(a) (i) A series combination of $L$, $C$ and $R$ is connected to an ac source $V = V_m \sin \omega t$. Obtain : (I) the impedance of the circuit using phasor diagram, (II) the expression for the instantaneous current $I$, and (III) the phase relationship of current to the applied voltage. (ii) Define power factor of an ac circuit. State the conditions under which it is : (I) maximum, (II) minimum. OR (b) (i) Prove that the voltage is ahead of the current in phase by $\frac{\pi}{2} ext{ rad}$ in an ac circuit containing an ideal inductor. (ii) The currents through two inductors of self-inductance $12 ext{ mH}$ and $24 ext{ mH}$ are increasing with time at the same rate. Draw graphs showing the variation of the : (I) magnitude of emf induced with the rate of change of current in each inductor. (II) energy stored in each inductor with the current flowing through it.