In a potentiometer experiment, it is found that no current passes through the galvanometer when the…

Without shunting conditions, 



$E_s=52\times x .....\left(\mathrm{i}\right)$, when, balanced, where, $x=$ potential gradient of wire, with shunting condition



On balancing, $E_s-\frac{E}{\left(r+R\right)}r=40\times x ....\left(\mathrm{ii}\right)$.
On solving:
$\frac{\left(\mathrm{i}\right)}{\left(\mathrm{ii}\right)}\Rightarrow \frac{1}{1-\frac{r}{r+R}}=\frac{52}{40}$
$\therefore r=1.5 \mathrm{\Omega }$