6.2 Inductance

What is inductance?

Inductance (L) measures a circuit element's opposition to changes in current, arising from induced EMF via Faraday's Law: EMF = -L(dI/dt). Measured in henries (H), inductance depends on geometry (coil turns, area, length) — for a solenoid, L = μ₀N²A/ℓ. A larger L means a bigger induced EMF opposing current changes.

Energy stored in an inductor

Like a capacitor stores energy in an electric field, an inductor stores energy in its magnetic field: U = ½LI². This energy is released as current decreases. Inductors resist sudden current changes, making them essential in circuits requiring smooth current flow, like LR circuits.

Mutual inductance

Mutual inductance (M) occurs when a changing current in one coil induces an EMF in a nearby coil: EMF₂ = -M(dI₁/dt). This principle underlies transformers, where energy transfers between coils without direct electrical contact, depending on their geometry and relative positioning.

Key terms

Inductance (L)

A measure of a circuit element's opposition to changes in current; unit is the henry (H).

Self-induced EMF equation

EMF = -L(dI/dt) — induced EMF opposes the rate of change of current.

Energy stored in an inductor

U = ½LI², stored in the inductor's magnetic field.

Solenoid inductance formula

L = μ₀N²A/ℓ, depending on turns (N), area (A), and length (ℓ).

Mutual inductance (M)

Describes how a changing current in one coil induces EMF in a nearby coil: EMF₂ = -M(dI₁/dt); basis of transformers.

Try an AP-style question

The current through a 0.5 H inductor changes at 4 A/s. What emf is induced?

1. 2 V
2. 0.125 V
3. 8 V
4. 4.5 V