Question

Twelve wires, each of equal resistance r, are joined to form a cube, as shown in the figure (32-E20). Find the equivalent resistance between the diagonally-opposite points a and f.
figure 32-E20

Answer 1

56r is the equivalent resistance between the points a and f that are diagonally opposite.

Explanation:

Between the points a and f, let the potential difference be V. Let current I leave from f and enter a. In the below figure, the current distribution in multiple branches is shown.

Consider the path abcf to calculate the potential difference between f and a. Apply Kirchoff’s law:

3r + i6r + i3r ⇒5ir6 = V

Between a and f, the effective resistance, Reff = Vi = 56r.