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 thekey k is closed. Find the internal resistance (in $\Omega$) of the battery $E_1$.

Answer 1

Let $\lambda$ is resistance per unit length of wire AB.
When k is opened $I\left(\lambda x_1\right)=E_1$ ...(1)
when k is closed $I\lambda x_2=E_{1}ir$ ...(2)
$\Rightarrow i=\frac{E_1}{R+r}$ ......... (3)
$\Rightarrow r=(\frac{x_1}{x_2}-1)R$
$=(\frac{0.75}{0.60}-1)24$
$\Rightarrow r=6\Omega$