The power factor of the circuit as shown in the figure is:

In an $A.C.$ circuit,the instantaneous values of $\text{e.m.f}.$ and current are $e = 10 \sin(50 \pi t) \text{ V}$ and $I = 10 \sin(50 \pi t + \frac{\pi}{3}) \text{ A}$. The average power consumed in the circuit is $... \text{ W}$.

In an $A$.$C$. circuit,the potential difference $V$ and current $I$ are given respectively by $V = 100 \sin(100t) \text{ V}$ and $I = 100 \sin(100t + \frac{\pi}{3}) \text{ mA}$. The power dissipated in the circuit will be (Given: $\cos \frac{\pi}{3} = \frac{1}{2}$)

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 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:

$A$ sinusoidal $AC$ current passes through a resistor of resistance $R$ in an $LCR$ series circuit. If the phase difference between the supplied voltage and the supplied current is $\theta$ and the peak value of the supplied current is $I_0$,then the power dissipated in the circuit is: