An alternating current is given as \(i = i_1\cos\omega t- i_2 \sin \omega t.\) The value of rms current is given by:
1. \( \frac{1}{\sqrt{2}}\left(i_1+i_2\right) \)
2. \( \frac{1}{\sqrt{2}}\left(i_i+i_2\right)^2 \)
3. \( \frac{1}{\sqrt{2}}\left(i_1^2+i_2^2\right)^{1 / 2} \)
4. \( \frac{1}{2}\left(i_1^2+i_2^2\right)^{1 / 2}\)

In an ac circuit, the current is given by \(i=5\sin(100t-\frac{\pi}{2})\) and the ac potential is \(V =200\sin(100 t)\) volt. The power consumption is:
1. \(20\) W
2. \(40\) W
3. \(1000\) W
4. \(0\)

In an \(LCR\) circuit having \(L = 8.0~\text{H}\), \(C= 0.5~\mu\text{F}\) and \(R = 100~\Omega\) in series, what is the resonance frequency?
1. \(600\) radian/sec
2. \(600\) Hz
3. \(500\) radian/sec
4. \(500\) Hz

A circuit consists of \(3\) ohms of resistance and \(4\) ohms of reactance. The power factor of the circuit is:
1. \(0.4\)
2. \(0.6\)
3. \(0.8\)
4. \(1.0\)

The power factor of a good choke coil is:

1. Nearly zero

2. Exactly zero

3. Nearly one

4. Exactly one

In a series \(LCR\) circuit, resistance \(R=10~\Omega\) and the impedance \(Z=20~\Omega\). The phase difference between the current and the voltage will be:
1. \(30^{\circ}\)
2. \(45^{\circ}\)
3. \(60^{\circ}\)
4. \(90^{\circ}\)