A 100 W bulb working on 200 V and a 200 W bulb on 100 V, have their resistances in the ratio
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 8 : 1 \)
The resistance of a bulb follows from its rated power and voltage:
\( \displaystyle P = \frac{V^{2}}{R} \;\Rightarrow\; R = \frac{V^{2}}{P} \)
\( \displaystyle R_1 = \frac{(200)^{2}}{100} = 400\,\Omega \)
\( \displaystyle R_2 = \frac{(100)^{2}}{200} = 50\,\Omega \)
\( \displaystyle \frac{R_1}{R_2} = \frac{400}{50} = 8 : 1 \)