Lesson 2
6 Redrawing Complex Circuits
Ken Dickson-Self
Typically, complex circuits are not arranged in nice, neat, clean schematic diagrams for us to follow. They are often drawn in such a way that makes it difficult to follow which components are in series and which are in parallelwith each other. The purpose of this section is to show you a method useful for re-drawing circuit schematics in a neat and orderly fashion. Like the stage-reduction strategy for solving series-parallel combination circuits, it is a method easier demonstrated than described.
Let’s start with the following (convoluted) circuit diagram. Perhaps this diagram was originally drawn this way by a technician or engineer. Perhaps it was sketched as someone traced the wires and connections of a real circuit. In any case, here it is in all its ugliness:
With electric circuits and circuit diagrams, the length and routing of wire connecting components in a circuit matters little. (Actually, in some AC circuits it becomes critical, and very long wire lengths can contribute unwanted resistance to both AC and DC circuits, but in most cases wire length is irrelevant.) What this means for us is that we can lengthen, shrink, and/or bend connecting wires without affecting the operation of our circuit.
The strategy I have found easiest to apply is to start by tracing the current from one terminal of the battery around to the other terminal, following the loop of components closest to the battery and ignoring all other wires and components for the time being. While tracing the path of the loop, mark each resistor with the appropriate polarity for voltage drop.
In this case, I’ll begin my tracing of this circuit at the negative terminal of the battery and finish at the positive terminal, in the same general direction as the electrons would flow. When tracing this direction, I will mark each resistor with the polarity of negative on the entering side and positive on the exiting side, for that is how the actual polarity will be as electrons (negative in charge) enter and exit a resistor:
Any components encountered along this short loop are drawn vertically in order:
Now, proceed to trace any loops of components connected around components that were just traced. In this case, there’s a loop around R1formed by R2, and another loop around R3 formed by R4:
Tracing those loops, I draw R2 and R4 in parallel with R1 and R3(respectively) on the vertical diagram. Noting the polarity of voltage drops across R3 and R1, I mark R4 and R2 likewise:
Now we have a circuit that is very easily understood and analyzed. In this case, it is identical to the four-resistor series-parallel configuration we examined earlier in the chapter.
Let’s look at another example, even uglier than the one before:
The first loop I’ll trace is from the negative (-) side of the battery, through R6, through R1, and back to the positive (+) end of the battery:
Re-drawing vertically and keeping track of voltage drop polarities along t