n resistances, each of r ohm, when connected in parallel give an equivalent resistance of R ohm. If these resistances were connected in series, the combination would have a resistance in ohms, equal to

Equivalent resistance of n resistances each of r ohm in parallel is given by

$\frac{1}{\mathrm{R}}=\frac{1}{\mathrm{r}}+\frac{1}{\mathrm{r}}+....+\mathrm{n}\mathrm{times}=\frac{\mathrm{n}}{\mathrm{r}}$

so,  r = nR
When these resistances are connected in series, effective resistance is

$\begin{array}{l}{\mathrm{R}}^{\text{'}}=\mathrm{r}+\mathrm{r}+.....+\mathrm{n}\mathrm{times}=\mathrm{nr}\\ \therefore {\mathrm{R}}^{\text{'}}=\mathrm{n}\left(\mathrm{nR}\right)={\mathrm{n}}^2\mathrm{R}\end{array}$