c
When the cells are connected in series, current

\(\mathrm{I}_{1}\) is given by :

\(I_{1}=\frac{n E}{R+n r}\)   \(. .(i)\)

When the cells connected in parallel, current

\(\mathrm{I}_{2}\) is given by :

\(\mathrm{I}_{2}=\frac{\mathrm{E}}{\mathrm{R}+\frac{\mathrm{r}}{\mathrm{n}}}=\frac{\mathrm{nE}}{\mathrm{nR}+\mathrm{r}}\)  \(\ldots(\mathrm{ii})\)

As \(I_{1}=I_{2}\)

So, \(\frac{\mathrm{nE}}{\mathrm{R}+\mathrm{nr}}=\frac{\mathrm{nE}}{\mathrm{nR}+\mathrm{r}}\)

\(\therefore \quad \mathrm{R}+\mathrm{nr}=\mathrm{nR}+\mathrm{r}\)

or \((n-1) r=(n-1) R\) or \(r=R\)