A coil of self-inductance \(L\) is connected in series with a bulb \(\mathrm{B}\) and an AC source. The brightness of the bulb decreases when:

1.	number of turns in the coil is reduced.
2.	a capacitance of reactance \(X_C = X_L\) is included in the same circuit.
3.	an iron rod is inserted in the coil.
4.	frequency of the AC source is decreased.

The current (\(I\)) in the inductance is varying with time (\(t\)) according to the plot shown in the figure. 

          
Which one of the following is the correct variation of voltage with time in the coil?

1.		2.
3.		4.

The current \(i\) in a coil varies with time as shown in the figure. The variation of induced emf with time would be:
     

1.		2.
3.		4.

A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of 2 mm/s. The induced e.m.f. in the loop when the radius is 2 cm is:

1. \(3.2\pi ~\mu V\)

2. \(4.8\pi ~\mu V\)

3. \(0.8\pi ~\mu V\)

4. \(1.6\pi ~\mu V\)

A rectangular, a square, a circular, and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity, $\overrightarrow{\mathrm{v}}=\mathrm{v}\hat{\mathrm{i}}$. The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops out of the field region, will not remain constant for:

The primary and secondary coils of a transformer have \(50\) and \(1500\) turns respectively. If the magnetic flux \(\phi\) linked with the primary coil is given by \(\phi=\phi_0+4t,\) where \(\phi\) is in Weber, \(t\) is time in seconds, and \(\phi_0\)  is a constant, the output voltage across the secondary coil is:
1. \(90~\mathrm{V}\)
2. \(120~\mathrm{V}\)
3. \(220~\mathrm{V}\)
4. \(30~\mathrm{V}\)

Two coils of self-inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:

1. 10 mH

2. 6 mH

3. 4 mH

4. 16 mH

In which of the following devices, the eddy current effect is not used?

A \(800\) turn coil of effective area \(0.05~\text{m}^2\) is kept perpendicular to a magnetic field \(5\times 10^{-5}~\text{T}\). When the plane of the coil is rotated by \(90^{\circ}\)$$around any of its coplanar axis in \(0.1~\text{s}\), the emf induced in the coil will be:
1. \(0.02~\text{V}\)
2. \(2~\text{V}\)
3. \(0.2~\text{V}\)
4. \(2\times 10^{-3}~\text{V}\)