Question

A lamp rated at 1002 - 220 vsupply and another lamp rated at 150 w - 220 supply are connected in series across 220v. supply calculate the respective voltageacross each lamp and also power consumption. What will be the total power is the two lamps are connected in parallel across 220 volt supply.

Answer 1

Given,
$$\begin{gathered} {\mathrm{P}}_1=100\mathrm{W} \\ {\mathrm{V}}_1=220\mathrm{V} \\ {\mathrm{P}}_2=150\mathrm{W} \\ {\mathrm{V}}_2=220\mathrm{V} \\ \mathrm{Using}\mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}} \\ {\mathrm{P}}_1=\frac{{{\mathrm{V}}_1}^2}{{\mathrm{R}}_1}\mathrm{Or}{\mathrm{R}}_1=\frac{{{\mathrm{V}}_1}^2}{{\mathrm{P}}_1}=\frac{220\times 220}{100}=484\mathrm{ohm} \\ \mathrm{Similarly}, \\ {\mathrm{R}}_2=\frac{{{\mathrm{V}}_2}^2}{{\mathrm{P}}_2}=\frac{220\times 220}{150}=\frac{22\times 44}{3}=\frac{968}{3}=322.7\mathrm{ohm} \\ \mathrm{If}\mathrm{lamps}\mathrm{are}\mathrm{connected}\mathrm{in}\mathrm{series}, \\ \mathrm{Resultant}\mathrm{resistance},\mathrm{R}={\mathrm{R}}_1+{\mathrm{R}}_2=484+322.7=806.7\mathrm{ohm} \\ \mathrm{Total}\mathrm{power}, \\ \mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}}=\frac{220\times 220}{806.7}=59.9\mathrm{W} \\ \mathrm{If}\mathrm{lamps}\mathrm{are}\mathrm{connected}\mathrm{in}\mathrm{parallel}, \\ \mathrm{Resultant}\mathrm{resistance},\mathrm{R}=\frac{{\mathrm{R}}_1{\mathrm{R}}_2}{{\mathrm{R}}_1+{\mathrm{R}}_2} \\ =\frac{484\times \frac{968}{3}}{484+\frac{968}{3}}=193.6\mathrm{Ohm} \\ \mathrm{Total}\mathrm{power}, \\ \mathrm{P}=\frac{220\times 220}{193.6}=250\mathrm{W} \end{gathered}$$