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  • 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 w

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.The internal resistance (in ) \Omega of the battery E_{1}.

Option: 1

1

 


Option: 2

3


Option: 3

5


Option: 4

6


Answers (1)

best_answer

Let \lambda is resistance per unit length of wire AB. When k is opened 

I\left(\lambda \mathrm{x}_1\right)=E_1---------------(i)

k is closed

\mathrm{I}\left(\lambda \mathrm{x}_2\right)=\mathrm{E}_1-\mathrm{ir}-------------------(ii)

\begin{aligned} & \mathrm{I}\left(\lambda \mathrm{x}_2\right)=\mathrm{E}_1-\mathrm{ir} . \\ & \mathrm{i}=\frac{\mathrm{E}_1}{\mathrm{R}+\mathrm{r}} \ldots \ldots \ldots \ldots \end{aligned}(3)

\Rightarrow \mathrm{r}=\left(\frac{\mathrm{x}_1}{\mathrm{x}_2}-1\right) \mathrm{R}=\left(\frac{0.75}{0.60}-1\right) 24 \quad \therefore \mathrm{r}=6 \Omega

 

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