Question

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

figure (32-E20).

Answer 1

Taking circuit ABFGA,

$\frac{i}{3r}+\frac{i}{6r}+\frac{i}{3r}=V$

$\Rightarrow (\frac{2i}{3r}+\frac{i}{6r})=V$

$\Rightarrow \left(\frac{5i}{6r}\right)=V$

$\Rightarrow R_{eff}=\frac{V}{i}=\frac{5}{6r}$