Discussion
The mutual inductance between a pair of coils is 3 H. If the current in one coil changes from 0 A to 2 A in 0.5 s, the induced emf produced in the other coil is
Answer: D
The induced emf is 12 V.
\[ \begin{aligned} e &= M\frac{dI}{dt} = 3 \times \frac{2 - 0}{0.5} \\ &= 3 \times 4 = 12\ \text{V} \end{aligned} \]
6 V is M times the change in current, without dividing by the 0.5 s over which it changes.
The emf in the second coil depends on the rate of change of current in the first, not on the current itself, so once the current stops changing at 2 A the induced emf falls to zero. The 12 V is its value while the current is rising at a steady 4 A/s.
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