The emf of a cell having internal resistance 1$\mathrm{\Omega }$ is balanced against a length of 330 cm on a potentiometer wire. When an external resistance of 2$\mathrm{\Omega }$ is connected across the cell, the balancing length will be :

Here, balancing length without an external
resistance l₁= 300 cm.
When external resistance 2Ω is connected
across the cell, balancing length is l₂,
internal resistance is 1Ω.
To measure the internal resistance with a potentiometer,
$r=\frac{R\left(I_1-I_2\right)}{I_2}$
we need to find l₂

$\begin{array}{l}\mathrm{I}=\frac{2\left(330-{\mathrm{I}}_2\right)}{{\mathrm{I}}_2}\\ {\mathrm{I}}_2=660-2{\mathrm{I}}_2\\ {\mathrm{I}}_2=220\mathrm{cm}\end{array}$