Explanation:
C Voltage $\mathrm{V}$ is applied between the points $\mathrm{A}$ and $\mathrm{B}$,
$\mathrm{V}=\mathrm{IR}=\mathrm{I}_{0} \mathrm{r}$
Where, $\mathrm{R}=$ Resistance of whole the grid
$\mathrm{I}=$ Current through the grid
$\mathrm{I}_{\mathrm{o}}=$ Current through the segment $\mathrm{AB}$
Now, from symmetry, $I / 4$ is the part of the current, flowing through all the four wire segments (square grid cells), meeting at the point A and similarly the amount of current flowing through the wires, meeting at $\mathrm{B}$ is also $\mathrm{I} / 4$. Thus a current $\mathrm{I} / 2$ flows through the conductor $\mathrm{AB}$,
$\mathrm{I}_{\mathrm{o}}=\mathrm{I} / 2$
Hence, $\mathrm{R}=\frac{\mathrm{r}}{2}$
