Rlc Series Step

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Step response of an underdamped series R-L-C circuit — ringing and overshoot before settling.

Series R-L-C step circuit: a 10 V DC source drives a 20 Ω resistor, a 0.1 H inductor and a 10 μF capacitor in one loop. The loop current is $I_L$ and $V_{\mathrm{cap}}$ is the capacitor voltage.

A 10 V DC source is switched onto a series R-L-C branch (20 Ω, 0.1 H, 10 μF). With light damping (ζ ≈ 0.1) the capacitor voltage overshoots its 10 V target to about 17.3 V, then rings down at the damped natural frequency (f₀ ≈ 159 Hz) until it settles. This is the second-order counterpart to the first-order R-L and R-C steps, and a good circuit for seeing how the time step affects a fast oscillation. Open it, press Run, and watch V_cap ring while the loop current I_L oscillates. Used in the EMT course, Chapter 3 (solving the network each step).

The inductor and capacitor trade energy back and forth while the 20 Ω resistor bleeds it away — that exchange is the ringing, and the resistor is why it dies out. The run uses a fine 20 µs step over 40 ms so the ≈159 Hz oscillation (a 6.3 ms period) is resolved smoothly. Raise R toward 2√(L/C) ≈ 200 Ω and the overshoot vanishes into a critically damped rise; lower it and the ringing lasts longer. Coarsen the time step and watch the resolved waveform degrade — the cautionary lesson of Chapter 3.