n identical light bulbs, each designed to draw P power from a certain supply, are joined in series across that supply. The total power which they will draw is

Let R be the resistance of each bulb. Resistance of n bulbs = n R
Current in each bulb $=\mathrm{i}=\frac{\mathrm{V}}{\mathrm{nR}}$
Power drawn by each bulb
$\begin{array}{r}{\mathrm{P}}^2={\mathrm{i}}^2\mathrm{R}=\frac{{\mathrm{V}}^2}{{\mathrm{n}}^2{\mathrm{R}}^2}\times \mathrm{R}\\ =\frac{{\mathrm{V}}^2}{{\mathrm{n}}^2\mathrm{R}}=\frac{\mathrm{P}}{{\mathrm{n}}^2}\left(\because \mathrm{R}=\frac{{\mathrm{V}}^2}{\mathrm{P}}\right)\end{array}$
Total power drawn $=\mathrm{n}\times \left(\frac{\mathrm{P}}{{\mathrm{n}}^2}\right)=\frac{\mathrm{P}}{\mathrm{n}}$