Question

Consider an infinite mesh as shown in the figure. Each side of the mesh has resistance R. Consider hexagonal part ABCDEF of infinite mesh and equivalent resistance between any two points of hexagon is measured. Equivalent resistance between A and B is $\frac{\alpha R}{\beta }$. The least value of $\alpha +\beta$ is .(Here, $\alpha \&\beta$ are whole number)(Answer upto two digits after the decimal point)

Answer 1

If we connect positive terminal of a current source of current $I$ to A and negative to infinity then the current through branches will be as shown.
If we connect negative terminal of a current source of current $I$ to B and positive to infinity then the current through branches will be as shown.


By super-position of two situations net current in AB branch will be $\frac{2I}{3}$.

Potential difference between A and B will be $\frac{2I}{3}R$.

So, the effective resistance between A and B will be $\frac{V_{AB}}{I}=$ $\frac{2R}{3}$.