In a potentiometer experiment the balancing with a cell is at length $240\, cm$. On shunting the cell with a resistance of $2$ $\Omega$, the balancing length becomes $120\, cm$. The internal resistance of the cell is ................. $\Omega $
AIEEE 2005, Medium
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$[2]$ all resistances are increased by $10\,ohms$
$[3]$ all resistances are made five times
$[4]$ the battery and the galvanometer are interchanged