An electric bulb rated 200 V - 100 W is connected to a 160 V power supply. The power consumed by it would be :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 64 W
The resistance of the bulb is fixed by its rating; at a different supply voltage the power changes as \( V^{2}/R \).
\( \displaystyle R = \frac{V_{\mathrm{rated}}^{2}}{P_{\mathrm{rated}}} = \frac{(200)^{2}}{100} = 400\,\Omega \)
\( \displaystyle P = \frac{V^{2}}{R} = \frac{(160)^{2}}{400} = \frac{25600}{400} = 64\,\mathrm{W} \)
Shortcut: With fixed resistance, \( P \propto V^{2} \): \( P = 100\times\left(\displaystyle\frac{160}{200}\right)^{2} = 100\times0.64 = 64\,\mathrm{W} \).