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 $W$)

Define the power for $AC$ circuit. Obtain an equation of average power for $L-C-R$ series $AC$ circuit.

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 $ac$ circuit with voltage $V$ and current $I$,the power dissipated is

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 $W$)

$(a)$ 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.