Physics

Physics

Problem

When the current in the primary circuit of two coupled coils changes uniformly from 3 A3\,\text{A} to 1 A1\,\text{A} in 0.010 s0.010\,\text{s}, an electromotive force of 2.5 V2.5\,\text{V} is induced in the secondary. Determine the mutual inductance between the coils.
Intuitive explanation

Mutual inductance describes how a changing current in one coil induces a voltage in another—it's the core of transformer action. The key insight is that the induced EMF in the secondary depends only on how fast the current is changing in the primary, not on the current values themselves. Use Faraday's law for mutual inductance: E=MdIdt\mathcal{E} = M\frac{dI}{dt}, where MM is what you're solving for and dIdt\frac{dI}{dt} is the rate of current change.

Intuitive explanation

Mutual inductance describes how a changing current in one coil induces a voltage in another—it's the core of transformer action. The key insight is that the induced EMF in the secondary depends only on how fast the current is changing in the primary, not on the current values themselves. Use Faraday's law for mutual inductance: E=MdIdt\mathcal{E} = M\frac{dI}{dt}, where MM is what you're solving for and dIdt\frac{dI}{dt} is the rate of current change.

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