# Damping in RLC Circuits

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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