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Question

The resistance per unit length of a wire is 106 Ω/m. It is bent in the form of a circle of diameter 2 m. A wire of same material and cross sectional area is connected across its diameter. The total resistance across its diameter AB will be

A
43π×106Ω
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B
23π×106Ω
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C
0.88×106Ω
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D
14×106Ω
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Solution

The correct option is C 0.88×106Ω
Resistance per unit length,
a=106For upper arc R1=aπrFor lower arc R2=aπr
For wire AB=2ra

1Reff=1R1+1R2+1R3=1aπr+1aπr+12ar
Reff=0.88×106Ω

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