Question

Twelve wires, each of resistance $2\Omega$ are connected to form a cube. Find the equivalent resistance between the adjacent corners of any face of the cube

• A. $\frac{6}{7}\Omega$
• B. $\frac{7}{6}\Omega$
• C. $\frac{3}{4}\Omega$
• D. $\frac{4}{3}\Omega$

Answer 1

Answer: (B)

From loops $FEHGF$ and $DCGFD$
$4y-5z=0$ and $x-2y-z=0$
$\therefore y=\frac{5}{14}x$
If $R$ is the resistance between corners $C$ and $D$,
$(x+2y)R=xr$
$R=\left(\frac{x}{x+2y}\right)$
$r=\frac{xr}{\left(x+\frac{5}{7}x\right)}=\frac{7}{12}r$
Here, $r=2\Omega$
$\Rightarrow R=\frac{7}{12}\times 2$
$=\frac{7}{6}\Omega$