Question

A wire is bent into a circle of radius $r$. If $s$ is the resistance per unit length of the wire, then the effective resistance at the ends of the diameter is:

• A. $rs/2$
• B. $\pi r/2s$
• C. $\pi rs/2$
• D. $\pi s/2r$

Answer 1

Answer: (C)

$\pi rs/2$

$L_1=\pi r{L}_2=\pi r$
$R_1=s\pi r{R}_2=s\pi r$
These two wire will be in parallel

$R_{eq}=\frac{R_1{R}_2}{R_1+R_2}=\frac{\pi rs}{2}$