Question

A finite square grid, each link having resistance r is fitted in a resistanceless conducting circular wire. Determine equivalent resistance between A and B.

Answer 1

If we connect a battery between $A$ and $B$,

then different points will be at the same potentials.

$(1,2,3,4);(5,6,7,8);(9,10,11,12,13,14,15,16)$ and $(17,18,19,20)$

The resulting circuit can be drawn as shown below.

Solve to get

$R_{AB}=\frac{21}{40}r\Rightarrow R_{AB}=\frac{21}{40}\times \frac{80}{7}=6\Omega$