Question

Twelve wires, each having resistance $r$, are joined to form a cube as shown in figure. Find the equivalent resistance between the diagonally opposite points $a$ and $f$.

Answer 1

Let both terminals connected with 'V' Volt

Taking circuit $ABHGA$,

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

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

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

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