In the last article, we saw how voltage and current will either pulse or oscillate depending on the resistance when a circuit is subjected to a sudden change. We called these two circumstances the oscillating case and the impulse case, respectively. In this article we will explore oscillating current in more detail.

Let's lower the resistance to achieve a more sustained oscillation.

Suppose the battery is 12 volts, the resistance of the resistor is 0.1 ohm, the inductance of the inductor is 1 henry, and the capacitance of the capacitor is 1 farad.

Set to the moment the switch closes, so and .

Plug in these values:

so

and

Now we can graph the current over time:

and the voltage across the capacitor over time:

We see that with low resistance the oscillations are sustained at a regular frequency. This is called the resonant frequency of the circuit.

By looking at the trigonometric components of the voltage and current equations, we can represent the period of oscillation by an angle :

where f is the resonant frequency.

If the resistance is negligible: