A rod of length l rotates with uniform angular velocity $\mathrm{\omega }$ about an axis passing through its one end and perpendicular to its length. If a uniform magnetic field exists perpendicular to the axis of rotation, then induced emf across the two ends of the rod is :

1. $\frac{1}{2}B\omega l^2$

2. $B\omega l^2$

3. $\mathit{2}\mathit{ }B\omega l^2$

4. zero

Energy stored in an inductor can be made four times when

1. inductance is doubled

2. Current is made $\sqrt{2}$ times

3. current is doubled

4. can never to be made

The current passing through a choke coil of 5 H is decreasing at the rate of 3 As^-1. The emf induced in the coil is 

1. 15 V

2. -15 V

3. $\frac{5}{3}V$

4. $\frac{-5}{3}V$

If all linear dimensions of an inductor are tripled, then self-inductance will become (keeping the total number of turns per unit length constant)

1.  3 times

2.  9 times

3.  27 times

4. 1/3 times

A coil of resistance 20$\Omega$ and inductance 5H has been connected to a 200 V battery. The maximum energy stored in the coil is

1. 250 J

2. 125 J

3. 500 J

4. 100 J

A small square loop of wire of side l is placed inside a large square of wire of side L (L>>l). The loops are co-planar and their centres coincide. The mutual inductance of the system is proportional to :

1. l/L

2. ${\mathrm{l}}^2/\mathrm{L}$

3. L/l

4. ${\mathrm{L}}^2/\mathrm{l}$

The key \(K\) is inserted at time \(t=0\). The initial \((t=0)\) and final \(t\rightarrow \infty\) currents through the battery are:
                              

1. \(\frac{1}{15}~\text{A},~\frac{1}{10}~\text{A}\)
2. \(\frac{1}{10}~\text{A},~\frac{1}{15}~\text{A}\)
3. \(\frac{2}{15}~\text{A},~\frac{1}{10}~\text{A}\)
4. \(\frac{1}{15}~\text{A},~\frac{2}{25}~\text{A}\)

Two coils have a mutual inductance of 5 mH. Current changes in the first coil according to the equation I = $I_0$cos wt, where $I_0$ = 10 A and $\mathrm{\omega } = 100\mathrm{\pi }$ rad/s. Maximum value of e.m.f. induced in the second coil is

1.  5$\pi$ volt

2.   2$\pi$ volt

3.  4$\pi$ volt

4.  $\pi$ volt

The current through a choke coil increases from zero to 6 A in 0.3 seconds and an induced emf of 30 V is produced. The inductance of the coil is

1.  5 H

2.  2.5 H

3.  1.5 H

4.  2 H

Lenz's law is a consequence of the law of conservation of 

1. Charge

2. Momentum

3. Mass

4. Energy