In an experiment to measure the internal resistance of a cell by potentiometer, it is found that the balance point is at a length of $2\,m$ when the cell is shunted by a $5\,\Omega $ resistance; and is at a length of $3\,m$ when the cell is shunted by a $10\,\Omega $ resistance. The internal resistance of the cell is, then ................ $\Omega $
Medium
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$r = \left( {\frac{{{l_1} - {l_2}}}{{{l_2}}}} \right) \times R'$$ = \left( {\frac{{{l_1} - 2}}{2}} \right) \times 5$ ... $(i)$
and $r = \left( {\frac{{{l_1} - 3}}{3}} \right) \times 10$ ... $(ii)$
On solving $(i)$ and $(ii)$
$r = 10 \,\Omega$
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