RLC Resonance

Ideal series RLC: Z=R+j(ωL−1/ωC), f₀=1/(2π√LC), Q=√(L/C)/R. AC voltage and currents are RMS. Active power=I²R; component RMS voltages IR, IωL, I/(ωC) can exceed input near resonance. Current-transfer phase is arg(1/Z), not impedance phase; this circuit response remains defined for zero drive. Exact half-power edges satisfy |Z|=√2R and I=Ires/√2; their geometric mean is f₀ and difference R/(2πL), not arithmetic symmetry. Frequency and impedance axes are logarithmic.

The independent DC step uses signed step voltage, zero initial capacitor voltage/current and an analytical under/critical/overdamped solution. No numerical simulation or artificial animation. The plot shows up to seven decay constants or eight damped periods; the plot tooltip states its duration. A time outside it is still evaluated, without a misplaced marker. Frequency probe defaults to f₀; the f₀ button restores automatic tracking. Drafts and view survive navigation/reload. R=.01…10⁶Ω,L=10⁻⁹…10H,C=10⁻¹²…1F; AC0…1000V,step±1000V. Arithmetic bounds, no ratings. No parasitics, nonlinear components or loading.