Question

A finite square grid, each link having resistance $r=\frac{40}{7}\Omega$, is fitted in a resistance less conducing circular wire. Determine the equivalenet resistance between A and B ( in$\Omega$)

Answer 1

Here we can see that at all the four corner's of the square it has same potential 'A' as it is same wire, and hence no current will flow through that circular wire
Here from the point 'B' equal amount of current will flow to all the four sides as it is symmetrical
$\therefore$ By symmetry we can mark the potential as A,B,C,D,E,F in the figure and the equivalent circuit would look like this, Here between each points the resistence are kept in parallel and so the equivalent resistence would look like this
now solving the circuit, here the resistence betweeen C and F in the upper wire and lower wire are in series, and both are parallel to each other, finally the resistence are in series as and now we can see that the resistence $\frac{R}{8}$, $\frac{3R}{20}$, and $\frac{R}{4}$ are in series.
We know that equivalent resistence in series $R_{eq}=R_1+R_2+R_3$
$\therefore$ $R_{AB}=3\Omega$