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 \(\dfrac{\pi}{3}\). If \(C\) is instead removed from the circuit, the phase difference is again \(\dfrac{\pi}{3}\) 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:

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)

An inductor of inductance \(L\), a capacitor of capacitance \(C\) and a resistor of resistance \(R\) are connected in series to an AC source of potential difference \(V\) volts as shown in Figure. The potential difference across \(L\), \(C\) and \(R\) is \(40~\text{V}\), \(10~\text{V}\) and \(40~\text{V}\), respectively. The amplitude of the current flowing through the \(LCR\) series circuit is \(10\sqrt{2}~\text{A}\). The impedance of the circuit will be:

1. \(4~\Omega\)
2. \(5~\Omega\)
3. \(4\sqrt{2}~\Omega\)
4. \(\dfrac{5}{\sqrt{2}}~\Omega\)

A series \(LCR\) circuit containing \(5.0~\text{H}\) inductor, \(80~\mu \text{F}\) capacitor and \(40~\Omega\)$\mathrm{}$ resistor is connected to \(230~\text{V}\) variable frequency AC source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be: