Question

Two electric bulbs, rated at $(25\text{W},220\text{V})$ and $(100\text{W},220\text{V})$, are connected in series across a $220\text{V}$ voltage source. If the $25\text{W}$ and $100\text{W}$ bulbs draw powers $P_1$ and $P_2$ respectively, then :

• A. $P_1=16\text{W},P_2=9\text{W}$
• B. $P_1=16\text{W},P_2=4\text{W}$
• C. $P_1=9\text{W},P_2=16\text{W}$
• D. $P_1=4\text{W},P_2=16\text{W}$

Answer 1

The correct option is B $P_1=16\text{W},P_2=4\text{W}$

$\text{As}R=\frac{V^2}{P},\text{so}{R}_1=\frac{{220}^2}{25}=1936\Omega \text{and}{R}_2=\frac{{220}^2}{100}=484\Omega$

Current flowing through the bulbs connected in series $i$ $=\frac{220}{1936+484}=0.09\text{A}$

$P_1=i^2{R}_1=(0.09{)}^2\times 1936=16\text{W}$

Similarly, $P_2=i^2{R}_2=(0.09{)}^2\times 484=4\text{W}$