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Determining electron density in copper

Assignment:

Twelve equal resistances R form the edges of a cube as shown.

a. A battery is connected between A and G. Can you find one set of three points that are at the same potential? Can you find another set?
b. Now imagine that you have a sheet of copper connecting the first set, and another sheet of copper connecting the second set. This does not affect the currents in the resistors. You can now show that R_AG = (5/6)R.

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