LEVEL – I

1. An inductor coil of inductance L is divided into two equal parts and both parts are connected in parallel. The net inductance is :

(A) L

(B) 2L

(C) L/2

(D) L/4

2. An e.m.f. of 5 millivolt is induced in a coil when in a nearby placed another coil, the current changes by 5 ampere in 0.1 second. The coefficient of mutual induction between the two coils will be :

(A) 1 Henry

(B) 0.1 Henry

(C) 0.1 millihenry

(D) 0.001 millihenry

3. In figure when key is pressed the ammeter A reads i ampere. The charge passing in the galvanometer circuit of total resistance R is Q. The mutual inductance of the two coils is :

(A) Q/R

(B) QR

(C) QR/i

(D) i/QR

4. The equivalent inductance between points P and Q in figure is :

(A) 2 H

(B) 6 H

(C) 8/3 H

(D) 4/9 H

5. A metal disc of radius R rotates with an angular velocity ω about an axis perpendicular to its plane passing through its centre in a magnetic field of induction B acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is:

(A) BπR^{2}

(B) 2Bπ^{2}R^{2}/ω

(C) BπR^{2}ω

(D) BR^{2}ω/2

6. In the circuit shown in the adjoining diagram E = 10 volts, R_{1} = 2 ohms, R_{2} = 3 ohms, R_{3} = 6 ohms and L = 5 henry. The current i_{1} just after pressing the switch S is :

(A) 2.5 amp

(B) 2 amp

(C) 5/6 amp

(D) 5/3 amp

7. A rectangular coil pqrs is moved away from an infinite, straight wire carrying a current as shown in figure. Which of the following statements is correct?

(A) There is no induced current in coil pqrs

(B) The induced current in coil pqrs is in the clockwise sense

(C) The induced current in the coil pqrs is in anticlockwise direction

(D) None of the above

8. The switch S is closed in the circuit shown at time t = 0. The current in the resistor at t = 0 and t = ∞ are respectively.

(A) 0, 0 Amp.

(B) 1, 0 Amp.

(C) 0, 1 Amp.

(D) 1, 1 Amp.

9. The two loops shown in the figure, have their planes parallel to each other. A clockwise current flows in the loop X as viewed from X towards Y. The two coils will repel each other, if the current in the loop X is :

(A) increasing

(B) decreasing

(C) constant

(D) none of the above cases

10. A coil of area 500 cm^{2} having 1000 turns is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude 4 × 10^{-5} weber/m^{2}. If it is rotated by 180° about an axis passing through one of its diameter in 0.1 sec, find the average induced emf.

(A) zero.

(B) 30 mV

(C) 40 mV

(D) 50 mV

###### ANSWER:

1. (D) 2. (C) 3. (C) 4. (A) 5. (D) 6. (B) 7. (B) 8. (D) 9. (A) 10. (C)

LEVEL – I

11. For the L shaped conductor in a uniform magnetic field B shown in figure, the emf across its ends when it rotates with angular velocity ‘ω’ about an axis through one of its ends O and normal to its plane will be

(A) 2 Bωl^{2}

(B) Bωl^{2}

(C) (1/2) Bωl^{2}

(D) 4 Bωl^{2}

12. A coil of inductance 8.4 mh and resistance 6 Ω is connected to a 12 V battery. The current in the coil is 1.0 A approximately after time

(A) 500 ms

(B) 20 s

(C) 35 ms

(D) 1 ms

13. A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region is

(A) is zero

(B) proportional to r

(C) proportional to 1/ r

(D) proportional to 1/r^{2}

14. A conductor of length 5 cm, and resistance 2Ω is moving on frictionless rails with a constant velocity of 5 cm/s in a magnetic field of intensity 3 tesla as shown below. If conductor is connected to a circuit as shown, by two lead wires of almost negligible resistance, then current flowing in it is

(A) 0.25 A

(B) 2.5 Amp

(C) 2.5 mA

(D) 0.25 ×10^{4} amp

15. A wire cd of length l , mass m, is sliding without friction on conducting rails ax and by as shown in figure. The vertical rails are connected to one another via an external resistance R. The entire circuit is placed in a region of space having a uniform magnetic field B. The field is ⊥ to the plane of circuit & directed outwards. The steady speed of rod cd is

(A) mg R/Bl

(B) mg R/B^{2}l^{2}

(C) mg R/Bl^{2}

(D) mg R/B^{2}l

16. A thin circular-conducting ring having N turns of radius R is falling with its plane vertical in a horizontal magnetic field B. At the position MNQ, the speed of ring is v, the induced e.m.f. developed across the ring is

(A) Zero

(B) BVπR^{2}N/2 and M is at higher potential

(C) N πBRv and Q is at higher potential

(D) 2RBvN and Q is at lower potential

17. A circular loop of radius 1m is kept in a magnetic field of strength 2 T directed perpendicular to the plane of loop. Resistance of the loop wire is 2/π Ω/m. A conductor of length 2 m is sliding with a speed 1 m/s as shown in the figure. Find the instantaneous force acting on the rod [Assume that the rod has negligible resistance]

(A) 8 N

(B) 16 N

(C) 32 N

(D) 64 N

18. Two coils A and B have 200 and 400 turns respectively. A current of 1 A in coil A causes a flux per turn of 10^{-3} Wb to link with A and a flux per turn of 0.8 × 10^{-3} Wb through B. The ratio of self-inductance of A and the mutual inductance of A and B is :

(A) 5/4

(B) 1/1.6

(C) 1.6

(D) 1

19. A uniform conducting rod of mass M and length l oscillates in a vertical plane about a fixed horizontal axis passing through its one end with angular amplitude θ . There exists a constant and uniform horizontal magnetic field of induction B perpendicular to the plane of oscillation. The maximum e.m.f. induced in the rod is

(A) $ \displaystyle \frac{B}{8} \sqrt{27 l^3 g (1- cos\theta)} $

(B) $ \displaystyle \frac{B}{8} \sqrt{27 l^3 g (1 + cos\theta)} $

(C) $ \displaystyle B \sqrt{\frac{3 l^3 g (1- cos\theta)}{4}} $

(D) $ \displaystyle B \sqrt{\frac{3 l^3 g (1+ cos\theta)}{4}} $

20. A copper rod moves with a constant angular velocity ω , about a long straight wire carrying a current I. If the ends of the rod from the wire are at distances a and b, then the e.m.f. induced in the rod is

(A) $ \displaystyle \frac{\mu_0 i \omega a}{2 \pi} ln(\frac{b}{a}) $

(B) $ \displaystyle \frac{\mu_0 i \omega b}{2 \pi} ln(\frac{b}{a}) $

(C) zero

(D) $ \displaystyle \frac{\mu_0 i \omega (a + b)}{4 \pi} ln(\frac{b}{a}) $

###### ANSWER:

11. (B) 12. (D) 13. (C) 14. (C) 15. (B) 16. (D) 17. (B) 18. (B) 19. (C) 20. (C)

LEVEL – I

21. The time required for a current to attain the maximum value in a d.c. circuit containing L and R, depends upon :

(A) R only

(B) L only

(C) L/R

(D) none of these

22. Consider the shown arrangement. When key k is pressed, the steady value of current in 20 Ω resistance is :

(A) 0.1 A

(B) 0.25 A

(C) 0.017 A

(D) zero

23. The resistances P, Q, R and S in the bridge shown are adjusted such that the deflection in the galvanometer G is zero when both the keys K1 and K2 are inserted. The galvanometer will show a momentary deflection, if :

(A) first K2 is inserted and then K1

(B) first K1 is inserted and then K2

(C) K1 and K2 are both inserted but an additional resistance is put in the arm BD

(D) in all the above cases

24. When a ‘J’ shaped conducting rod is rotating in its own plane with constant angular velocity ω about one of its ends P , in a uniform magnetic field B^{->} (directed normally into the plane of paper)then magnitude of emf induced across it will be

(A) $ \displaystyle B \omega \sqrt{L^2 + l^2} $

(B) $ \displaystyle \frac{1}{2}B \omega L^2 $

(C) $ \displaystyle \frac{1}{2}B \omega (L^2 + l^2) $

(D) $ \displaystyle \frac{1}{2}B \omega l^2 $

25. The equivalent inductance between points P and Q in the figure is

(A) 9 H

(B) (24/13) H

(C) (12/13) H

(D) 12 H

###### ANSWER:

21. (D) 22. (D) 23. (A) 24. (C) 25. (A)