AIIMS 2019 Physics Internal Resistance of a Cell MCQ Question

When a cell with an electromotive force (emf) $\mathcal{E}$ and internal resistance $r$ is connected to an external resistance $nr$, the total resistance in the circuit becomes $r + nr = (n + 1)r$. The terminal voltage $V$ can be calculated using Ohm's law, where $V = \mathcal{E} - I \cdot r$. The current $I$ through the circuit is given by $I = \frac{\mathcal{E}}{(n + 1)r}$, leading to $V = \mathcal{E} - \frac{\mathcal{E} \cdot r}{(n + 1)r} = \frac{n}{n + 1} \mathcal{E}$. Thus, the ratio of the terminal voltage to the emf is $\frac{V}{\mathcal{E}} = \frac{n}{n + 1}$, confirming option C.

Options A and B are incorrect because they do not account for the total resistance in the circuit, leading to incorrect ratios. Option D is irrelevant as it does not provide a valid answer.