Inductance and Inductors
Inductance questions test self- and mutual induction, back EMF, energy storage, and transient response. You must apply e = −L di/dt, combine inductors correctly, and explain why inductor current cannot change instantly.
Core rules
- Inductance L is measured in henries (H); 1 H = 1 Wb/A.
- Self-induction produces a back EMF in the same coil when its own current changes.
- Mutual induction transfers EMF between coils linked by changing flux, the basis of transformers.
- Induced EMF: e = −L di/dt; the minus sign reflects Lenz's law.
- Inductors in series add; in parallel, reciprocals add, provided there is no mutual coupling.
- Energy stored: E = ½LI²; time constant τ = L/R.
Worked example
The current in a 2.0 H inductor changes from 1 A to 4 A in 0.10 s. Find the average back EMF. di = 4 − 1 = 3 A; dt = 0.10 s. e = −L di/dt = −2.0 × 3 / 0.10 = −60 V. The magnitude is 60 V; the sign shows opposition to the current increase. Reasoning: use the change in current, not the final current, and keep the sign convention.
Traps
- Assuming inductor current can change instantly.
- Using final current instead of current change in di/dt.
- Ignoring the voltage spike when an inductive circuit is interrupted.
- Combining parallel inductors by direct addition.