A resistance of $2 \Omega$ is comnected across one gap of a metre-bridge (the length of the wire is $100 \mathrm{~cm}$ ) and an unknown resistance, greater than $2 \Omega$, is connected across the other gap. When these resistance are interchanged, the balance point shifts by $20 \mathrm{~cm}$. Neglecting any corrections, the unknown resistance is
IIT 2007, Medium
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$ \frac{2}{\mathrm{x}}=\frac{\ell}{100-\ell} $ ...............$(I)$
$ \frac{\mathrm{x}}{2}=\frac{\ell+20}{80-\ell}$ ...............$(II)$
Solving $(i)$ and $(ii)$ $x=3 \Omega$
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