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(D) Let $E$ be the $EMF$ and $r$ be the internal resistance of each cell. The external resistance is $R = 2 \Omega$.Case $1$: Cells in series.The tota

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(D) Let $E$ be the $EMF$ and $r$ be the internal resistance of each cell. The external resistance is $R = 2 \Omega$.Case $1$: Cells in series.The total $EMF$ is $2E$ and the total internal resistance is $2r$. The current $I$ is given by:$I = \frac{2E}{R + 2r}$ ... $(i)$Case $2$: Cells in parallel.The total $EMF$ is $E$ and the total internal resistance is $\frac{r}{2}$. The current $I$ is given by:$I = \frac{E}{R + \frac{r}{2}} = \frac{2E}{2R + r}$ ... (ii)Since the current $I$ is the same in both cases,we equate $(i)$ and (ii):$\frac{2E}{R + 2r} = \frac{2E}{2R + r}$$R + 2r = 2R + r$$r = R$Given $R = 2 \Omega$,therefore $r = 2 \Omega$.

Two identical cells give the same current through an external resistance of $2 \Omega$ regardless of whether the cells are connected in series or in parallel. The internal resistance of each cell is: (in $Omega$)

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