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When electric bulbs of same power, but different marked voltage are connected in series across the power line, their brightness will be:
A) Proportional to their marked voltage.
B) Inversely proportional to their marked voltage.
C) Proportional to the square of their marked voltage.
D) Inversely proportional to the square of their marked voltage (E) the same for all of them.

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Last updated date: 28th Feb 2024
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IVSAT 2024
Answer
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Hint: The power is defined as the rate at which the electrical energy is transferred from one place to another with respect to time. The brightness of any circuit depends upon the power of the circuit. The more the power of the circuit the more will be the brightness out of the bulbs.

Formula used:
The formula for the power in the circuit is given by,
\[ \Rightarrow P = \dfrac{{{V^2}}}{R}\]
Where power is P, the potential difference is V and the resistance is R of the circuit.

Complete step by step solution:
It is given in the problem that when electric bulbs of same power, but different marked voltage are connected in series across the power line then we need to select the correct answer for this problem.
As the problem says that all the bulbs have different voltages but the same power.
The formula for the power in the circuit is given by,
\[ \Rightarrow P = \dfrac{{{V^2}}}{R}\]
Where power is P, the potential difference is V and the resistance is R of the circuit.
The formula represents that the power is proportional to the square of potential voltage, so the power will be proportional to the square of the marked voltage of the bulbs.

The correct answer for this problem is option C.

Note: If the bulbs are connected in series then the potential difference across each of the bulbs will be decreasing after each of the bulbs. If the bulbs were connected in parallel then the potential difference across each bulb will be the same as the power source.