LC circuit

Connect a charged capacitor to an inductor and the energy sloshes back and forth between them — from electric field to magnetic field and back — making the current oscillate. An LC circuit is an electrical pendulum. It answers the question: what makes a circuit ring at one particular frequency?

Precisely, the capacitor (C) stores energy in its electric field and the inductor (L) stores it in its magnetic field, and the charge trades between them just like simple harmonic motion. It oscillates at the natural frequency f = 1 / (2 pi sqrt(L C)), with angular frequency omega = 1 / sqrt(L C). In the ideal case the total energy stays constant, merely swapping form — exactly the way a mass on a spring trades kinetic and potential energy.

LC circuits set the frequency of radios, oscillators, and filters; tuning a radio simply adjusts L or C to match a station. The honest caveat is that a real LC circuit has some resistance, so the oscillation gradually dies away (it is damped), just as a real pendulum eventually stops. The loss-free LC that rings forever is an idealization.