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6 Inductors

Inductors

Induced EMF \varepsilon=-L\frac{\Delta I}{\Delta t} Opposes the change in current (Lenz’s law). L = inductance (H). Energy stored E = ½ L I²

⭐ Why opening a switch makes a spark (back EMF)

  • ε = −L(ΔI/Δt). The induced voltage depends on how fast the current changes, not on how big it was.
  • Opening a switch drops the current to zero in a very short time, so ΔI/Δt is enormous.
  • That produces a very large induced voltage — large enough to ionise the air and produce a spark across the switch contacts (2025).
  • The minus sign is Lenz’s law: the induced EMF opposes the change that caused it, so it acts to keep the current flowing.
✓

Which way does the induced voltage point?

Ask what the inductor is opposing. Current increasing → the induced EMF opposes it, acting against the supply, so current rises gradually rather than instantly. Current decreasing → the induced EMF acts to maintain the current, which is why it can drive a spark across a gap that has just opened. ✕

It is the RATE of change that matters, not the size

A large STEADY current through an inductor induces NO back-EMF at all — ε = −L(ΔI/Δt) depends entirely on how fast the current changes, not how big it is. A small current changing very quickly (like a switch snapping open) produces a far bigger back-EMF than a large current that changes slowly.

Practise just this