Question

A wire of resistance $4R$ is bent in the form of a circle. What is the effective resistance between the ends of the diameter?

Answer 1

When a wire of resistance $4R$ is bent in the form of circle, then the resistance of each segment across the diameter becomes $2R$ as shown in the figure.

Equivalent resistance between A and B: $\frac{1}{R_{AB}}=\frac{1}{R_1}+\frac{1}{R_B}$ (in parallel combination)

$\therefore$ $\frac{1}{R_{AB}}=\frac{1}{2R}+\frac{1}{2R}$

$\frac{1}{R_{AB}}=\frac{2}{2R}$

$⟹$ $R_{AB}=R$