Question

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

• A. $\frac{R}{2}$
• B. $\frac{R}{4}$
  
• C. $\frac{R}{5}$
• D. $2R$

Answer 1

The correct option is B $\frac{R}{4}$


Resistance, $R=\frac{\rho l}{a}$
$\Rightarrow R\propto l$
For half wire, resistance = $\frac{R}{2}$
Since two half wires are in parallel,
$R_{eq}=\frac{\frac{R}{2}\times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{R}{4}$