Question

Two bulbs consume same power when operated at $200V$ and $300V$ respectively. When these bulbs are connected in series across a DC source of $500V$, then

• A. ratio of potential differences across them is 3/2
• B. ratio of potential differences across them is 9/4
• C. ratio of powers consumed across them is 4/9
• D. ratio of powers consumed across them is 2/3

Answer 1

Answer: (C)

$P=\frac{V^2}{R}$
$\therefore R=\frac{V^2}{P}$
or $R\propto V^2$
i.e., $\frac{R_1}{R_2}={\left[\frac{200}{300}\right]}^2=\frac{4}{9}$
When connected in series potential drop and power consumed are in the ratio of their resistances.
So. $\frac{P_1}{P_2}=\frac{V_1}{V_2}=\frac{R_1}{R_2}=\frac{4}{9}$