In an $ac$ circuit with voltage $V$ and current $I$,the power dissipated 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 series $R-L$ circuit is given by $\cos \theta = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$.

The $r.m.s.$ current in an $ac$ circuit is $2 \ A$. If the wattless current is $\sqrt{3} \ A$,the power factor is:

$A$ series $LCR$ circuit is connected to an $AC$ source of $220\,V, 50\,Hz$. The circuit contains a resistance $R = 80\,\Omega$,an inductor of inductive reactance $X_L = 70\,\Omega$,and a capacitor of capacitive reactance $X_C = 130\,\Omega$. The power factor of the circuit is $\frac{x}{10}$. The value of $x$ is:

In an $ac$ circuit,the power factor

In an $A.C.$ circuit,the $e.m.f.$ $(\varepsilon)$ and the current $(i)$ at any instant are given respectively by $E = E_o \sin \omega t$ and $i = I_o \sin(\omega t - \phi)$. The average power in the circuit over one cycle of $A.C.$ is: