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

A coil of inductive reactance of \(31~\Omega\) has a resistance of \(8~\Omega\). It is placed in series with a condenser of capacitive reactance \(25~\Omega\). The combination is connected to an AC source of \(110\) V. The power factor of the circuit is:
1. \(0.56\)
2. \(0.64\)
3. \(0.80\)
4. \(0.33\)

The power factor of the given circuit is:
             

The potential differences across the resistance, capacitance and inductance are \(80\) V, \(40\) V and \(100\) V respectively in an \(LCR\) circuit. What is the power factor of this circuit?
1. \(0.4\)
2. \(0.5\)
3. \(0.8\)
4. \(1.0\)

An inductor of inductance \(L\) and resistor of resistance \(R\) are joined in series and connected by a source of frequency \(\omega\). The power dissipated in the circuit is:
1. \(\dfrac{\left( R^{2} +\omega^{2} L^{2} \right)}{V}\)

2. \(\dfrac{V^{2} R}{\left(R^{2} + \omega^{2} L^{2} \right)}\)

3. \(\dfrac{V}{\left(R^{2} + \omega^{2} L^{2}\right)}\)

4. \(\dfrac{\sqrt{R^{2} + \omega^{2} L^{2}}}{V^{2}}\)

A circuit consists of \(3\) ohms of resistance and \(4\) ohms of reactance. The power factor of the circuit is: