In an $ac$ circuit with voltage $V$ and current $I$,the power dissipated 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.

In an $A.C.$ circuit,$V$ and $I$ are given by:
$V = 100 \sin(100 t) \text{ V}$
$I = 100 \sin(100 t + \pi/3) \text{ mA}$
The power dissipated in the circuit is:

The current and voltage functions in an $AC$ circuit are:
$I = 100 \sin(100t) \, mA$
$V = 100 \sin(100t + \frac{\pi}{3}) \, V$
The power dissipated in the circuit is ...... $W$.

What will be the phase difference between virtual voltage and virtual current when current in the circuit is wattless (in $^{\circ}$)?

$A$ 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: