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A resistance of $20 \Omega$ is connected in the left gap of a metre bridge and an unknown resistance greater than $20 \Omega$ is connected in the right gap. When these resistances are interchanged, the balance point shift by $20 \mathrm{~cm}$. The unknown resistance is
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The correct answer is:
$30 \Omega$
Let the unknown resistance be $R$ and the balance point be at $l \mathrm{~cm}$ initially.
using, $\frac{R_2}{R_1}=\frac{l}{100-l}$
Case 1: $R_1=20 \Omega$ and $R_2=R$
Using equation (1) and (2) we get,
$\frac{l}{100-l}=\frac{80-l}{l+20}$
$\Rightarrow l=40 \mathrm{~cm}$
From equation (1),
$\frac{20}{R}=\frac{40}{100-40}$
$\Rightarrow R=30 \Omega$
using, $\frac{R_2}{R_1}=\frac{l}{100-l}$
Case 1: $R_1=20 \Omega$ and $R_2=R$
Using equation (1) and (2) we get,
$\frac{l}{100-l}=\frac{80-l}{l+20}$
$\Rightarrow l=40 \mathrm{~cm}$
From equation (1),
$\frac{20}{R}=\frac{40}{100-40}$
$\Rightarrow R=30 \Omega$
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