(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.

Year	Paper Code	Set	Position
CBSE 2025	Series Other	Set 1	Question 31
CBSE 2025	Series Other	Set 1	Question 32
CBSE 2025	Series Other	Set 1	Question 33

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)