RC / RL / RLC Lab

All circuits are ideal series connections. RC frequency output is capacitor voltage VC/Vin; RL and RLC output is resistor voltage VR/Vin, equivalently current normalized by Vin/R. Voltage transfer shows 20 log10|H| in dB and phase relative to the source. Series impedance shows |Z| in Ω and its phase. Their phases have opposite signs for the resistor output.

RC: τ=RC, fc=1/(2πRC). RL: τ=L/R, fc=R/(2πL). At fc the voltage gain is 1/√2, or −3.0103 dB. Series RLC: f0=1/(2π√LC), Q=√(L/C)/R, ζ=1/(2Q). At resonance Z=R and resistor gain is unity. Exact half-power angular frequencies are (√(R²+4L/C)±R)/(2L); their geometric mean is ω0 and their difference is R/L. They are not generally f0±Δf/2.

Step response begins with capacitor voltage and inductor current zero. RC plots VC(t); RL and RLC plot I(t). RC tends to the applied voltage, RL to V/R, and series RLC current tends to zero because the capacitor blocks DC. Negative and zero voltage steps are allowed. The curves are closed-form evaluations, not an animated numerical simulation. Probe any positive frequency or nonnegative time independently of plotting samples.

First-order plots span seven time constants. RLC covers the decay interval or the first eight damped oscillations, whichever is shorter; the caption indicates truncation. Very overdamped responses additionally sample the fast initial rise. The time probe can evaluate later times. Initial values, parasitic effects, nonlinear parts and frequency-dependent losses are not modeled.

Inputs: R in Ω, L in mH, C in µF, step in V. The component domain is R=0.01–1e6 Ω, L=1e−9–10 H, C=1e−12–1 F; these are arithmetic limits, not component ratings. Drafts, mode, view and probes use existing platform state. References: OpenStax series circuits; MIT damping ratio.