MHTCET 17 Apr 2026 Shift 1 Paper

Concept:The power supplied to an inductor and the energy stored in it both depend on the inductance and the current flowing through it.Explanation:For an inductor, the instantaneous power is given by$$P = L i \frac{di}{dt}$$Both coils have the same constant rate of increase of current, so their $\frac{di}{dt}$ values are equal.Since the power dissipated in both coils is the same,$$L_{1} i_{1} \frac{di}{dt} = L_{2} i_{2} \frac{di}{dt}$$Cancelling $\frac{di}{dt}$ from both sides,$$L_{1} i_{1} = L_{2} i_{2}$$Therefore,$$\frac{i_{1}}{i_{2}} = \frac{L_{2}}{L_{1}}$$The energy stored in an inductor is$$U = \frac{1}{2} L i^{2}$$Hence, the ratio of stored energies is$$\frac{U_{1}}{U_{2}} = \frac{L_{1} i_{1}^{2}}{L_{2} i_{2}^{2}}$$Substituting the current ratio,$$\frac{U_{1}}{U_{2}} = \frac{L_{1}}{L_{2}} \left(\frac{L_{2}}{L_{1}}\right)^{2} = \frac{L_{2}}{L_{1}}$$Answer:$$\frac{U_{1}}{U_{2}} = \frac{L_{2}}{L_{1}}$$Therefore, the correct option is D, $\frac{L_{2}}{L_{1}}$.