← CA-5 · CAPACITORS, INDUCTORS & FIRST-ORDER CIRCUITS

Inductors

YOU WILL BE ABLE TO

Describe what an inductor is and state v = L·di/dt.
Compute stored energy, and combine inductors in series and parallel.
Explain why inductor current cannot change instantaneously.
Recognise the capacitor–inductor duality.

The inductor is a coil of wire, and its behaviour comes from the magnetic field that any current creates. Change the current and the changing field induces a voltage across the coil that opposes the change (Faraday and Lenz, from your physics prerequisite). The inductor is the capacitor's perfect mirror: it resists changes in CURRENT the way a capacitor resists changes in VOLTAGE.

v = L\,\frac{di}{dt}

inductor element law, henries

The inductor under the passive sign convention: v = L di/dt. Steady current means zero voltage.

L is the inductance in henries (H); practical parts run from microhenries to hundreds of millihenries. The dual consequences, mirroring Lesson 1 point for point: at DC steady state di/dt = 0, so v = 0 — a settled inductor is a SHORT CIRCUIT, just a length of wire. Inductor current cannot jump — that would demand infinite voltage — so current is the inductor's continuous state variable. And the magnetic field stores recoverable energy:

w = \tfrac{1}{2}Li^2

stored energy, joules

WORKED EXAMPLE

The voltage spike

A 10 mH inductor carries 2 A, and a switch opens, forcing the current toward zero in about 1 ms.
v = L di/dt ≈ 0.010 × (2/0.001) = 20 V — and a faster interruption gives proportionally more.
Interrupt 2 A in a microsecond and the law demands ~20 000 V: the inductor will get its voltage, typically by arcing across the opening switch contacts. This is not a nuisance footnote — it is why relay and motor drivers always include protection, built properly in ME-6.

≈ 20 V for the 1 ms break — and the faster the break, the bigger the spike

WORKED EXAMPLE

Energy in a motor winding

A motor winding of 100 mH carries 3 A.
w = ½Li² = ½ × 0.1 × 9 = 0.45 J.
That energy does not vanish when the drive transistor switches off — it must go SOMEWHERE, every switching cycle. Where you send it is the difference between a working motor driver and a dead one.

0.45 J

PRACTICE

A 50 mH inductor's current rises at 100 A/s. What voltage appears across it?

How much energy is stored in a 20 mH inductor carrying 500 mA?

Find the equivalent of a 3 mH and a 6 mH inductor in series, and in parallel.

Using duality, translate this capacitor fact into its inductor twin: "A capacitor holds its voltage across a switching instant and looks like an open circuit at DC."