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In the simple potentionmeter circuit, wh...

In the simple potentionmeter circuit, where the length `AB` of the potentiometer wire is `1 m`, the resistors `X` and `Y` have values of `5 Omega` and `2 Omega`, respectively. When `X` is shunted by a wire, the balance point is found to be `0.625 m` from `A`. What is the resistance of the shunt?

Text Solution

Verified by Experts

Let `R` be the resistance of the shunted wire. The effective resistance of `R` and `5 Omega` in parallet is `5 R//(5 + R)`. At balance point,
`(5R//(5 + R))/(2) = (0.625)/(1 - 0.625) = (0.625)/(0.0375) =(5)/(3)`
On solving, we get `R = 10 Omega`.
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