Several electric bulbs of the same rated power but different rated (marked) voltages are connected in series across the mains. How does the brightness of each bulb depend on its marked voltage?

proportional to the square of its marked voltage
proportional to its marked voltage
inversely proportional to its marked voltage
inversely proportional to the square of its marked voltage

Correct answer: proportional to the square of its marked voltage

Solution

In series the current is common, so actual power = I² R; since R = V²/P with P fixed, R (and hence brightness) is proportional to the square of the marked voltage.

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