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Incandescent bulbs are rated so that filament resistance rises with temperature. At room temperature, 100 W, 60 W and 40 W bulbs (all for the same supply voltage) have filament resistances R100, R60 and R40. Which relation holds among these resistances?

1. 1/R100 = 1/R40 + 1/R60
2. R100 = R40 + R60
3. R100 > R60 > R40
4. 1/R100 > 1/R60 > 1/R40

Correct answer: 1/R100 > 1/R60 > 1/R40

Solution

Since P = V²/R at fixed V, the 100 W bulb has the smallest R, so 1/R100 > 1/R60 > 1/R40.

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