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.

Choose the correct option for the above statements:

An aeroplane in which the distance between the tips of wings is 50 m is flying horizontally with a speed of 360 km/hr over a place where the vertical component of earth magnetic field is $2.0\times {10}^{-4}$ $\mathrm{weber}/{\mathrm{m}}^2$. The potential difference between the tips of wings would be:

The current in a coil varies with time t as $\mathrm{I}$ $=$ $3{\mathrm{t}}^2+$ $2\mathrm{t}$. If the inductance of coil be 10 mH, the value of induced e.m.f. at \(t=2~\mathrm{s}\) will be:
1. \(0.14~\mathrm{V}\)
2. \(0.12~\mathrm{V}\)
3. \(0.11~\mathrm{V}\)
4. \(0.13~\mathrm{V}\)

A coil having an area $A_0$ is placed in a magnetic field which changes from $B_0$ $to$ $4B_0$ in time interval t. The average EMF induced in the coil will be:

1. $\frac{3A_0{B}_0}{t}$

2. $\frac{4A_0{B}_0}{t}$

3. $\frac{3B_0}{A_{0}t}$

4. $\frac{4B_0}{A_{0}t}$

An electric potential difference will be induced between the ends of the conductor shown in the diagram when the conductor moves in the direction of:

1. P
2. Q
3. L
4. M

The number of turns in a coil of wire of fixed radius & length is 600 and its self-inductance is 108 mH. The self-inductance of a coil of 500 turns will be:

1.  74 mH

2.  75 mH

3.  76 mH

4.  77 mH

A circular disc of radius 0.2 m is placed in a uniform magnetic field of induction $\frac{1}{\pi }$ $\left(\frac{Wb}{m^2}\right)$ in such a way that its axis makes an angle of ${60}^{°}$ with $\overrightarrow{B}$. The magnetic flux linked to the disc will be:
1. 0.02 Wb
2. 0.06 Wb
3. 0.08 Wb
4. 0.01 Wb

A magnetic rod is inside a coil of wire which is connected to an ammeter. If the rod is stationary, which of the following statements is true?

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