Question

A $200\text{W}$ and $100\text{W}$ bulbs, both will operate at $220\text{V}$, are connected in series to a $220\text{V}$ power supply. The power consumed by the combination is-

• A. $75\text{W}$
• B. $56\text{W}$
• C. $66\text{W}$
• D. $46W$

Answer 1

The correct option is C $66\text{W}$

Given, $P_1=200\text{W};P_1=100\text{W}$

$P=\frac{V^2}{R}\Rightarrow R=\frac{V^2}{P}$

$\Rightarrow R_1=\frac{V^2}{P_1}=\frac{(220{)}^2}{200}=242\Omega$

$\Rightarrow R_2=\frac{V^2}{P_2}=\frac{(220{)}^2}{100}=484\Omega$

In series, $R_s=R_1+R_2=242+484=726\Omega$

Power consumed by this combination is,

$P=\frac{V^2}{R_s}=\frac{(220{)}^2}{726}\approx 66\text{W}$


<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.