In an electrical circuit \(R,\) \(L,\) \(C\) and an \(\mathrm{AB}\) 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. \(\sqrt{3} / 2\)

An inductor of \(20~\text{mH}\), a capacitor of \(100~\mu \text{F}\), and a resistor of \(50~\Omega\) are connected in series across a source of emf, \(V=10 \sin (314 t)\). What is the power loss in this circuit?
1. \( 0.79 ~\text{W} \)
2. \( 0.43 ~\text{W} \)
3. \( 2.74 ~\text{W} \)
4. \( 1.13 ~\text{W}\)

An AC source rated \(100~\mathrm{V}\) (rms) supplies a current of \(10~\mathrm{A}\) (rms) to a circuit. The average power delivered by the source:

Choose the correct option:

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

For a series \(\mathrm{LCR}\) circuit, the power loss at resonance is:
1. \(\frac{V^2}{\left[\omega L-\frac{1}{\omega C}\right]}\)

2. \( \mathrm{I}^2 \mathrm{~L} \omega \)

3. \(I^2 R\)

4. \( \frac{\mathrm{V}^2}{\mathrm{C} \omega} \)