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

1. R/4
2. 4R
3. R/8
4. R/2

Correct answer: R/4

Solution

When the wire is bent into a circle, it forms two equal resistances (R/2 each) in parallel between the diametrically opposite points. The equivalent resistance of two parallel resistances R/2 is given by 1/Req = 1/(R/2) + 1/(R/2), which simplifies to Req = R/4.

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