Question

Two bulbs consume same power when operated at $200\, V$ and $300 \,V$ respectively. When these bulbs are connected in series across a DC source of $500\, V$, 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. $\frac{P_{1}}{P_{2}}=\frac{V_{1}}{V_{2}}=\frac{R_{1}}{R_{2}}=\frac{4}{9}$