Question

It is observed in a potentiometer experiment that no current passes through the galvanometer across when the terminals of a cell are connected across a certain length of the potentiometer wire. On shuting the cell by a 2 $\Omega$ resistance, the balancing length is reduced to half. The internal resistance of the cell is :-

Answer 1

In initial (un-shunted) balance length is $\mu$, then shunted balance

length is $l_2=l_1/2$ against external resistance $R=2\Omega$

so internal resistance :-

$r=(\frac{l}{l_2}-1)R=(2-1)\times 2=2\Omega$