A wire of uniform cross-section, length $L$ and resistance $R$ is b...

Question

A wire of uniform cross-section, length $L$ and resistance $R$ is bent into a complete circle. Find the resistance between any two diametrically opposite points.

Accepted Answer

or
Each semicircle has resistance $R/2$. The two semicircles are in parallel:
$$R_{eq} = \frac{(R/2)(R/2)}{(R/2)+(R/2)} = \frac{R^2/4}{R} = \frac{R}{4}$$

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