A coil of self-inductance L is connected in series with a bulb 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 figure shows a circuit that contains three identical resistors with resistance R = 9.0$\Omega$ each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf $\epsilon =18$. The current 'i' through the battery just after the switch closed is:

1. 0.2A

2. 2A

3. 4 A

4. 2mA

A coil of inductive reactance of \(31~\Omega\) has a resistance of \(8~\Omega\). It is placed in series with a condenser of capacitive reactance \(25~\Omega\). The combination is connected to an AC source of \(110\) V. The power factor of the circuit is:
1. \(0.56\)
2. \(0.64\)
3. \(0.80\)
4. \(0.33\)

If the current through the resistor is \(I\) and the voltage across the capacitor is \(V\), then:
1. \(V_a < V_b\)
2. \(V_a > V_b\)
3. \(i_a > i_b\)
4. \(V_a = V_b\)

In an electrical circuit R, L, C, and an AC voltage source are all connected in series. When L is removed from the circuit, the phase difference between the voltage and the current in the circuit is ${\tan }^{-1}\sqrt{3}$. If instead, C is removed from the circuit, the phase difference is again ${\tan }^{-1}\sqrt{3}$. The power factor of the circuit is:

1. 1/2 

2. $1/\sqrt{2}$

3. 1

4. $\sqrt{3}/2$

In an AC circuit, the emf (e) and the current (I) at any instant are given respectively by 
e = E₀sin wt 
I = I₀ sin $\left(\omega t-\varphi \right)$ 
The average power in the circuit over one cycle of AC is:

1.  $\frac{{\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}}{2}$

2.  $\frac{{\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}}{2} \sin \mathrm{\varphi }$

3.  $\frac{{\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}}{2} \cos \mathrm{\varphi }$

4.  ${\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}$

The variation of EMF with time for four types of generators are shown in the figures. Which amongst them can be called AC?

(1) (a) and (d)

(2) (a), (b), (c), (d)

(3) (a) and (b)

(4) only (a)

In an LR-circuit, the inductive reactance is equal to the resistance R of the circuit. An e.m.f. $E=E_0\cos \left(\omega t\right)$ applied to the circuit. The power consumed in the circuit is:

(1) $\frac{E_0^2}{R}$

(2) $\frac{E_0^2}{2R}$

(3) $\frac{E_0^2}{4R}$

(4) $\frac{E_0^2}{8R}$