## Resistance of a Network of Resistors on the Edges of a Cube

The resistances of purely parallel and purely series circuits can be found from the formulaefor resistors in parallel andfor resistors in series, and for circuits that can be drawn on paper, we can find resistances because any circuit is a combination of series and parallel circuits. The following circuit however, does not fit into any of the categories.

The resistance can be found by using the symmetry if the network.

At A, the current splits into thirds as shown and at H, D and B, into sixths. At G, C and E those sixths recombine into thirds. Applying Ohms Law,to the route AHGF(any such route will do) gives

so that on adding and dividing bywe obtainwhereis the total resistance of the network.