A coil has an inductance of 2.5 H and a resistance of 0.5 r. If the coil is suddenly connected across a 6.0 volt battery, then the time required for the current to rise 0.63 of its final value is 

(1) 3.5 sec

(2) 4.0 sec

(3) 4.5 sec

(4) 5.0 sec

If a current of 10 A flows in one second through a coil, and the induced e.m.f. is 10 V, then the self-inductance of the coil is 

(1) $\frac{2}{5}H$

(2) $\frac{4}{5}H$

(3) $\frac{5}{4}H$

(4) 1 H

In the figure magnetic energy stored in the coil is:

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 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: