Inductors
An inductor stores energy in a magnetic field created by current in a coil. It resists sudden changes in current, the mirror image of a capacitor's behaviour.
Structure and inductance
An inductor is usually a coil of wire, often wound on a magnetic core. Current through the coil creates a magnetic field, and a changing current changes the field, which induces a voltage opposing the change, by Faraday's and Lenz's laws. Inductance L, in henries (H), measures this: \(v = L\frac{di}{dt}\). More turns, a larger cross-section, and a high-permeability core increase inductance.
Behaviour of inductors
Because v = L di/dt, an inductor's current cannot change instantly; trying to change it abruptly produces a large voltage. With steady DC current, the voltage is zero, so in DC steady state an ideal inductor acts as a short circuit, with only its small winding resistance limiting current. Inductors therefore smooth current, just as capacitors smooth voltage.
Energy storage
An inductor stores energy \(w = \frac{1}{2}Li^2\) in its magnetic field. A 10 mH inductor carrying 2 A stores \(\frac{1}{2} \times 0.01 \times 4 = 20\) mJ. When the current is suddenly interrupted, by opening a switch, this energy produces a voltage spike that can arc across contacts or destroy transistors.
Flyback protection
When a transistor switches off a relay coil or motor winding, the collapsing magnetic field drives a high reverse voltage. A flyback (freewheeling) diode across the coil gives the current a safe path to decay, clamping the spike. Forgetting it is a classic electronics mistake that destroys driver transistors.
Combining inductors
Inductors combine like resistors, provided they are not magnetically coupled: in series, inductances add; in parallel, reciprocals add. When coils share magnetic flux, mutual inductance M couples them, which is the principle of transformers covered in the power unit.
Types and uses
Air-core inductors suit radio frequencies; ferrite and iron-core inductors give larger inductance for power circuits. Inductors appear in switch-mode power supplies, which store and release energy at high frequency to convert voltages efficiently; in filters, which separate frequencies; in chokes, which block high-frequency noise; and in wireless charging coils and sensors.
Duality with capacitors
Capacitors and inductors are duals: capacitor equations swap voltage and current, and C and L, to give inductor equations. A capacitor is an open circuit to DC and resists voltage changes; an inductor is a short circuit to DC and resists current changes. Capacitors store energy in electric fields, inductors in magnetic fields. Ideal versions of both store energy without dissipating it.
Worked example
A 50 mH inductor's current falls uniformly from 0.4 A to 0 in 1 ms. The rate is \(\frac{di}{dt} = \frac{-0.4}{0.001} = -400\) A/s, so \(v = L\frac{di}{dt} = 0.05 \times (-400) = -20\) V. If a switch instead broke the current in 1 \(\mu\)s, the voltage would be about 20,000 V, showing why flyback diodes are essential. The energy released, \(\frac{1}{2} \times 0.05 \times 0.16 = 4\) mJ, is the same either way.
Key takeaways
An inductor is a coil whose changing current induces an opposing voltage: v = L di/dt, with inductance in henries. Inductor current cannot change instantly; in DC steady state an ideal inductor is a short circuit. Stored energy is w = L i^2 / 2, released as voltage spikes when current is interrupted, so flyback diodes protect switches driving coils. Uncoupled inductors combine like resistors; coupled coils have mutual inductance. Inductors appear in power supplies, filters, chokes, and wireless charging. Inductors and capacitors are duals, storing energy in magnetic and electric fields.
Flashcard
Coil storing energy in a magnetic field
Check your understanding
A relay coil is switched off by a transistor with no protection. What is the main danger?