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

• Correct answer
  A

  $\frac{R}{4}$
• B

  $\frac{R}{8}$
• C

  $4 R$
• D

  $\frac{R}{2}$

Solution

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

Hence, the correct answer is option: 'A'.