In an $AC$ circuit,current is $3 \ A$,voltage is $210 \ V$,and power is $63 \ W$. The power factor is . . . . . . .

In an $AC$ circuit,$V$ and $I$ are given below. Find the power dissipated in the circuit:
$V = 50 \sin(50t) \ V$
$I = 50 \sin(50t + \frac{\pi}{3}) \ mA$ (in $W$)

Two electric circuits $A$ and $B$ are shown in the figure. The ratio of power factor of circuit $B$ to that of circuit $A$ is

In an $LCR$ series circuit,an alternating e.m.f. '$e$' and current '$i$' are given by the equations $e = 160 \sin(100t) \text{ V}$ and $i = 250 \sin(100t + \frac{\pi}{3}) \text{ mA}$. The average power dissipated in the circuit is: (in $\text{ W}$)

In an $A.C.$ circuit containing $L$, $C$ and $R$ in series, the ratio of apparent power to the true power is ($Z=$ impedance of the circuit and $R=$ resistance).

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 $\cos \theta = \frac{2R}{\sqrt{R^2 + \omega^2 L^2}}$.