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A Quicker Way to Solve Series-Parallel Circuits

Before students learn Kirchhoff’s rules, they are typically taught how to solve “combined series-parallel” circuits. The method presented in many textbooks begins by drawing a series of simplified circuits, replacing series and/or parallel elements with their equivalent resistances, eventually reducing the circuit to a voltage source and a single resistor. If we are only looking for the source current, then all is well. But to find the currents and voltage drops for the individual components of the circuit, students are expected to work backwards through their series of diagrams, “un-simplifying” at each step, until they are back to the original circuit. Alas, all is no longer well: students often get bogged down in this lengthy process. However, there is an alternative method that is quicker and uses a single diagram. My students make fewer mistakes with this approach, obtaining results that they can check in a manner that foreshadows what they will learn about Kirchhoff’s rules.Before students learn Kirchhoff’s rules, they are typically taught how to solve “combined series-parallel” circuits. The method presented in many textbooks begins by drawing a series of simplified circuits, replacing series and/or parallel elements with their equivalent resistances, eventually reducing the circuit to a voltage source and a single resistor. If we are only looking for the source current, then all is well. But to find the currents and voltage drops for the individual components of the circuit, students are expected to work backwards through their series of diagrams, “un-simplifying” at each step, until they are back to the original circuit. Alas, all is no longer well: students often get bogged down in this lengthy process. However, there is an alternative method that is quicker and uses a single diagram. My students make fewer mistakes with this approach, obtaining results that they can check in a manner that foreshadows what they will learn about Kirchhoff’s rules.