The power factor of an $AC$ circuit containing peak current $2 \ A$ and peak voltage $1 \ V$ is $1/2$. The angle between voltage and current is: (in $^{\circ}$)

Assertion $(A):$ If the frequency of the applied $AC$ is doubled,then the power factor of a series $R-L$ circuit decreases.
Reason $(R):$ Power factor of series $R-L$ circuit is given by $\cos \theta = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$.

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 $...... \text{ W}$.

Power factor of an ideal choke coil (i.e.,$R=0$) is

In an $AC$ circuit,the current flowing is $I=5 \sin \left(100 t-\frac{\pi}{2}\right) A$ and the potential difference is $e=200 \sin (100 t) V$. The power consumption is equal to (in $W$)

Power consumed in an $AC$ circuit becomes zero if