Question

For the arrangement of the potentiometer shown in the figure, the balance point is obtained at a distance $75 \,cm$ from $A$ when the key $k$ is open. The second balance point is obtained at $60 \,cm$ from $A$ when the key $k$ is closed. Find the internal resistance (in $\Omega$ ) of the battery $E_{1}$.

Answer 1

Let $\lambda$ be the resistance per unit length of wire $A B$.
When $k$ is opened:
$I\left(\lambda x_{1}\right)=E_{1}\,\,\, ...(i)$
When $k$ is closed:
$I\left(\lambda x_{2}\right)=E_{4}-i r \,\,\,...(ii)$
$i=\frac{E_{1}}{R+r}\,\,\,...(iii)$
$\Rightarrow r=\left(\frac{x_{1}}{x_{2}}-1\right) R=\left(\frac{0.75}{0.60}-1\right) 24$
$ \Rightarrow r=6 \,\Omega$