A \(40\) $\mathrm{\mu }$F capacitor is connected to a \(200\) V, \(50\) Hz AC supply. The rms value of the current in the circuit is, nearly:
1. \(2.05\) A
2. \(2.5\) A
3. \(25.1\) A
4. \(1.7\) A

An AC voltage source is connected to a series \(LCR\) circuit. When \(L\) is removed from the circuit, the phase difference between current and voltage is \(\frac{\pi}{3}\). If \(C\) is instead removed from the circuit, the phase difference is again \(\frac{\pi}{3}\) between current and voltage. The power factor of the circuit is:
1. \(0.5\)
2. \(1.0\)
3. \(-1.0\)
4. zero

A light bulb and an inductor coil are connected to an AC source through a key as shown in the figure below. The key is closed and after some time an iron rod is inserted into the interior of the inductor. The glow of the light bulb:

A circuit when connected to an AC source of \(12~\text{V}\) gives a current of \(0.2~\text{A}\). The same circuit when connected to a DC source of \(12~\text{V}\), gives a current of \(0.4~\text{A}\). The circuit is:
1. series \({LR}\)
2. series \({RC}\)
3. series \({LC}\)
4. series \({LCR}\)

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

(a)	(b)
(c)	(d)

The instantaneous values of alternating current and voltages in a circuit are given as,
\(i=\frac{1}{\sqrt{2}}\sin\left ( 100\pi t \right )~\text{Ampere}\)
\(e=\frac{1}{\sqrt{2}}\sin\left ( 100\pi t+\pi /3 \right )~\text{Volt}\)
What is the average power consumed by the circuit in watts?

The r.m.s. value of the potential difference V shown in the figure is:

1. ${\mathrm{V}}_0/\sqrt{3}$

2. ${\mathrm{V}}_0$

3. ${\mathrm{V}}_0/\sqrt{2}$

4. ${\mathrm{V}}_0/2$

A coil has a resistance of \(30~ \mathrm{ohm}\) and inductive reactance of \(20 ~\mathrm{ohm}\) at a \(50~\mathrm{ Hz}\) frequency. If an \(\mathrm{ac}\) source of \(200 ~\mathrm{volts,}\) \(100~\mathrm{ Hz}\) is connected across the coil, the current in the coil will be:

The value of the quality factor is:
1. $\frac{\omega L}{R}$

2. $\frac{\omega }{RC}$

3. $\sqrt{LC}$

4. L/R

In a circuit \(L\), \(C\), and \(R\) are connected in series with an alternating voltage source of frequency \(f\). The current leads the voltage by \(45^\circ\). The value of \(C\) is:
1. \(\frac{1}{2 \pi f(2 \pi f L-R)}\)
2. \(\frac{1}{2\pi f(2 \pi f L+R)}\)
3. \(\frac{1}{ \pi f(2 \pi f L-R)}\)
4. \(\frac{1}{\pi f(2 \pi f L+R)}\)