Circuit Topology

A "circuit" is any arrangement of "components" (which we will meet later) and conductors (ie., wires) which don't have "loose" ends. That is, they are composed of closed loops which are connected together in various ways. For examples:

In circuits, two (or more) components are said to be in "series" if any electrons which go through the second one must have come from the first. They are said to be in parallel if they provide alternate paths for the electrons to go when starting and coming together again at common points. These notions are related to "graph theory", and can be a little tricky for the uninitiated.

The "topology" of a circuit defines how its various parts are connected (in series and parallel). The reason it is tricky is that it is based on connectivity, and NOT on visual appearance. For instance, the components in these circuit fragments are all in "series":

while these are all in "parallel":

Finally, these are NEITHER in series nor in parallel:

Clearly, this is non-intuitive. So we present some heuristics to help you decypher these puzzles:

1. Components in series share one "lead" (connection), with no other junctions or components in between (actually, a battery can be in between).

2. Components in parallel share both leads, with a junction at each shared lead, and no components in between.

3. It is best to analyze components in pairs, since more than two components in series (parallel) must still be in series (parallel) pair by pair.

4. Wires, as conductors, are equipotential "lines". Hence junctions can be moved to clarify or simplify a circuit provided that you don't move a junction through a component or add a new junction.

To help clarify things (although it may seem at first that we are further muddying them!), take a look at a quicktime animation (42K) of a single circuit(!). Try to separate the appearance of the circuit from how it is connected (its topology); when you can see that all of the frames are the same circuit, you will understand.

Problems

The next section is about circuits.

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©1996, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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