Question

In the circuit shown in figure, all wires have equal resistance $r$. The equivalent resistance between $A$ and $B$ is $\frac{xr}{5}$. Find $x$.

Answer 1

The circuit can be redrawn as shown. There is a plane of symmetry passing through AB, cutting the prism shaped circuit in two halves.

This leads to conclude that there can be no current passing in arms FD and CE.

Thus the only arms to be considered are- AFEB, ADCB and AB.

Resistance of arm AFEB $=3r$

Resistance of arm ADCB $=3r$

Resistance of arm AB $=3\Omega$

These all are connected in parallel. Thus the equivalent resistance becomes

$\frac{3r}{5}$.