resonance

Push a child on a swing at just the right rhythm and small pushes build a big swing, that is resonance. An electrical circuit with both a capacitor and an inductor has a natural rhythm too, and at one special frequency energy sloshes back and forth between them with very little effort, producing a big response.

In an LC circuit the inductor's reactance rises with frequency while the capacitor's falls; at the resonant frequency they are equal and cancel. That happens at f0 = 1/(2 times pi times the square root of (L times C)). Example: L = 10 mH with C = 100 nF resonates at f0 = 1/(2 times pi times the square root of (0.01 times 0.0000001)), about 5 kHz. At resonance a series LC looks like almost a short (just the leftover resistance), while a parallel LC looks like almost an open, each strongly favouring that one frequency.

Resonance is how a radio tunes to one station, how oscillators set their frequency, and how filters get sharp peaks. Honest caveat: resonance is double-edged. The same effect that lets you select a frequency can produce dangerous voltage or current build-up, and unwanted resonances between stray inductance and capacitance cause ringing and EMI in real boards.