An electric motor operating on a 60 V dc supply draws a current of 10 A. If the efficiency of the motor is 50%, the resistance of its winding is 

(1) 3Ω

(2) 6Ω

(3) 15Ω

(4) 30Ω

Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ >> R₂, the mutual inductance M between them will be directly proportional to 

(1) R₁/R₂

(2) R₂/R₁

(3) $R_1^2/R_2$

(4) $R_2^2/R_1$

Consider the situation shown in the figure. The wire AB is sliding on the fixed rails with a constant velocity. If the wire AB is replaced by semicircular wire, the magnitude of the induced current will:

A circular loop of radius R carrying current i lies in the x-y plane. If the centre of the loop coincides with the origin, then the total magnetic flux passing through the x-y plane will be:

A small square loop of wire of side l is placed inside a large square loop of wire of side L (L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to 

(1) l / L

(2) l² / L

(3) L/l

(4) L²/l

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:

1. is zero
2. decreases as $\frac{1}{r}$
3. increases as r
4. decreases as $\frac{1}{r^2}$

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be:

A conducting rod of length 2l is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field $\overrightarrow{B}$ exists parallel to the axis of rotation. The e.m.f. induced between the two ends of the rod is:

1. \(B\omega l^2\)
2. $\frac{1}{2}B\omega l^2$
3. $\frac{1}{8}B\omega l^2$
4. Zero

As shown in the figure, P and Q are two coaxial conducting loops separated by some distance. When the switch S is closed, a clockwise current I_P flows in P (as seen by E) and an induced current $I_{Q_1}$ flows in Q. The switch remains closed for a long time. When S is opened, a current $I_{Q_2}$ flows in Q. Then the directions of $I_{Q_1}$ and $I_{Q_2}$ (as seen by E) are 

(1) Respectively clockwise and anticlockwise

(2) Both clockwise

(3) Both anticlockwise

(4) Respectively anticlockwise and clockwise

A conducting wireframe is placed in a magnetic field that is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires AB and CD are

(1) B to A and D to C

(2) A to B and C to D

(3) A to B and D to C

(4) B to A and C to D