Question

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

• A. $\frac{R}{4}$
• B. $\frac{R}{8}$
• C. $4R$
• D. $\frac{R}{2}$

Answer 1

Answer: (A)

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 resistances
$R^{\prime }=\frac{\frac{R}{2}\times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{\frac{R^2}{4}}{R}=\frac{R}{4}$