Self-inductance and back emf, Lenz's law, the energy stored in an inductor, the growth and decay of current in an RL circuit, and inductive reactance.

What this key area is asking

The SQA wants you to understand self-inductance and the back emf an inductor produces, apply Lenz's law, use the energy stored in an inductor $E = \tfrac{1}{2}LI^2$, describe the growth and decay of current in an RL circuit, and understand inductive reactance in a.c. circuits.

Self-inductance and back emf

When the current through a coil changes, the magnetic flux it produces changes, and by Faraday's law this induces an emf. This back emf opposes the change in current, so an inductor resists being switched on or off quickly. The faster the current changes, the larger the back emf, which is why breaking an inductive circuit can produce a large voltage spike.

Lenz's law

If the current is increasing, the back emf opposes it (trying to keep the current down); if decreasing, the back emf acts to maintain it. Lenz's law guarantees energy conservation: the induced effect can never reinforce its own cause, or you would get energy from nothing. It is the principle behind electromagnetic braking and the reason inductors smooth current changes.

Energy stored in an inductor

Building up the current does work against the back emf, and that work is stored in the magnetic field. When the circuit is broken, the current falls rapidly, the field collapses, and the stored energy is released, frequently as a spark across the opening switch. This mirrors the capacitor's $\tfrac{1}{2}CV^2$, with current and inductance replacing voltage and capacitance.

RL circuits and inductive reactance

The gradual growth and decay are the inductive analogue of the capacitor's exponential charging, set by the ratio $L/R$. In a.c., because the inductor opposes change most strongly when the current changes fastest, it impedes high frequencies more than low ones. An inductor therefore passes low frequencies (and d.c.) readily while opposing high frequencies, exactly opposite to a capacitor, which is why the two are paired in filters.

Examples in context

Spark suppression circuits protect switches that control inductive loads such as motors and relays, because breaking the current produces a large back emf. Transformers rely on the changing flux of one coil inducing an emf in another, the mutual version of self-inductance. Inductors in power supplies smooth current ripple, opposing rapid changes. Induction hobs and electromagnetic braking use Lenz's law, where induced currents oppose the motion that creates them.

Try this

Q1. Write the relationship for the back emf of an inductor in terms of $L$ and the rate of change of current. [1 mark]

• Cue. $\varepsilon = -L\frac{dI}{dt}$.

Q2. Write the relationship for the energy stored in an inductor carrying current $I$. [1 mark]

• Cue. $E = \tfrac{1}{2}LI^2$.

Q3. State how an inductor's opposition to a.c. changes as the frequency increases. [1 mark]

• Cue. It increases (the inductive reactance rises with frequency).