$A$ lamp consumes only $50 \%$ of maximum power in an $AC$ circuit. What is the phase difference between the applied voltage and the circuit current?

The coefficient of induction of a choke coil is $0.1\,H$ and resistance is $12\,\Omega$. If it is connected to an alternating current source of frequency $60\,Hz$,then the power factor will be:

In an $AC$ circuit,the voltage and current are described by $V = 200 \sin(314t - \frac{\pi}{6}) \text{ V}$ and $i = 50 \sin(314t + \frac{\pi}{6}) \text{ mA}$ respectively. The average power dissipated in the circuit is $...... \text{ W}$.

In an $AC$ circuit,the instantaneous values of emf and current are $e = 200 \sin(314t) \text{ V}$ and $I = \sin(314t + \frac{\pi}{3}) \text{ A}$. The average power consumed in watt is

Current in the circuit is wattless, if

The current and voltage functions in an $AC$ circuit are:
$I = 100 \sin(100t) \, mA$
$V = 100 \sin(100t + \frac{\pi}{3}) \, V$
The power dissipated in the circuit is ...... $W$.