Question

For the arrangement of the potentiometer shown in the figure, the balance point is obtained at a distance $75cm$ from $A$ when the key $k$ is open. The second balance point is obtained at $60cm$ from $A$ when the key $k$ is closed. Find the internal resistance (in $\Omega$ ) of the battery $E_1$.

Answer 1

Answer: 6

Let $\lambda$ be the resistance per unit length of wire $AB$.
When $k$ is opened:
$I\left(\lambda x_1\right)=E_1...(i)$
When $k$ is closed:
$I\left(\lambda x_2\right)=E_4-ir...(ii)$
$i=\frac{E_1}{R+r}...(iii)$
$\Rightarrow r=\left(\frac{x_1}{x_2}-1\right)R=\left(\frac{0.75}{0.60}-1\right)24$
$\Rightarrow r=6\Omega$