Physics - Current Electricity Question with Solution | TestHub

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 $I=\frac{E_0}{\rho L+r}$, where $L$ is the total length of the wire.

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

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

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:

$E=kl\Rightarrow l=\frac{E}{k}$

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