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

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:

$A$ 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:

$(a)$ For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain.
$(b)$ Power factor can often be improved by the use of a capacitor of appropriate capacitance in the circuit. Explain.

If the power factor in a circuit is unity,then the impedance of the circuit is

In an $AC$ circuit,$V$ and $I$ are given by $V = 150 \sin(150t) \, V$ and $I = 150 \sin(150t + \frac{\pi}{3}) \, A$. The power dissipated in the circuit is ....... $W$.