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