Elements that remember

Resistors dissipate energy. Capacitors and inductors store it, which makes them the first elements whose behaviour depends on what happened a moment ago.

• A capacitor is two conducting plates separated by a dielectric, C = εA/d, measured in farads. It stores energy in an electric field and holds charge q = Cv.
• An inductor is a coil, measured in henries. It stores energy in a magnetic field set up by the current through it.
• Both are passive and both are linear, so every theorem from the previous lessons still applies.

The two defining relations

Each element ties one quantity to the rate of change of the other, and every consequence follows from that.

• Capacitor: i = C dv/dt. Voltage across a capacitor cannot change instantaneously, since that would demand infinite current.
• Inductor: v = L di/dt. Current through an inductor cannot change instantaneously, since that would demand infinite voltage. This is why opening a switch on an inductor produces a spark.
• Stored energy: w = ½Cv² for a capacitor, w = ½Li² for an inductor.

In DC steady state, and in combination

Once nothing is changing, the derivatives vanish and both elements become trivial.

• A capacitor behaves as an open circuit to DC, an inductor as a short circuit. Redraw the circuit that way and solve it with Ohm and Kirchhoff.
• Capacitors in parallel add (Ceq = C1 + C2), and in series they combine like parallel resistors. Parallel plates add area, series plates add separation.
• Inductors follow the resistor rules: series add, parallel combine reciprocally.