Damping in RLC Circuits

This Demonstration shows the variation with time of the current I in a series RLC circuit (resistor, inductor, capacitor) in which the capacitor is initially charged to a voltage . The resonant frequency of the circuit is and the plotted normalized current is . There are three types of behavior depending on the value of the quality factor : overdamping when (no oscillation); critical damping when , (no oscillation and the most rapid damping); and underdamping when (damped oscillations).


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Snapshot 1: overdamping
Snapshot 2: critical damping
Snapshot 3: underdamping
The capacitor charge satisfies the differential equation , where the resonance frequency is given by and the quality factor . It is convenient to work with a normalized current . Initially the capacitor is charged to voltage and the current is 0.
For critical damping, and the current is For overdamping and underdamping, and the current is , where . So when , both and are complex, leading to a damped oscillating current. But when , both and are real and negative, so that the current is damped without any oscillations.
J. R. Reitz, F. J. Milford, and R. W. Christy, Foundations of Electromagnetic Theory, New York: Addison–Wesley, 1993.
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