Question

Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draws powers $P_{1}and{P}_2$ respectively, then

Answer 1

Let the resistance of 25 W and 100 W bulb be $R_{1}and{R}_2$ respectively.

We know that,
$R=\frac{V^2}{P^{\prime }}$

Given $V=220V,P_1^{\prime }=25W,P_2^{\prime }=100W$

$R_1=\frac{{220}^2}{25}$

$R_2=\frac{{220}^2}{100}$

Current passing through the electric bulb is I, then

$I=\frac{220V}{R_1+R_2}=\frac{220}{\frac{(220{)}^2}{25}+\frac{(220{)}^2}{100}}$

$I=\frac{220}{220[\frac{220}{25}+\frac{220}{100}]}=\frac{1}{8.8+2.2}$

$I=\frac{1}{11}A$

$P_1=I^2{R}_1={\left(\frac{1}{11}\right)}^2\times \frac{(220{)}^2}{25}=16W$

$P_2=I^2{R}_2={\left(\frac{1}{11}\right)}^2\times \frac{(220{)}^2}{100}=4W$

Hence, $P_{1}and{P}_2$ is 16 W and 4 W respectively.

Option (C) is correct.