(a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of a side a as shown inthe figure given below.

(b) Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with constant velocity, V=10ms^-1. Calculate the induced emf in the loop at the instant when x=0.2m. Take a=0.1 m and assume that the loop has a large resistance.

3

(a)

A series LCR circuit with \(R=20\Omega \) , L=1.5H and \(C=35\mu F\) is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

3

(a)

A coil of inductance 0.50H and resistance \(100\Omega \) is connected to a 240V, 50 Hz ac supply. 

(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

3

(a)

A \(100\mu F\) capacitor in series with a \(40\Omega \) is connected to a 110 V, 60 Hz supply.

(a) What is the maximum current in the circuit?

(b) What is the time lag between the current maximum and the voltage maximum?

3

(a)

Explain why the coils of the resistance box are wound over themselves.

3

(a)

Define the term self inductance. Write two factors on which the self inductance of a coil depends.

3

(a)

What is an ideal inductor?

3

(a)

Predict the direction of induced current in the situations described by the following Fig.

3

(a)

An air cored solenoid with length 30 cm, area of cross-section \(25㎠\) and number of turns 500 carries a current of 2.5 A. The current is suddenly switched off in a brief time of \({ 10 }^{ -3 }s\) . How much is the average back e.m.f. induced across the ends of the open switch in the circuit? Ignore the variation in the magnetic field near the ends of the solenoid.

3

(a)

An air cored solenoid with length 30cm, area of cross-section 25cm² and number of turns 500 carries a current of 2.5A. The current is suddenly switched off in a brief time of 10^-3s. How much is the average back e.m.f. induced across the ends of the open switched in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.

3

(a)

A 100 resistor is connected to a 220V, 50Hz ac supply.
(a) What is the rms value of current in the circuit?
(b) What is the net power consumed over a full cycle?

3

(a)

A 60\(\mu\)F capacitor is connected to a 110V, 60Hz a.c.supply. Determine the r.m.s. value of current in the circuit.

3

(a)

Obtain the resonant frequency \(\left( { \omega }_{ r } \right) \) of a series LCR circuit with L=2.0H, C = 32\(\mu\)F and R=10 ohm. What is the Q value of this circuit?

3

(a)

A charged 30\(\mu \)F capacitor is connected to a 27mH inductor. What is the angular frequency of free oscillations of the circuit?

3

(a)

Define the term self-inductance of a solenoid. Obtain the expression for the magnetic energy stored in an inductor of self-inductance L to build up a current I through it.

3

(a)