Question

Two bulbs of 40 W and 60 W are connected to a 220 V source. The ratio of their resistances will be:

• A. \(4 : 3\)
• B. \(3 : 4\)
• C. \(2 : 3\)
• D. \(3 : 2\)

Hint:

Remember: Resistance is inversely proportional to power for same voltage: \[ R \propto \frac{1}{P}. \]

Answer 1

The Correct Option is A

Power \(P\), voltage \(V\), and resistance \(R\) are related by: \[ P = \frac{V^2}{R} \implies R = \frac{V^2}{P}. \] For the two bulbs: \[ R_1 = \frac{220^2}{40}, \quad R_2 = \frac{220^2}{60}. \] Therefore, the ratio of resistances: \[ \frac{R_1}{R_2} = \frac{220^2/40}{220^2/60} = \frac{60}{40} = \frac{3}{2}. \] But since \(R_1\) corresponds to the 40 W bulb and \(R_2\) to 60 W bulb, ratio \(R_1 : R_2 = 3 : 2\). Note: This matches option (D), so correct answer is (D) \(3 : 2\).