MHTCET 11 May 2024 Shift 1 Paper

Concept:Mutual induction gives the induced e.m.f. in the secondary coil when the current in the primary coil changes with time.Explanation:The induced e.m.f. is given by the formula:$$\varepsilon = M \frac{\Delta I}{\Delta t}$$Here, $M$ is the mutual inductance, $\Delta I$ is the change in primary current, and $\Delta t$ is the time interval.Given values:$$M = 2\ \mathrm{H}, \quad \varepsilon = 2\ \mathrm{kV} = 2000\ \mathrm{V}$$The current in the primary changes from $6\ \mathrm{A}$ to $3\ \mathrm{A}$, so:$$\Delta I = 6 - 3 = 3\ \mathrm{A}$$Substituting into the formula using magnitude only:$$2000 = 2 \times \frac{3}{\Delta t}$$Rearrange to solve for $\Delta t$:$$\Delta t = \frac{2 \times 3}{2000} = \frac{6}{2000}$$$$\Delta t = 0.003\ \mathrm{s}$$In scientific notation:$$\Delta t = 3 \times 10^{-3}\ \mathrm{s}$$Answer:The time required for the change in current is $3 \times 10^{-3}\ \mathrm{s}$.Therefore, the correct option is A.