Thermal effect of current
Question

# Two electric bulbs rated P1 and P2 watt at V volt are connected in series across V volt mains, then their total power consumption P is:

Moderate
Solution

## Resistance of Ist bulb $={\mathrm{R}}_{1}=\frac{{\mathrm{V}}^{2}}{{\mathrm{P}}_{1}}$Resistance of IInd bulb $={\mathrm{R}}_{2}=\frac{{\mathrm{V}}^{2}}{{\mathrm{P}}_{2}}$When both bulbs are connected in series,${\mathrm{R}}_{\mathrm{eq}.}={\mathrm{V}}^{2}\left[\frac{1}{{\mathrm{P}}_{1}}+\frac{1}{{\mathrm{P}}_{2}}\right]=\frac{{\mathrm{V}}^{2}\left({\mathrm{P}}_{1}+{\mathrm{P}}_{2}\right)}{{\mathrm{P}}_{1}{\mathrm{P}}_{2}}$Hence, power consumed $\mathrm{P}=\frac{{\mathrm{V}}^{2}}{\mathrm{R}}$                                           $=\frac{{\mathrm{V}}^{2}}{{\mathrm{V}}^{2}\left(\frac{{\mathrm{P}}_{1}+{\mathrm{P}}_{2}}{{\mathrm{P}}_{1}{\mathrm{P}}_{2}}\right)}=\frac{{\mathrm{P}}_{1}{\mathrm{P}}_{2}}{{\mathrm{P}}_{1}+{\mathrm{P}}_{2}}$                                         Hence, (c) is correct.

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