1). A slender rod 1 m long rotates about an axis through one end and perpendicular to the rod, with an angular velocity 2 rev.s–1. The plane of rotation of the rod is perpendicular to a uniform magnetic field 0.5 T.

(a) What is the induced e.m.f. in the rod ?

Ans: 3.14 V

(b) What is the potential difference between its terminals?

Ans: 3.14 V.

2). A coil of 5 turns has dimension 9 cm × 7 cm. It rotates at the rate of 15 p rad/sec in a uniform magnetic field whose flux density is 0.8 weber/metre2. What maximum e.m.f. is induced in the coil ? What is the e.m.f. 1/90 sec. after it reaches the value zero ?

ANS: Q30, 0.594 volt.

3).A coil of mean area of 500 cm2 and having 1000 turns is held perpendicular to a uniform field of 0.4 gauss. The coil is turned through 180º in 1/10 second. Calculate the average induced e.m.f.

Ans: 0.04 V

4). A very small circular loop of area 5 × 10–4 m2, resistance 2 ohm and negligible inductance is initially coplanar and concentric with a much larger fixed circular loop of radius 0.1 m. A constant current of 1 ampere is passed in the bigger loop and the smaller loop is rotated with angular velocity w rad/sec about a diameter. Calculate

(i) the flux linked with the smaller loop (ii) induced e.m.f.

(iii) induced current in the smaller loop as a function of time.

Ans: (i) 2p × 10–6 weber/m2 (ii) p × 10–9 w sin wt volt (iii)

6).A rod PQ of length L moves with a uniform velocity v parallel to a long straight wire carrying a current i, the end P remaining at a distance r from the wire. Calculate the e.m.f. induced across the rod.

7). Space is divided by the line AD into two regions. Region I is field free and the region II has a uniform magnetic field B directed into the plane of paper. ACD is semicircular conducting loop of radius r with centre at O (Fig. 25.53), the plane of the loop being in the plane of the paper. The loop is now made to rotate with a constant angular velocity w about an axis passing through O and perpendicular to the plane of the paper. The effective resistance of the loop is R.

(i) Obtain an expression for the magnitude of the induced current in the loop.

(ii) Show the direction of the current when the loop is entering into the region II.

(iii) Plot a graph between the induced e.m.f. and time of rotation for two periods of rotation.

8). A resistance of 10 ohm is joined in series with an inductance of 0.5 henry. What capacitance should be put in series with the combination to obtain the maximum current ? What will be the potential

difference across the resistance, inductance and capacitor ? The current is being supplied by 200 volts and 50 cycles per second mains.

9). A LCR circuit has L = 10 mH, R = 3 ohm and C = 1mF connected in series to a source of 15 cos wt volt. Calculate the current amplitude and the average power dissipated per cycle at a frequency that is 10% lower than the resonant frequency.

1). An a.c. generator consist of a coil of 50 turns, area 2.5m2 rotating at an

angular speed of 60 rad/s in uniform magnetic field of B = 0.3 T between two

fixed pole pieces. Given R = 500.

(i) Find the maximum current drawn from the generator?

(ii) What will be the orientation of the coil wrt. B to have max and zero

magnetic flux?

2).

(a) A simple A C generator having a constant magnetic field is connected

to a resistive load. Mention the reason for the effect of doubling the

speed of rotation on the following.

(a) Frequency of rotation (b) the generated emf.

(b) Obtain the frequency of a series L C circuit at resonance.

(a) Show diagrammatically two different arrangements used for

winding the primary and secondary coils in a transformer.

(b) Assuming the transformer to be an ideal one, write the expressions

for the ratio of its output voltage to input voltage.

(c) The core of transformer is made of magnetic material. Give any two

properties of such materials used.

(d) Write any four types of energy losses in transformer.

Q1. A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s -1, at right angles to the horizontal component of the earth’s magnetic field, 0.30 × 10 -4 Wb m2. The instantaneous value of the emf induced in the wire and the direction

(a) 1.5 x 10-3 V (b) 1.5 x 10-4 V (c) 2 x 10-3 V (d) 2 x 10-4 V

Q2. Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced. What is the self-inductance of the circuit?

(a) 2 H (b) 3 H (c) 4 H (d) 5 H

Q3. An ideal transformer has Np turns in the primary and Ns turns in the secondary. If the voltage per turn is Vp in the primary and Vs in the secondary, Vs/Vp is equal to

(a) 1 (b) Ns/Np (c) Np/Ns (d) (Np/Ns)2

Q4. The induced emf in a coil is proportional to

(a) magnetic flux through the coil (b) area of the coil

(c) rate of change of magnetic flux through the coil (d)product of magnetic flux and area of the coil

Q5. The reactance of a capacitor at 50 Hz is 10Ω. Its reactance at 100 Hz is

(a) 2.5 Ω (b) 5 Ω (c) 10 Ω (d) 20 Ω

Q6. An electric heater consumes 1000 watts power when connected across a 100 volt D.C. supply. If this heater is to be used with 200V, 50 Hz A.C. supply, the value of the inductance to be connected in series with it is

(a) 5.5H (b) 0.55H (c) 0.055H (d) 1.1H

Q7. An alternating emf V = 6 cos1000t is applied across a series LR circuit of 3 mH inductance and 4 Ω resistance. The amplitude of the current is

(a) 0.6A (b) 1.2A (c) 1.4A (d) 1.8A

Q8. An alternating current of 1.5mA and angular frequency ω=¿300 rad s-1 flows through 10kΩ resistor and a 0.50µF capacitor in series. Find the impedance of the circuit and the r.m.s. voltage across the capacitor.

(a) 1.2 x 103Ω, 10V (b) 1.4 x 104Ω, 20V

(c) 1.2 x 104Ω, 10V (d) 1.4 x 103Ω, 20V

Q9. An alternating voltage E= 100√ 2 sin(100t ) volts is connected to a 1µF capacitor through an ac ammeter.

What will be the current through the ammeter?

(a) 5mA (b) 10mA (c) 15mA (d) 20mA

Q10. In the given circuit inductance L¿ 50

π2×10−2

H,

capacitance C=200µF and R=100Ω are attached as shown. An alternating voltage V= 5sin 100 π t is applied across the circuit. Find current in R and voltage across inductor as a fuction of time t.

(a) Zero, 5sin 50πt

(b) 10mA, 10sin 100πt

(c) Zero, 5sin 100πt

(d) 10mA, 10sin 50πt

1.(a)

2.(c)

3.(a)

4.(c)

5.(b)

6.(c)

7.(b)

8.(c)

9.(b)

10.(c)