I came up with this question as I tried to extend the problem of maximizing the resistance in a circle by selecting two points where to connect the electrodes. The solution for this problem is obvious - antipodal points, however, naturally my other problem is more complex, and I don't know how to go about solving it.

I have a circuit which looks like this: circuit

All the rings are connected at all intersection points and all have equal crossectional area and density.

The problem: Where would you connect two electrodes so that the effective resistance of the circuit would be maximal?

I know you could try doing some complex mathematics with Kirchhoff laws, but is there a simpler way?

  • $\begingroup$ Interesting problem. I think that using symmetry arguments it may be possible to topologically simplify that mess of intersecting wires in the middle to just a Y-shaped connection consisting of three resistors of equal value. But I still don't see a simple solution to the problem. $\endgroup$ – Samuel Weir May 15 '17 at 22:17

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