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# A resistance of $2 \Omega$ is connected across one gap of a meter-bridge and an unknown resistance, greater than $2 \Omega$, is connected across the other gap. When these resistances are interchanged, the balance point shifts by $20cm$. The unknown resistance is

$\begin {array} {1 1} (A)\;3\Omega & \quad (B)\;4\Omega \\ (C)\;5\Omega & \quad (D)\;6\Omega \end {array}$

Before swapping, $\large\frac{2}{R}$ $= \large\frac{x}{100-x}$
After swapping, $\large\frac{R}{2}$ $= \large\frac{x+20}{80-x}$
On solving the above equations and eliminating $x$, we get $R = 3 \Omega$
Ans : (A)
edited Mar 14, 2014