Resonance

Resonance is familiar in sound: a tuning fork makes another fork of the same frequency vibrate with a large amplitude, but forks of different frequencies produce only small effects.

• In an electrical tuned (resonant) circuit — a series LCR circuit with a variable-frequency AC source, a variable capacitor and an inductor, with a hot-wire ammeter — as the source frequency is varied the effective current changes: it is small when the source frequency is far from the circuit's natural frequency, increases as the frequencies approach, and is maximum when they coincide.
• At resonance:

• X_L = X_C, so the net reactance is zero;
• Z = R (minimum); the current I = V/R is maximum;
• the voltage and current are in phase (θ = 0);
• the resonant frequency is f = 1/(2π√(LC));
• V_L and V_C are equal and opposite; each can be much larger than the supply voltage (since V_L = I X_L = (V/R) X_L).

To tune a circuit to a given frequency, change C (variable capacitor) or L (number of turns or an iron core).