Resonance in an LC Circuit

An inductor's reactance X_L = 2πfL grows with frequency, while a capacitor's reactance X_C = 1/(2πfC) shrinks. At the resonant frequency f₀ = 1/(2π√(LC)) the two cancel, and the circuit exchanges energy between the magnetic field of the coil and the electric field of the capacitor.

Quality Factor and Bandwidth

With a series resistance R, the circuit's Q equals √(L/C) divided by R. Higher Q sharpens the response — bandwidth is f₀/Q — which is exactly how a tuner rejects adjacent stations. Low-loss components and minimal resistance keep Q high.

Real-World Use

LC tanks appear in oscillators, filters, impedance matching, and wireless charging. Enter real component values — microhenry coils and picofarad capacitors — and the calculator reports the exact frequency the circuit will resonate at.