When a wire of uniform cross-section a length / and resistance R is bent into a complete circle, the resistance between any two of diametrically opposite points will be

It is obvious from fig. that two wires of resistances R / 2 and R / 2 are connected in parallel between two points A and 8. Therefore, the equivalent resistance between two diametrically opposite points will be
${\mathrm{R}}_{\mathrm{eq}}=\frac{{\mathrm{R}}_1{\mathrm{R}}_2}{{\mathrm{R}}_1+{\mathrm{R}}_2}=\frac{(\mathrm{R}/2)\times (\mathrm{R}/2)}{(\mathrm{R}/2)+(\mathrm{R}/2)}\text{ or }{\mathrm{R}}_{\mathrm{eq}}=\frac{\mathrm{R}}{4}$