Question:
Two electric bulbs, rated at $(25 \mathrm{~W}, 220 \mathrm{~V})$ and $(100 \mathrm{~W}, 220 \mathrm{~V})$, are connected in series across a $220 \mathrm{~V}$ voltage source. If the $25 \mathrm{~W}$ and $100 \mathrm{~W}$ bulbs draw powers $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ respectively, then:
Correct Option: 1
Solution:
(1) As $\mathrm{R}=\frac{\mathrm{V}^{2}}{\mathrm{P}}$, so $\mathrm{R}_{1}=\frac{220^{2}}{25}$ and $\mathrm{R}_{2}=\frac{220^{2}}{100}$
Current flown $\mathrm{i}=\frac{220}{\mathrm{R}_{1}+\mathrm{R}_{2}}$
$\mathrm{P}_{1}=\mathrm{i}^{2} \mathrm{R}_{1}=\frac{220^{2}}{\left(\frac{220^{2}}{25}+\frac{220^{2}}{100}\right)} \times \frac{220^{2}}{25}=16 \mathrm{~W}$
Similarly, $P_{2}=i^{2} R_{2}=4 W$