Question

Two coils are placed near each other. When the current in one coil is changed at the rate of 5 A/s, an emf of 2 mV is induced in the other. The mutual inductance of the two coils is:

• A. 0.4 mH
• B. 25 mH
• C. 10 mH
• D. 25 H \bigskip

Hint:

The mutual inductance is calculated using the formula \( \mathcal{E} = M \frac{dI}{dt} \), where the induced emf is proportional to the rate of change of current.

Answer 1

The Correct Option is A

The induced emf \( \mathcal{E} \) in a coil due to a changing current in a nearby coil is related to the mutual inductance \( M \) by the formula:
\[ \mathcal{E} = M \frac{dI}{dt} \] where: - \( \mathcal{E} = 2 \, \text{mV} = 2 \times 10^{-3} \, \text{V} \) is the induced emf, - \( \frac{dI}{dt} = 5 \, \text{A/s} \) is the rate of change of current. Rearranging to solve for \( M \):
\[ M = \frac{\mathcal{E}}{\frac{dI}{dt}} = \frac{2 \times 10^{-3} \, \text{V}}{5 \, \text{A/s}} = 4 \times 10^{-4} \, \text{H} = 0.4 \, \text{mH} \] Thus, the mutual inductance of the two coils is \( M = 0.4 \, \text{mH} \). \bigskip