Average power in the $L-C-R$ circuit depends upon

Define the power for $AC$ circuit. Obtain an equation of average power for $L-C-R$ series $AC$ circuit.

In an $AC$ circuit,the $emf$ $(e)$ and the current $(i)$ at any instant are given respectively by:
$e = E_{0} \sin \omega t$
$i = I_{0} \sin (\omega t - \phi)$
The average power in the circuit over one cycle of $AC$ is:

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

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 a series $R-L$ circuit is given by $\cos \theta = \frac{2R}{\sqrt{R^2 + \omega^2 L^2}}$.

The instantaneous values of current and potential difference in an alternating circuit are $i = \sin \omega t$ and $E = 100 \cos \omega t$ respectively. The $r.m.s.$ value of the wattless current (in $A$) in the circuit is: