Question

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

• A. R/8
• B. 4R
• C. R/2
• D. R/4

Answer 1

The correct option is D R/4

$\text{Step 1: Draw resistance structure}$ $\text{[Ref. Fig.]}$

Resistance of both part will be $R/2$ because wire is uniform.

$\text{Step 2: Equivalent resistance between A and B}$,

Each resistor has both terminals connected to both terminals of the others so both are in parallel-

$R_{eqparallel}=\frac{R_1{R}_2}{R_1+R_2}$

$\Rightarrow R_{AB}=\frac{\frac{R}{2}\times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{R}{4}$

Hence equivalent resistance between any two of diametrically opposite points will be $\frac{R}{4}$

Option $\left(D\right)$ correct.