Damping in RLC Circuits

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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 (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: overdamping
Snapshot 2: critical damping
Snapshot 3: underdamping
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.
Permanent Citation