THE FIELDS OF MOVING CHARGES — Edward Purcell & David Morin
Physics — E&M · resistances-in-a-cube
Problem
Resistances in a cube **
A cube has a resistor R along each edge. Find the equivalent resistance between two nodes that correspond to:
(a) diagonally opposite corners of the cube;
(b) diagonally opposite corners of a face;
(c) adjacent corners.
You do not need to solve a number of simultaneous equations; instead use symmetry arguments. Hint: If two vertices are at the same potential, they can be collapsed to one point without changing the equivalent resistance between the two given nodes.