In potentiometer experiment, null point is obtained at a particular point for a cell on potentiometer wire 'x' cm long. If length of potentiometer wire is increased by few cm without changing the cell, the balancing length will (Driving source is not changed)

Let the driving cell have EMF $E_0$ and internal resistance $r$. Let the resistance per unit length of the potentiometer wire be $\rho$.

The current in the potentiometer wire is given by $I = \dfrac{E_0}{\rho L + r}$, where $L$ is the total length of the wire.

The potential gradient $k$ (potential drop per unit length) is:

$k = I \rho = \dfrac{E_0 \rho}{\rho L + r}$

When the length of the potentiometer wire $L$ is increased, the denominator $(\rho L + r)$ increases, which causes the potential gradient $k$ to decrease.

For a cell of EMF $E$, the balancing length $l$ is given by the condition:

$E = k l \Rightarrow l = \dfrac{E}{k}$

Since the EMF of the cell $E$ remains constant and the potential gradient $k$ decreases, the balancing length $l$ must increase.