Physics - Current Electricity Question with Solution | TestHub

When wire is bent to form a complete circle then $2\pi r=R\Rightarrow r=\frac{R}{2\pi }$Resistance of each semicircle $=\pi r=\frac{\pi R}{2\pi }=\frac{R}{2}$ Thus, net resistance in parallel combination of two semicircular resistance $R^{\prime }=\frac{\frac{R}{2}\times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{\frac{R^2}{4}}{R}=\frac{R}{4}$