Voltage across an inductor

From the relation $\Phi_B^\text{self} = L\,i$ and Faraday’s law we immediately obtain the voltage that appears across an inductor when the current changes.

Voltage across an inductor

The potential difference across an inductor carrying a current $i(t)$ is: $\ev{V_L = -L\,\frac{di}{dt}}$

The minus sign means that the inductor opposes changes in current: it is the electrical analogue of inertia. If the current tries to increase, the inductor generates a voltage that brakes it; if it tries to decrease, the inductor generates a voltage that sustains it. In both cases the inductor works against the change.

This is why the current in a circuit containing an inductor cannot change instantaneously: it would require an infinite $di/dt$, and hence an infinite voltage. The inductor “smooths out” changes in current, just as a mass smooths out changes in velocity.

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Topics: Electromagnetic induction Concepts: Inductance and self-induction

Related exercises: Problem — Energy in a solenoid’s field · Problem — Graphs of self-induction · RL transient: the time constant