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A resistance of 2 $Ω$ is connected across one gap of a metre bridge (the length of the wire is 100cm) and an unknown resistance greater than 2 $Ω$ , is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm neglecting any corrections, the unknown resistance is

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3 $Ω$

4 $Ω$

5 $Ω$

6 $Ω$

answer is A.

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Detailed Solution

$\frac{x}{2} = \frac{ℓ}{100 - ℓ}$ ......(1) When they are interchanged

$\begin{array}{l} \frac{2}{x} = \frac{ℓ^{1}}{100 - ℓ^{1}} = \frac{ℓ + 20}{100 - (ℓ + 20)} \\ \frac{2}{x} = \frac{ℓ + 20}{80 - ℓ} \end{array} \begin{array}{l} o n s o l v i n g w e g e t \\ ℓ = 40 cm \\ ∴ x = 3 Ω \end{array}$

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