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Question

A wire of resistor R is bent into a circular ring of radius r. Equivalent resistance between two points X and Y on its circumference, when angle XOY is α, can be given by

A
Rα4π2(2πα)
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B
R2π(2πα)
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C
R(2πα)
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D
4πRα(2πα)
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Solution

The correct option is A Rα4π2(2πα)
Here RXWY=R2πr×(rα)=Rα2π (α=1r) and RXZY=R2πr×(2πα)=R2π(2πα)
Req=RXWYRXZYRXWY+RXZY=Rα2π×R2π(2πα)Rα2π+R(2πα)2π=Rα4π2(2πα)

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