In an $a.c.$ circuit,voltage and current are given by: $V=100 \sin (100 t) \ V$ and $I=100 \sin (100 t + \frac{\pi}{3}) \ mA$ respectively. The average power dissipated in one cycle is: (in $W$)

The power factor of the circuit as shown in the figure 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.

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

In an $AC$ circuit,the current is $i = 5 \sin(100t - \frac{\pi}{2}) \ A$ and the voltage is $e = 200 \sin(100t) \ V$. The power consumption in the circuit is (given $\cos 90^{\circ} = 0$): (in $W$)

$A$ capacitor $C = 2 \mu F$ and an inductor with $L = 10 H$ and coil resistance $R = 5 \Omega$ are connected in series in a circuit. When an alternating current of $r.m.s.$ value $I_{rms} = 2 A$ flows in the circuit,the average power in watts in the circuit is: