Vol. IV — Electronics · Tool
An inductor and a capacitor exchange energy at one natural frequency. Change L and C — f₀, ω₀, and Z₀ update as you type. Optional series R adds Q and bandwidth.
Resonant frequency for an LC tank is f₀ = 1 / (2π√(LC)). At that point the inductive and capacitive reactances cancel in magnitude, and the tank rings at ω₀ = 2πf₀. The characteristic impedance Z₀ = √(L/C) sets the scale of those reactances at resonance.
With series resistance R > 0, quality factor Q = Z₀ / R and the −3 dB bandwidth is about f₀ / Q. Higher Q means a sharper peak; more R damps the ring. Ideal L and C (R blank or zero) still give f₀, ω₀, and Z₀ — Q and bandwidth stay blank until you set R.
Pair this with Reactance for XL / XC at a chosen frequency, RL time and RC time for the transient twins, or the converters bench for everyday ohms and watts.