Capacitor-Inductor Duality

Quick Answer

Capacitors and inductors are mirror images. Swap capacitance for inductance, voltage for current, series for parallel and the electric field for the magnetic one, and a statement about the first becomes the matching statement about the second. Learn either component properly and most of the other one comes free.

The pairing runs all the way down. A capacitor opposes a change of voltage, and its current is set by how fast the voltage moves; an inductor opposes a change of current, and its voltage is set by how fast the current moves. Capacitance stores energy in an electric field between plates, inductance in a magnetic field around a coil, and the two energy expressions differ only in which symbol sits where.

The swap carries into circuits. Capacitors in parallel add; inductors in series add. A capacitor blocks steady current and passes fast changes, an inductor passes steady current and obstructs fast changes, and reactance falls with frequency for the one and rises with it for the other. The RC time constant is a resistance multiplied by a capacitance, while its RL counterpart is an inductance divided by a resistance, because resistance itself swaps places with conductance under the same mapping.

None of that is coincidence or a memory trick. Series and parallel connection, voltage and current, and Kirchhoff's two laws are each the dual of the other, so a planar network has a dual network in which every statement holds with the words exchanged. The voltage source and its current-source twin are the same idea one level up.