UNIT: 4 (ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS)

ONE MARK QUESTIONS

1) Predict the direction of induced current in a metal ring when the ring is moved towards a straight conductor with a constant speed v. The conductor is carrying a current I in the direction shown in the figure.

2) Mention two characteristics properties of the material suitable for making core of a transformer.

3) Predict the directions of induced currents in metal rings 1 and 2 lying in the same plane where current I in the wire is increasing steadly.

4) On what factors does the magnitude of the emf induced in the circuit due to magnetic flux depend?

5) The motion of copper plate is damped when it is allowed to oscillate between the two poles of a magnet. What is the cause of this damping?

6) Show that the current leads the voltage in phase by π2 in an ac circuit containing an ideal

capacitor.7) In a series LCR circuit, obtain the conditions under which (i) the impedance of the circuit

is minimum and (ii) wattles current in the circuit.8) ) In a series LCR circuit V L=V C≠V R, What is the power factor for this circuit?9) The power factor of an ac circuit is 0.5. What is the phase difference between current

and voltage in this circuit.10) Define quality factor of resonance in series LCR circuit. What is its SI unit?11) An ac source of voltage V=V 0sinωt is connected to an ideal inductor. Draw graphs of

voltage V and current i versus ωt .12) ) A bar magnet is moved in the direction indicated by the arrow between two coils PQ

and CD. Predict the direction of the induced current in each coil.

ANSWER OF ONE MARK QUESTIONS

1. Clock wise2. Low coercivity and low retentivity3. Clockwise in ring 1 and anticlockwise in ring24. Rate of flux, area and orientation.5. By phasor diagram6. X L=XC 7. (i)Eddy current (ii) inductive or capacitive circuit with R= 08. 19. 60˚

10. Q=ωr

2∆ω . no unit

11.

12. P to Q in coil 1 and C to D in coil 2

TWO MARKS QUESTIONS1. Show that magnetic energy required to build up the current I in a coil of self-inductance

L is given by 12LI 2.

2. State the underlying principle of a transformer. How is the large scale transmission of electric energy over long distances done with the use of transformers?

3. A light bulb is rated 100 W for 220V ac supply of 50Hz. Calculate

(a) the resistance of the bulb (b) the rms current through the bulb 4. State Lenz’s law. A metallic rod held horizontally along east-west direction, is allowed to fall under gravity. Will there be an emf induced at its ends? Justify your answer.5. A rectangular frame of wire is placed in a uniform magnetic field directed outwards normal to the paper. AB is connected to a spring which is stretched to A’B’ and then released at time

t= 0. Explain qualitatively how induced e.m.f in the coil would vary with time. (Neglect damping

of oscillations of spring)

6. A conducting rod of lengthl, with one end pivoted, is rotated with a uniform angular speed ω in a vertical plane, normal to a uniform magnetic field B. Deduce an expression for the emf induced in the rod. If resistance of rod is R, What is the current induced in it.

7. How is the mutual inductance of a pair of coils affected when (i) Separation between the coils is increased?(ii) the number of turns in each coil is increased?(iii) a thin iron sheet is placed between the two coils, other factors remaining the same?Justify your answer in each case.

8. A series of LCR circuit is connected to a ac source (200V, 50Hz). The voltage across the resistor, capacitor and inductor are respectively 200V, 250V and 250V. (i) The algebraic sum of the voltages across the three elements is greater than the voltage of the source. How the paradox is resolved?(ii) Given the value of the resistance of R is 40Ω, calculate the current in the circuit.9. For a given ac, i=im sinωt , show that the average power dissipated in a resistor R over a

complete cycle is 12im

2 R.

10. Given the input current 15 A and the input voltage of 100 V for a step-up transformer having 90% efficiency, Find the output power and the voltage in the secondary if the output current is 3 A.

11. A rectangular coil of area A, having number of turns N is rotated at ' f ' revolutions per second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2πf NBA.

SOLUTION

Hints

1. Derivation2. Mutual induction. Step up transformer3. R= 484 Ω

4. Statement. Emf is induced.

5. When the spring is stretched and released the wire AB will execute SHM. So induced emf will vary periodically.v=AωsinωtE=Bvl=BAωlsin ωt (where A= BB’ = AA’)

6. d E=B dAdt

=Bv dl

E=∫0

l

Bl ωdl=12Bωl2

I= ER

=12Bωl2

R

7. ans

8. (a) V=V R+V L+V C=700V >200VThe paradox can be resolved by using phasor diagram.V eff=V R=200V

(b) R= 400 Ω and I eff=V eff

R=5 A

9. Derivation. For resistive circuit

Pav=E v I v cosφor 12im

2 R.

10.I PI s

=100×153

=500V

Po=ηP i=1350watt

E s=Po

I s=450 volt

11. E=−dφdt

=NBAωsinωt∨Emax=NBAω=NBA 2πf

THREE MARKS QUESTIONS

1. Derive expression for self inductance of a long air-cored solenoid of length l, cross-sectional area A and having number of turns N.2. Describe briefly, with the help of a labeled diagram, the working of a step up transformer.3. (a) Define mutual inductance and write its SI units.(b) Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound one over other.

4. A wheel of 8 metallic spokes each 50cm long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth’s magnetic field. The Earth’s magnetic field at the plane is 0.4 G and the angle of dip is 60⁰. Calculate the emf induced between the axle and the rim of the wheel. How will be the emf is affected if the number of spokes were increased?

5.) Using phasor diagram for a series LCR circuit connected to an AC source of voltage

v=v0 sinωτ , derive the relation for the current flowing in the circuit and the phase angle between the voltage across the resistor and the net voltage in the circuit.

6. ) The current flowing in the two coils of self inductance L1=16mH∧L2=12mH are increasing at the same rate. If the power supplied to the two coils are equal, find the ratio of (i) induced voltage, (ii) the currents and (iii) the energies stored in the two coils at a given instant.

7. An inductor of reactance X L is connected in series with a bulb B to an ac source. Explain briefly how does the brightness of the bulb change when (i) number of turns of the inductor is reduced and (ii) a capacitance of reactance XC=X L is included in the circuit.

8. (i) An ac source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero.

(ii) A lamp is connected in series with an inductor and an ac source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the conductor? Explain.

9. (i) An ac source is connected to an ideal capacitor show that the average power supplied by the source over a complete cycle is zero.(ii) A bulb is connected in series with a capacitor and an ac source. What happens to the brightness of the bulb when the key is plugged in and capacitance of capacitor is gradually reduced? Explain.

10. A capacitor of unknown capacitance, a resistor of 100Ω and an inductor of self inductance

L= 4π2 henery are connected in series to an ac source of 200 V and 50 Hz. Calculate the value of

the capacitance and impedance of the circuit when the current is in phase with the voltage. Calculate the power dissipated in the circuit.

SOLUTION

Hints

1. derivation2. Brief explanation3. (a) definition and hennery (b) derivation

4. E=12Bωl2

BH=B cos δ

E=12B cos δωl2=3.14×10−5 volt

5. Derivation

The phasor diagram of the RLC Series Circuit when the circuit is acting as an inductive circuit that means (VL>VC) is shown below and if (VL< VC) the circuit will behave as a capacitive circuit.

Steps to draw the Phasor Diagram of the RLC Series Circuit

Take current I as the reference as shown in the figure above The voltage across the inductor L that is VL is drawn leads the current I by a 90-degree

angle. The voltage across the capacitor c that is Vc is drawn lagging the current I by a 90 degree

angle because in capacitive load the current leads the voltage by an angle of 90 degrees. The two vectors VL and VC are opposite to each other.

Where,

6. (i) E=−L dIdt

E1

E2=L1

L2=4

3

(ii) P=E I ⟹E1 I1=E2 I 2

E2

E1=I 1

I 2=3

4

(iii) U=12L I 2

U 2

U 1=I 2

I 1×I2

I1×L2

L1=4

3

7. (i) When number of turns in the inductor is reduced

L decreases, z reduces and I increases so brightness increases.(ii) Brightness decreases(iii) Brightness increases

8. (i) For inductive circuit average power is zero.(ii) Brightness decreases

9. (i) For capacitive circuit average power is zero.(ii) Brightness decreases

XC=1ωC

As C decreases, Z increases so brightness decreases

10. C= 1Lω2 =2.5×10−5 F

Z=R=100Ω and power= 400 watt

FIVE MARKS QUESTIONS

1. )(a) Draw a schematic sketch of an ac generator describing its basic elements. State briefly its working principle. Show a plot of variation of (i) magnetic flux and (ii) alternating emf versus time generated by a loop of wire rotating in a magnetic field(b) Why is choke coil needed in the use of fluorescent tubes with ac mains?2. ) What are eddy currents? How are they produced? In what sense eddy current are considered undesirable in a transformer? How can they be minimized? Give two applications of eddy currents.3. (a) An ac source of voltage V=V 0sinωt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expressions for impedance of the circuit and phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called?(b) In a series LR circuit X L=R and power factor of the circuit is P1. When capacitor with

capacitance C such that X L=XC is put in series, the power factor becomesP2. CalculateP1

P2.

4. (i) What is the function of a transformer. State it principle of working with the help of a diagram. Mention various energy losses in this device.(ii) The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 220 V and 1100 W. Calculate (a) Number of turns in secondary(b) Current in primary(c ) voltage across secondary(d) Current in secondary(e) Power in secondary

5. ) (a) When a bar magnet is pushed towards (or away) from the coil connected to a galvanometer deflects. Identify the phenomenon causing this deflection and write the factors on which the amount and direction of the deflection depends. State the laws describing this phenomenon.(b) Sketch the change in flux, emf and force when a conducting rod MN of resistance R and length l moves freely with speed v on a rectangular conducting frame placed in uniform magnetic field as shown in the figure.

6. A 2µF capacitor, 100Ω resistor and 8 H inductor are connected in series with an ac source. (i) What should be the frequency of the source such that the current drawn in the circuit is maximum? What is this frequency called?(ii) If the peak value of emf of the source is 200 V, find the maximum current.(iii) Draw a graph showing variation of amplitude of circuit current with changing frequency of applied voltage in a series LRC circuit for two different values of resistance R1∧R2 (R1>R2 ) (iv) Define the term sharpness of resonance. Under what condition, does a circuit become more selective?

7. A device X is connected to an ac sourceV=V 0sinωt . The variation of voltage, current and power in one cycle is shown in the following graph.(a) Identify the device X.(b) Which of the curves A, B and C represent the voltage, current and power consumed in the circuit? Justify your answer.( c ) How does its impedance vary with frequency of the ac source? Show graphically.(d) Obtain an expression for the current in the circuit and its phase relation with ac voltage.

8. (a) Draw graphs showing the variations of inductive reactance and capacitive reactance with frequency of the applied ac source.(b) Draw the phasor diagram for a series RC circuit connected to an ac source.( c) An alternating voltage of 220 V is applied across a device X, a current of 0.25A flows, which

lag behind the applied voltage in phase by π2 radian. If the same voltage is applied across

another device Y, the same current flows but now it is in phase with the applied voltage.(i) Name the device X and Y.(ii) Calculate the current flowing in the circuit when the same voltage is applied across the series combination of X and Y.9.(a)Show that the energy of the system oscillates between inductor and capacitor. Write two reasons why LC oscillation is not realistic.(b) Explain how Lenz’s law is in accordance with the conservation of energy.

10. Figure shows a rectangular loop conducting PQRS in which the arm PQ is free to move. A uniform magnetic field acts in the direction perpendicular to the plane of the loop. Arm PQ is moved with a velocity v towards the arm RS. Assuming that the arms QR, RS and SP have negligible resistances and the moving arm PQ has the resistance r,obtain the expression for the (i) the current in the loop (ii) the force and (iii) the power required to move the arm PQ with graph.

SOLUTION

Hints

1. Brief explanation. Principle of AC generator- It works on the principle of electromagnetic induction.

In an A.C. generator, mechanical energy is converted to electrical energy by virtue of

electromagnetic induction.

* Rotation of rectangular coil in a magnetic field causes change in flux (Φ = NBACosωt).

Change in flux induces emf in the coil which is given by

ε= -dΦ/dt = NBAωSinωt ε ε= ε0Sinω

* Current induced in the coil I = ε/R = ε0Sinωt/R = I0Sinωt

,In case of choke coil power dissipation is very negligible

3.

4. (i) Function: Transformer is used for convertinglow alternating voltage at high current into high voltage at low current and vice-versa. Principle: It works on the principle of mutual induction. Various Energy loses in transformer are - (a) Flux losses.

(b) Copper and Iron losses.( c) Hysteresis Losses(d) Humming Losses.Step-Up Transformer:Converts low voltage A.C. into high voltage A.C. It increase the voltage

5. (a) Phenomenon : Electromagnetic Induction

Factors: Strength of the magnetic field of the magnetSpeed of motion of the bar magnetDirection depends on the north /south polarity of the magnet and the direction of motionof the magnet .

6) ω0=1

√LC=250

f 0=2502π

=39.7Hz

(b) I 0=V 0

R=2 A

(d) Q= Q=ω0

2∆ω is a measure of sharpness of resonance.

8) (c) X is inductor Y is a resistor.In series the current remains same.