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.