Having completed our examination of strictly series and strictly parallel AC circuits, we turn our attention now to somewhat more complex circuits, namely those circuits comprised of components in mixed series-parallel arrangements. This chapter deals with a subset of series-parallel RLC circuits, specifically those that are driven by a single effective current or voltage source, and which may be simplified using series and parallel component combinations. The rules and techniques explored for strictly series networks are still applicable to series connected subsections of larger circuits. The same is true for the rules and techniques established for strictly parallel circuits regarding parallel subsections. Thus, the key to analyzing series-parallel circuits is in recognizing those portions of the circuit that form series or parallel sub-circuits, and then applying the series and parallel analysis rules to those sections. Ohm's law, KVL and KCL may be used in turn to solve portions of the problem until all currents and voltages are found. As individual voltages and currents are determined, this makes it easier to apply these rules to determine other values.
It is often useful to determine the effective impedance of individual sections at the outset in order to facilitate circuit analysis. Indeed, continuing the process until the entire network is reduced to a series-only or parallelonly simplified version is a good starting point. That is, each of the complex impedances that make up the series-only or parallel-only simplified equivalent is made up from a sub-circuit which in turn potentially is made up of other sub-circuits, and so on. The art of examining a complex series-parallel network and being able to immediately determine which elements constitute a series connection and which constitute a parallel connection is an essential skill and worthy of practice.