CBSE Class 12 Physics Electromagnetic Induction And Alternating Current Worksheet Set A

 

 

ONE MARK QUESTIONS

Question. The power factor of an ac circuit is 0.5. What is the phase difference between current and voltage in this circuit.
Answer : 60⁰

Question. Define quality factor of resonance in series LCR circuit. What is its SI unit?
Answer : Q = ωr /2Δω

Question. An ac source of voltage V= V_0 sin⁡ωt is connected to an ideal inductor. Draw graphs of voltage V and current i versus ωt.
Answer : 

Question. 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 : P to Q in coil 1 and C to D in coil 2

TWO MARKS QUESTIONS

Question. Show that magnetic energy required to build up the current I in a coil of self-inductance L is given by 1/2 LI^2.
Answer : Derivation

Question. 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?
Answer : Mutual induction. Step up transformer

Question. 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
Answer : R= 484 Ω

Question. 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.
Answer : Statement. Emf is induced.

THREE MARKS QUESTIONS

Question. Derive expression for self inductance of a long air-cored solenoid of length l, cross-sectional area A and having number of turns N.
Answer : derivation

Question. Describe briefly, with the help of a labeled diagram, the working of a step up transformer.
Answer : Brief explanation

Question. (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.
Answer : (a) definition and hennery (b) derivation

Question. 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?
Answer :  E= 1/2 Bωl^2
B_H=B cos⁡δ
E= 1/2 B cos⁡δ ωl^2=3.14×〖10〗^(-5) volt

Question.) Using phasor diagram for a series LCR circuit connected to an AC source of voltage
v= v_0 sin⁡ωτ, 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.
Answer : 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.
 

FIVE MARKS QUESTIONS

Question. (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?
Answer : 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

Question. (a) An ac source of voltage V= V_0 sin⁡ωt 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 P_1. When capacitor with capacitance C such that X_L=X_C is put in series, the power factor becomesP_2. CalculateP_1/P_2 .
Answer : 

Question. (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
Answer : (i) Function: Transformer is used for converting
low 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 

 

1 What is the power dissipated in an AC circuit in which voltage and current are given by V = 230sin(ωt+π/2) and I = 10 sinωt? Give reason

 

2 Two identical loops ,one of copper and other of constantan ,are removed from a magnetic field within the same time interval. In which loop will the induced current be greater? Justify.

 

3 A conducting coil is moved relative to a magnetic field .Will there be induced emf and induced current always? Justify

 

4 What is the significance of power factor in i) electrical appliances ii) transmission of electric power?

 

5 Two identical bar magnets are dropped from the same height simultaneously , one falls through a copper tube and the other falls through air, will they reach ground at the same time? Justify.

 

6 The south pole of a magnet is brought near a conducting loop. What is the direction of induced current as observed by a person on the other side of the loop?

 

7 A radio frequency choke is air cored coil where as an audio frequency choke is iron cored. Give reason.

 

8 How does the self inductance of an air core coil change, when i) the number of turns in the coil is decreased? ii) an iron rod is introduced in the coil?

 

9 A bismuth rod is introduced in a solenoid carrying current ,how do i) its self inductance

ii) emf induced in the solenoid change?

 

10 A copper coil L wound on a soft iron core and a lamp B is connected to a battery E through a tap key K. when the key is closed, the lamp glows dimly .But when the key is suddenly opened , the lamp flashes for an instant to much greater brightness . Explain.

 

11 In any ac circuit ,is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit ?

 

12 A conducting loop of area A and resistance R is placed perpendicular to the magnetic field B. The loop is withdrawn completely from the field. Derive an expression for induced charge that flows through any cross section of the wire

 

13 The south pole of a magnet is brought near a conducting loop. What is the direction of induced current as observed by a person on the other side of the loop?

 

14 A bulb B and an inductor L are connected in series to the AC mains. The bulb glows with some brightness. How will the glow of the bulb change when a i) a soft iron core ii) bismuth core is introduced inside the inductor? Give reasons.

 

15 A coil of number of turns N, area A, is rotated at a constant angular speed w, in a uniform magnetic field B, and connected to a resistor R. Deduce expressions for :

(i) Maximum emf induced in the coil

(ii) Power dissipation in the coil.

 

16 A bulb B and a capacitor C are connected in series to the AC mains. The bulb glows with some brightness. How will the glow of the bulb change when a dielectric slab is introduced between the plates of the capacitor? Give reasons.

 

17

Mark the direction of induced current in the coil PQRS. State the rule used to find the direction of induced current. What would be the direction of induced current if the direction of magnetic field is reversed?

 

18

The figure shows a circular coil and a conductor AB carrying current from A to B. If the current is i) decreasing ii) increasing find the direction of induced current in the circular coil.

 

19 Draw a labelled circuit arrangement showing the windings of primary and secondary coil in a transformer. Explain the underlying principle and working of a step-up transformer. Write any two major sources of energy loss in this device.

 

20 A step-up transformer converts a low voltage into high voltage. Does it not violate the principle of conservation of energy? Explain.

 

21 Define the quality factor in an a.c. circuit. Why should the quality factor have high value in receiving circuits? Name the factors on which it depends.

22 Derive an expression for the average power consumed in a series LCR circuit connected to a.c. source in which the phase difference between the voltage and the current in the circuit is Φ.

 

Question. A circular coil of radius 5 cm has 500 turns of a wire. The approximate value of the coefficient of self induction of the coil will be:
a. 25 millihenry
b. 3 25 x 10⁻³ millihenry
c. 34 50 x 10⁻³⁴ millihenry
d. 3 50 x 10⁻³ henry
Answer : A

Question. The average emf induced in a coil in which a current changes from 0 to 2 A in 0.05 s is 8 V. The self inductance of the coil is:
a. 0.1 H
b. 0.2 H
c. 0.4 H
d. 0.8 H
Answer : B

Question. A coil of Cu wire (radius-r, self inductance-L) is bent in two concentric turns each having radius is. r/2 The self inductance now:
a. 2L
b. L
c. 4 L
d. L/2
Answer : A

Question. A rectangular coil of 300 turns has an average area of 25 cm × 10 cm. The coil rotates with a speed of 50 cps in a uniform magnetic field of strength 4 × 10^–2 T, about an axis perpendicular to the field. The peak value of the induced emf is: (in volt)
a. 3000 π
b. 300π
c. 30π
d. 3 π
Answer : C

Question. A wheel with ten metallic spokes each 0.50 m long is rotated with a speed of 120 rev/min in a place normal to the earth's magnetic field at the place. If the magnitude of the field is 0.04 G, the induced emf between the axle and the rim of the wheel is equal to:
a. 3 1.256 x 10⁻³ V
b. 6.28 × 10^–3 V
c. 4 1.256 10⁻⁴ V
d. 6.28 × 10^–6 V
Answer : D

Question. In the previous question at what time t instantaneous induced emf will be half of maximum induced emf:
a. 1/300 sec
b. 1/400 sec
c. 1/500 sec
d. 1/600 sec
Answer : D

Question. As shown in the figure a metal rod makes contact and complete the circuit. The circuit is perpendicular to the magnetic field with B = 0.15 Tesla. If the resistance is 3), force needed to move the rod as indicated with a constant speed of 2m/sec is:

a. 3.75 x 10^–3 N
b. 3.75 × 10^–2 N
c. 3.75×10² N N
d. 3.75×01_–4 N
Answer : A

Question. A metal conductor of length 1 m rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earth's magnetic field is 0.2 × 10^–4 T, then the e.m.f. developed between the two ends of the conductor is:
a. 5mV
b. 50μV
c. 5μV
d. 50mV
Answer : B

Question. In a region of uniform magnetic induction B = 10^–2 Tesla, a circular coil of radius 30 cm and resistance π² ohm is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is:
a. 2 4π mA
b. 30mA
c. 6 mA
d. 200mA
Answer : C

Question. In the following circuit, the bulb will become suddenly bright if:

a. Contact is made or broken
b. Contact is made
c. Contact is broken
d. Won’t becomes bright at all
Answer : C

Question. A solenoid has 2000 turns wound over a length of 0.30 metre. The area of its cross-section is 1.2 × 10^–3 m². Around its central section, a coil of 300 turns is wound. If an initial current of 2A in the solenoid is reversed in 0.25 sec, then the emf induced in the coil is:
a. 6 x 10⁻⁴ V
b. 4 x 10⁻³ V
c. 6 x 10⁻² V
d. 48 mV
Answer : D

Question. The mutual inductance between a primary and secondary circuit is 0.5 H. The resistance of the primary and the secondary circuits are 20 ohms and 5 ohms respectively. To generate a current of 0.4 A in the secondary, current in the primary must be changed at the rate of:
a. 4.0 A/s
b. 16.0 A/s
c. 1.6 A/s
d. 8.0 A/s
Answer : A

Question. An emf of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time t = ∞ and at t = 1 second is:
a. e^{1/ 2} / e^{1/ 2} − 1
b. e² / e² − 1
c. 1–e^–1
d. e^–1
Answer : B

Question. A simple electric motor has an armature resistance of one ohm and runs from a dc source of 12 volts. When unloaded it draws a current of 2 amperes. When a certain load is connected, its speed becomes one-half of its unloaded value. Then the current in ampere it draws is:
a. 7 amp
b. 6 amp
c. 2 amp
d. 4 amp
Answer : A

Question. A transformer is used to light 140 watt, 24 volt lamp from 240 volts ac mains. If the current in the mains is 0.7 A, then the efficiency of transformer is:
a. 63.8%
b. 84%
c. 83.3%
d. 48%
Answer : C

Question. Three inductances are connected as shown below.
Assuming no coupling, the resultant inductance will be:

a. 0.25 H
b. 0.75 H
c. 0.01 H
d. 1 H
Answer : D

Question. In the figure magnetic energy stored in the coil is:

a. Zero
b. Infinite
c. 25 J
d. None of these
Answer : C

Question. The peak value of an alternating e.m.f. E is given by E = E₀ cosω t is 10 volts and its frequency is 50Hz. At time t = 1/600 sec the instantaneous e.m.f. is:
a. 10 V
b. 5 3V
c. 5V
d. 1V
Answer : B

Question. The instantaneous values of current and potential difference in an alternating circuit are i = sinω t and E = 100 cosω t respectively. r.m.s. value of wattless current (in amp) in the circuit is:
a. 1
b. 1/√2
c. 100
d. Zero
Answer : B

Question. In an ac dynamo, the number of turns in the armature are made four times and the angular velocity 9 times, then the peak value of induced emf will become
a. 36 times
b. 12 times
c. 6 times
d. 18 times
Answer : A

Question. Primary voltage is , V_p resistance of the primary winding is . R_p Turns in primary and secondary are respectively N_p and Ns then secondary current in terms of primary voltage and secondary voltage respectively will be:

Answer : A

Question. In the circuit shown in the figure the ac source gives a voltage V = 20cos(2000t). Neglecting source resistance, the voltmeter and ammeter reading will be:

a. 0V,0.47A
b. 1.68V,0.47A
c. 0V,1.4A
d. 5.6V,1.4A
Answer : B

Question. What will be the equation of ac of frequency 75 Hz if its r.m.s. value is 20 A:
a. i = 20sin150πt
b. i = 20√2 sin(150πt)
c. i = 20/√2 sin(150πt)
d. i = 20√2 sin(75πt)
Answer : B

Question. At what time (From zero) the alternating voltage becomes 1/√2 times of its peak value. Where T is the periodic time:
a. T/2 sec
b. T/4 sec
c. T/8 sec
d. T/12 sec
Answer : C

Question. A 20 volts ac is applied to a circuit consisting of a resistance and a coil with negligible resistance. If the voltage across the resistance is 12 V, the voltage across the coil is:
a. 16 volts
b. 10 volts
c. 8 volts
d. 6 volts
Answer : A

Question. The potential difference V and the current i flowing through an instrument in an ac circuit of frequency f are given by 5cos V t ω = volts and I = 2 sin ωt amperes (where ω = 2π f ). The power dissipated in the instrument is:
a. Zero
b. 10 W
c. 5 W
d. 2.5 W
Answer : A

Question. If an ac main supply is given to be 220 V. What would be the average e.m.f. during a positive half cycle?
a. 198V
b. 386V
c. 256V
d. None of these
Answer : A

Question. In a series circuit R = 300Ω, L = 0.9 H , C = 2.0μ F and ω =1000rad / sec. The impedance of the circuit is:
a. 1300 Ω
b. 900 Ω
c. 500 Ω
d. 400 Ω
Answer : C

Question. In a series resonant LCR circuit, if L is increased by 25% and C is decreased by 20%, then the resonant frequency will:
a. Increase by 10%
b. Decrease by 10%
c. Remain unchanged
d. Increase by 2.5 %
Answer : C