In an $A.C.$ circuit,the current flowing in an inductance is $I = 5\,\sin\,(100\,t - \pi/2)\,A$ and the potential difference is $V = 200\,\sin\,(100\,t)\,V$. The power consumption is equal to......$W$.

$(a)$ 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.

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 $W$.

The average power dissipated in an $A.C.$ circuit is $2 \ W$. If the current flowing through the circuit is $2 \ A$ and the impedance is $1 \ \Omega$,what is the power factor of the $A.C.$ circuit?

An alternating voltage of $V = V_{0} \sin \omega t$ is applied across a circuit. As a result, a current $I = I_{0} \sin (\omega t - \frac{\pi}{2})$ flows in it. The power consumed per cycle is . . . . . . .

Average power in the $L-C-R$ circuit depends upon