# Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V),

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:

1. (1) $P_{1}=16 W, P_{2}=4 W$

2. (2) $\quad P_{1}=16 \mathrm{~W}, P_{2}=9 \mathrm{~W}$

3. (3) $\mathrm{P}_{1}=9 \mathrm{~W}, \mathrm{P}_{2}=16 \mathrm{~W}$

4. (4) $\mathrm{P}_{1}=4 \mathrm{~W}, \mathrm{P}_{2}=16 \mathrm{~W}$

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, $P_{2}=i^{2} R_{2}=4 W$