The balancing length for a cell is 560 c m in a potentiometer experiment. When an external resistance of 10…

Let the emf of cell is $\epsilon$ internal resistance is $\text{'}r\text{'}$ and potential gradient is $\mathrm{x}$ .
Only cell connected:
$\text{E}=560\mathrm{x} -----\left(1\right)$
After connecting the resistor
$\frac{\text{E}\times 10}{10+r}=500\mathrm{x} ------\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$\frac{560x\times 10}{10+\mathrm{r}}=500x$
$56=50+5\mathrm{r}$
$\mathrm{r}=\frac{6}{5}=1.2\mathrm{}\mathrm{\Omega }$
$$\begin{gathered} \mathrm{so}, \\ \mathrm{n}=12 \end{gathered}$$