MHTCET 18 Apr 2026 Shift 1 Paper

Concept: The magnetic potential energy stored in an inductor is the work done in establishing the current through it, given by $U = \frac{1}{2} L I^2$.Explanation:From the given data, the stored energy is $U = 49\ \mathrm{mJ} = 49 \times 10^{-3}\ \mathrm{J}$.The current is $I = 70\ \mathrm{mA} = 70 \times 10^{-3}\ \mathrm{A}$.The energy formula for an inductor is $U = \frac{1}{2} L I^2$.Rearrange the formula to express inductance $L$:$$L = \frac{2U}{I^2}$$Substitute the known values of $U$ and $I$ into this equation:$$L = \frac{2 \times 49 \times 10^{-3}}{(70 \times 10^{-3})^2}$$Simplify the numerator: $2 \times 49 \times 10^{-3} = 98 \times 10^{-3}$.Simplify the denominator: $(70 \times 10^{-3})^2 = 4900 \times 10^{-6}$.Now compute the inductance:$$L = \frac{98 \times 10^{-3}}{4900 \times 10^{-6}} = 20\ \mathrm{H}$$Therefore, the inductance of the inductor is $20\ \mathrm{H}$.Answer: Option C: $20\ \mathrm{H}$