Question

Two bulbs consume same energy 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 difference across them is 3/2
• B. ratio of potential difference across them is 4/9
• C. ratio of power produced in them is 4/9
• D. ratio of power produced in them is 2/3

Answer 1

Answer: (B), (C)

The correct options are
B ratio of potential difference across them is 4/9
C ratio of power produced in them is 4/9

$P=\frac{V^2}{R}$ or $R=\frac{V^2}{P}$ 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 is in the ratio of their resistances. So, $\frac{V_1}{V_2}=\frac{R_1}{R_2}=\frac{4}{9}$

Now, $P=I^{2}R$ Or $P\propto R$ (in series I is the same)

Or $\frac{P_1}{P_2}=\frac{R_1}{R_2}=\frac{4}{9}$