof the same amplitude E0 but with a phase

difference of 3

. The resultant emf is

(a) E 0 sin t3

(b) E 0 sin t

6

(c) 03 E t6

(d) 03 E sin t

2

84. An ac source producing emf

0V V [sin t cos2 t] is connected in serieswith a capacitor and a resistor. The currentfound in the circuit, is i = i1sin(t + 1) + i2cos(2t+ 2) then

(a) i1 < i2(b) i1 = i2(c) i1 > i2(d) i1 may be less than, equal to or greater than

i285. The ratio of time constants during current

growth and current decay of the circuit shownin the figure, is

(a) 1 : 1 (b) 3 : 2(c) 2 : 3 (d) 1 : 3

86. When a d.c. voltage of 200 V is applied to a coilof self inductance 2 3/ H , a current of 1Aflows through it, But by replacing d.c. source witha.c. source of 200V, the current in the coil isreduced to 0.5A. Then the frequency of a.c.supply is(a) 30 Hz (b) 60 Hz(c) 75 Hz (d) 50 Hz

87. 110V (rms) is applied across a series circuithaving resistance 11 and impendence 22 .The power consumed is

(a) 275 W (b) 366 W(c) 550 W (d) 1100 W

88. An LCR series circuit is under resonance.If Imis current amplitude, Vm is voltage amplitude,R is the resistance, Z is the impedance, XL isinductive reactance and Xc is the capacitivereactance, then

(a) mm

ZIV

(b) mL

VIX

(c)m

mC

VIX

(d) mm

VIR

89. Which of the following graphs represents thecorrect variation of inductive reactance XL, withfrequency v ?


72

(a) (b)

(c) (d)

90. The phase relationship between current andvoltage in a pure resistive circuit is bestrepresented by

(a) (b)

(c) (d)

91. A pure resistive circuit element X whenconnected to an ac supply of peak voltage 200 Vgives a peak current of 5A which is in phasewith the voltage, A second circuit element Y,when connected to the same ac supply also givesthe same value of peak current but the currentlags behind by 90º. If the series combination ofX and Y is connected to the same supply, whatwill be the rms value of current?

(a)10 A

2 (b)5 A2

(c)5 A2 (d) 5A

8. RESONANCE

92. In a series LCR circuit, the plot of mI Vs isshown in the figure. The bandwidth of this plotwill be

(a) zero (b) 0.1 rad s–1

(c) 0.2 rad s–1 (d) 0.4 rad s–1

93. A series LCR circuit has R = 5 , L = 40 mHand C = 1 µF, the bandwidth of the circuit is(a) 10 Hz (b) 20 Hz(c) 30 Hz (d) 40 Hz

94. An iductor 200 mH, capacitor 500 µF and resistor10 are connected in series with a 100 Vvariable frequency ac source. What is thefrequecy at which the power factor of the circuitis unity?(a) 10.22 Hz (b) 12.4 Hz(c) 19.2 Hz (d) 15.9 Hz

95. The Q factor of a series LCR circuit with L = 2H, C = 32 µF and R = 10 is(a) 15 (b) 20(c) 25 (d) 30

9. LC OSCILLATION96. A fully charged capacitor C with initial charge

Q0 is connected to a coil of self inductance L at t= 0. The time at which the energy is storedequally between the electric and the magneticfield is

(a) LC4

(b) 2 LC

(c) LC (d) LC

97. An ac generator consists of a coil of 200 turnseach of area 80 cm2 and rotating at an angularspeed of 200 rpm in a uniform magnetic field of4.8 × 10–2 T. The peak values of emf induced inthe coil is(a) 22.68 V (b) 15.36 V(c) 7.39 V (d) 18.67 V

98. A changed 30 µF capacitor is connected to a 27mH inductor. The angualr frequency of freeoscillations of the circuit is(a) 1.1 × 103 rad s–1 (b) 2.1 × 103 rad s–1

(c) 3.1 × 103 rad s–1 (d) 4.1 × 103 rad s–1

99. An LC circuit contains a 20 mH iductor and a25 µF capacitor with an initial change of 5 mC.The total energy stored in the circuit initially is


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(a) 5J (b) 0.5 J(c) 50 J (d) 500 J

10. INSTRUMENTS100. The loss of energy in the form of heat in the

iron core of a transformer is(a) iron loss (b) copper loss(c) mechanical loss (d) none of these

101. A step down transformer converts transmissionline voltage from 11000 V to 220 V. The primaryof the transformer hass 6000 turns andefficiency of the transfer is 60%. If the outputpower is 9 kW, then the input power will be(a) 11 kW (b) 12 kW(c) 14 kW (d) 15 kW

102.A small town with a demand of 800 kW of electricpower at 220 V is situtated 15 km away from anelectric plant generating power at 440 V. Theresistance of the two wire line carrying poweris 0.5 per km. The town gets power from theline through a 4000 – 220 V step downtransformer at a substation in the town. Theline power loss in the form of heat is(a) 4000 kW (b) 600 kW(c) 300 kW (d) 800 kW

103.The core of a transformer is laminated to reduce?(a) flux leakage (b) hysteresis(c) copper loss (d) eddy current

104. In a step up transformer the turn ratio is 1 : 2.A Leclanche cell (emf = 1.5 V) is connectedacross the primary. The voltage across thesecondary is(a) 3 V (b) 1.5 V(c) 0.75 V (d) zero

105.The current drawn by the primary of atransformer, which steps down 200 V to 20 V tooperate a device of resistance 20 is(a) 0.125 A (b) 0.225 A(c) 0.325 A (d) 0.425 A

11. INTEGER TYPE QUESTIONS1. A rectangular loop of sides 10 cm and 5 cm with

a cut is stationary between the pole pieces of anelectromagnet. The magnetic field of the magnetis normal to the loop. The current feeding theelectromagnet is reduced so that the fielddecreases from its initial value of 0.3 T at the

rate of 0.02 Ts–1. If the cut is joined and the loophas a resistance of 2, the power dissipated bythe loop as heat is n × 10–9 watt. What is thevalue of n.

2. A rectangular loop with a sliding connector oflength l = 1.0 m is situated in a uniform magneticfield B = 2 T perpendicular to the plane of loop.Resistance of connector is r = 2. Tworesistances of 6 and 3 are connected asshown in figure. Find the external force (in N)required to keep the connector moving with aconstant velocity v = 2 m/s.

3 6

B

3. A current in a coil of self-inductance 2H isincreasing as i = 2 sint2. Calculate the amountof energy (in J) spent during the period whenthe current changes from 0 to 2 A.

4. A circuit containing a two position switch isshown in figure. The switch S is in position 1,the rate of production of joule heat in R1 is H (inJ/s). What is the value of 8/49H?

R1

R2

R3

2BA

S

1

2L

10 mH

R4 = 3

R5 = 12µF

C

E1

E2

3V

12V

2

2

5. A wire in bent in the form of a V shape and placedin a horizontal plane. There exists a uniformmagnetic field B perpendicular to the plane ofthe wire. A uniform conducting rod starts slidingover the V-shaped wire with a constant speed v= 2m/s as shown in the figure. The wire has aresistance 0.1 per unit length. The inducedemf in the rod at given instant is B unit. Whatis the value of 2 ?

OM N

30° 30° 32

m

2 m/s


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6. The L-shaped conductor as shown is figuremoves a 10 m/s across a stationary L-shapedconductor in a 0.10 T magnetic field. The twovertices overlap so that the enclosed area is zeroat t = 0. The conductor has resistance of 0.010ohm per meter. The current at t = 0.10 secondis i (in Amp.), what is the value of

5 2i ?

10 m/s

B

7. In the figure shown a conducting wire PQ oflength, l = 1m, is moved in a uniform magneticfield B = 4T with constant velocity v = 2 m/stowards right. Given : R = 2, C = 1F and L = 4H.The force required to move the wire with thegiven constant velocity of 2 m/s at t = 2s is Fneuton. What is the value of F/4 ?

R CL

P

Q

BV

8. The rails of a railway track, insulated from eachother and the ground, are connected to amillivoltmeter. What is the reading (in mV) tothe millivoltmeter when a train travels at a speedof 18 km/h along the track given that thevertical component of earth’s magnetic field is0.2 × 10–4 weber/m2 and the rails are separatedby 1 m? Track is south to north.

9. Two parallel vertical metallic rails AB and CDare separated by 1 m. They are connected at twoends by resistances R1 and R2 as shown infigure. A horizontal metallic bar of mass 0.2 kgslides without friction vertically down the railsunder the action of gravity. There is a uniformhorizontal magnetic field of 0.6 T perpendicularto the plane of the rails. It is observed that whenthe terminal velocity is attained, the powersdissipated in R1 and R2 are 0.76 W and 1.2 Wrespectively. Find the terminal velocity (in m/s) of the bar L and the values of R1 and R2.

A

B

C

D

R1

R2

L

10. An infinitesimally small bar magnet of dipolemoment M is pointing and moving with thespeedv in the x-direction. A small closed circularconducting loop of radius a and negligible self-inductance lies in the yz-plane with its centreat x = 0, and its axis coinciding with the x-axis.The force oppositing the motion of the magnet,

if the resistance of the loop is R is a 2 2 40

84

M a V

Rx

(Assume that the distance x of the magnet fromthe centre of the loop is much greater than a),what is the value of ?

11. The electric current in a circuit is given byi = i0t/ for some time. The rms current for theperiod t = 0 to t = is t0/x, what is the value ofx2?

12. A 60 Hz AC voltage of 160 V impressed across anLR circuit results in a current of 2 A. If the powerdissipated is 200 W, the maximum value of theback emf arising in the inductance is V0 (in V),what is the value of V0/25 ?

13. An LCR series circuit with 100 resistance isconnected to an AC source of 200 V and angularfrequency 300 rad/s. When only the capacitanceis removed, the current legs behind the voltageby 60°. When only the inductance is removed.The current leads the voltage by 60°. Calculatethe current (in A).

14. An alternating e.m.f. of angular frequency w isapplied across an inductance. Theinstantaneous power developed in the circuithas an angular frequency x , what is the valueof x ?

15. The electric current in a circuit is given by i =i0(t/). The mean square current for the time

interval t = 0 to t = is 20ix

, what is the value of x(where is constant value)

16. In the circuit shown in figure. Calculate the


75

r.m.s. current (in A) through the source.

100

500/3

50 200 V

17. A current in a coil of self-inductance 2H isincreasing as i = 2 sint. Calculate the amountof energy (in J) spent during the period whenthe current changes from 0 to 2 A.

18. The rms value of voltage for triangular wave

having peak value V0 is shown in figure is 04V

x,

what is the value of x?

t

V

0

–V0

V0

T/2T

3 /2T2T

19. An ac source of angular frequency w is fed acrossa resistor R and a capacitor C in series. Thecurrent resistered is I. If now the frequency ofsource is changed to /3 (but maintaining thesame voltage), the current in the circuit is foundto be halved. The ratio of reactance to resistanceat the original frequency is . What is the valueof 15 2?


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1. FARADAY’S LAW, MAGNETIC FLUX & LENZ LAW1. c 2. d 3. d 4. c 5. a6. c 7. d 8. a 9. b 10. b11. d 12. d 13. d 14. b 15. a16. b 17. c 18. d 19. b

2. MOTIONAL & ROTATIONAL EMF20. b 21. a 22. b 23. a 24. d25. b 26. d 27. c 28. d 29. d30. c 31. b 32. c 33. d 34. d35. b

3. EDDY CURRENT36. b 37. c 38. c 39. b

4. INDUCTANCE40. c 41. b 42. b 43. b 44. a45. b 46. d 47. c 48. d 49. a50. b 51. b 52. b 53. b 54. c55. c 56. d 57. a 58. a 59. c60. c 61. b

5. LR CIRCUIT (GROWTH & DECAY)62. d 63. d 64. d 65. b 66. a

6. MEAN & RMS VALUE67. a 68. c 69. b 70. b 71. c

7. AC CIRCUITS & POWER72. b 73. c 74. a 75. c 76. c77. b 78. b 79. c 80. d 81. c82. b 83. c 84. b 85. b 86. d87. a 88. d 89. b 90. c 91. c

8. RESONANCE92. d 93. b 94. d 95. c

9. LC OSCILLATION96. a 97. b 98. a 99. b

10. INSTRUMENTS100. a 101. d 102. b 103. d 104. d105. a

11. INTEGER TYPE QUESTIONS1. (5) 2. (2) 3. (4) 4. (4) 5. (4)6. (5) 7. (8) 8. (1) 9. (1) 10. (9)11. (9) 12. (5) 13. (2) 14. (0) 15. (3)16. (5) 17. (4) 18. (3) 19. (9)

topper’s package physics - xii unit emi & ac circuits · 2020. 8. 8. · (a) b v d 0 0 (b) 2...

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