In an ac circuit, the instantaneous e.m.f. and current are given by
\(\begin{aligned} & e=100 \sin 30 t \\ & i=20 \sin \left(30 t-\frac{\pi}{4}\right) \end{aligned}\)
In one cycle of ac, the average power consumed by the circuit and the wattless current are, respectively:
1. \(50, 10\)
2. \(\frac{1000}{\sqrt{2}},10\)
3. \(\frac{50}{\sqrt{2}},0\)
4. \(50,0\)

For an \(LCR\) circuit driven with voltage of amplitude \(V_m\) and frequency \(\omega_0=\frac{1}{\sqrt{LC}}\) the current exhibits resonance. The quality factor, \(Q\) is given by:
1. \(\frac{\omega_0 L}{R}\)
2. \(\frac{\omega_0R}{L}\)
3. \(\frac{R}{\omega_0C}\)
4. \(\frac{CR}{\omega_0}\)

An alternating voltage \(V(t)=220 \sin 100 \pi t~\text{volts}\) is applied to a purely resistive load of \(50~\mathrm{\Omega}.\) The time taken for the current to rise from half of the peak value to the peak value is:
1. \(5~\text{ms}\)
2. \(7.2~\text{ms}\)
3. \(3.3~\text{ms}\)
4. \(2.2~\text{ms}\)

A circuit connected to an AC source of emf \(\varepsilon=\varepsilon_0\sin(100t)\) with \(t\) in seconds, gives a phase difference of \(\frac{\pi}{4}\) between the emf \(\varepsilon\) and current \(i\). Which of the following circuits will exhibit this?

A transformer consisting of \(300\) turns in the primary and \(150\) turns in the secondary gives output power of \(2.2~\text{kW}.\) If the current in the secondary coil is \(10~\text{A},\) then the input voltage and current in the primary coil are:
1. \(440~\text{V}~\text{and}~20~\text{A}\)
2. \(440~\text{V}~\text{and}~5~\text{A}\)
3. \(220~\text{V}~\text{and}~20~\text{A}\)
4. \(220~\text{V}~\text{and}~10~\text{A}\)