A circuit of resistacne $R$ is connected to $n$ similar cells. If the current in the circuit is the same when the cells are connected in series or in parallel. If the internal resistacne $r$ of each cell then
Medium
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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 $r=R$
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