Lets now consider the case of all three passive circuit elements in series, as in figure 2.4.

Applying Kirchoff's law around the loop and using *I*=*dQ*/*dt* gives

The solution will not only depend on the initial conditions but also
the relative values of *R*,*C* and *L*.

There are three possible solutions:

- under damped ( ): ,
- over damped ( ): , and
- critically damped ( ): .

*RCL* circuits have a variety of properties, especially when driven by
sinusoidal sources, which will not be investigated here.
My aim is simply to expose you to the area and get on to more
interesting topics.
Driven oscillating systems also appear in other areas of physics and
hopefully you will encounter them there.
The detailed considerations lead to discussions on resonance and
quality-factor *Q*.

Tue Jul 13 16:55:15 EDT 1999