The current in an inductor of self-inductance \(4\) H changes from \(4\) A to \(2\) A in \(1\) s. The e.m.f. induced in the coil is:
1. \(-2\) V
2. \(2\)  V
3. \(-4\) V
4. \(8\) V

The dimensions of mutual inductance (M) are:
1. [M²LT^-2A^-2]
2. [MLT^-2A²]
3. [M²L²T^-2A²]
4. [ML²T^-2A^-2]

An inductor coil of self-inductance \(10\) H carries a current of \(1\) A. The magnetic field energy stored in the coil is:
1. \(10\) J
2. \(2.5\) J
3. \(20\) J
4. \(5\) J

Two conducting circular loops of radii ${\mathrm{R}}_1 \mathrm{and} {\mathrm{R}}_2$ are placed in the same plane with their centres coinciding. If ${\mathrm{R}}_1>>{\mathrm{R}}_2$, the mutual inductance M between them will be directly proportional to:

1. $\frac{{\mathrm{R}}_1^2}{{\mathrm{R}}_2}$

2. $\frac{{\mathrm{R}}_2^2}{{\mathrm{R}}_1}$

3. $\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$

4. $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}$

The magnetic flux linked with a coil (in Wb) is given by the equation \(\phi=5 t^2+3 t+60\). The magnitude of induced emf in the coil at \(t=4\) s  will be:
1. \(33\) V
2. \(43\) V
3. \(108\) V
4. \(10\) V