Lets now consider the *LC* circuit in figure 2.3 which has
no resistive element.

Kirchoff's voltage law applied to the loop is

Substituting our previous expressions for and gives

Using *I* = *dQ*/*dt* gives

The circuit equation is second-order in *Q* and one possible solution
is

where is the initial charge on the capacitor and is an arbitrary phase constant. Considering the cases of , gives . The angular frequency is totally determined by the other parameters of the circuit

and is the natural or resonance frequency of the circuit.

We can also solve for the current and voltage across the capacitor

Notice that unlike the transient current and voltage responses of the
*RC* and *RL* circuits, the *LC* circuit oscillates.
The energy in the circuit is shared back and forth between the inductor
and capacitor.

Tue Jul 13 16:55:15 EDT 1999