(a) (i) Define self-inductance of a coil. Derive the expression for the energy required to build up a current $I$ in a coil of self-inductance $L$. (ii) The currents passing through two inductors of self-inductances $10\text{ mH}$ and $20\text{ mH}$ increase with time at the same rate. Draw graphs showing the variation of : (I) the magnitude of emf induced with the rate of change of current in each inductor. (II) the energy stored in each inductor with the current flowing through it. OR (b) (i) Define the term mutual inductance. Deduce the expression for the mutual inductance of two long coaxial solenoids of the same length having different radii and different number of turns. (ii) The current through an inductor is uniformly increased from zero to $2\text{ A}$ in $40\text{ s}$. An emf of $5\text{ mV}$ is induced during this period. Find the flux linked with the inductor at $t = 10\text{ s}$.

Year	Paper Code	Set	Position
CBSE 2025	Series 55-5	Set 1	Question 32
CBSE 2025	Series 55-5	Set 2	Question 31
CBSE 2025	Series 55-5	Set 3	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)