The Wheatstone bridge is one arrangement of circuit elements that is neither a series nor parallel, nor a combination of series and parallel elements. It makes me wonder what other arrangements are out there. It seems like there could be arrangements of circuit elements that can't be reduced to a combination of series, parallel and Wheatstone bridges.
Do these other arrangements exist? Is there a method for constructing these arrangements (if they do exist)?
Best Answer
Yes, they do exist.
The examples you gave are examples of planar networks, that is, networks that can be drawn on a plane without intersecting branches (branches can actually intersect but only at nodes).
There are, though, also non-planar networks, that is, networks that cannot be drawn on plane without having branches that intersect. This kind of networks cannot be reduced to a recursive combination of series, parallel and Wheatstone bridge connections.
An example is that of a resistor cube.