Question

In potentiometer experiment, the balancing length with a cell $E_1$ of unknown e.m.f. is $\ell_1$ cm. By shunting the cell with resistance $R$, the balancing length becomes $\ell_2$ cm, the internal resistance $r$ of a cell is

• A. $r = 0$
• B. $r = \frac{R}{2}$
• C. $r = 2R$
• D. $r = R$

Hint:

In a potentiometer experiment, the relation between balancing lengths helps in calculating the internal resistance.

Answer 1

The Correct Option is D

Step 1: Understanding potentiometer setup.
The internal resistance $r$ of the cell can be determined by the change in the balancing length when the cell is shunted with resistance $R$. The relation between the lengths before and after shunting is:
\[ \frac{\ell_2}{\ell_1} = \frac{R + r}{r} \]
Step 2: Solving for $r$.
\[ \frac{\ell_2}{\ell_1} = 1 + \frac{R}{r} \] \[ \frac{\ell_2 - \ell_1}{\ell_1} = \frac{R}{r} \] \[ r = \frac{R\ell_1}{\ell_2 - \ell_1} \] Since $\ell_1$ and $\ell_2$ are in the same ratio, we deduce that $r = R$.

Step 3: Conclusion.
The internal resistance of the cell is $r = R$.