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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).


	Contributed by: James Burgess

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.

Reference:

J. R. Reitz, F. J. Milford, and R. W. Christy, Foundations of Electromagnetic Theory, New York: Addison–Wesley, 1993.

Contributed by: James Burgess

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