Levels

Lab

The physics

In a series LCR circuit, the coil's reactance XL = ωL grows with ω. The capacitor's reactance XC = 1/(ωC) falls as ω grows.

Z = √(R² + (XL − XC)²)    I = V/Z

At resonance XL = XC. Then Z = R, and the current is largest.

ω₀ = 1/√(LC)    Imax = V/R

Below ω₀ the circuit acts like a capacitor, and the current leads. Above ω₀ the coil wins, and the current lags. The half-power band is R/L wide. At resonance the coil's voltage is Q times the supply.

Q = ω₀L/R    Δω = R/L

A coil and a capacitor side by side act the other way. At their ω₀ they block the line. A current then swings inside the pair.