Question

When electric bulbs of same power, but different marked voltages 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

Answer 1

The correct option is C proportional to the square of their marked voltage

As power rating is same, so resistance of bulb will be

$R=\frac{V_{rated}^2}{P_{rated}}\Rightarrow R\propto V_{rated}^2$

Power consumed by the bulb,

$P=I^{2}R$

As we know that in series, current is same.

$\therefore P\propto R\propto V_{rated}^2$

We know that the power consumed by the bulb is directly proportional to brightness.

So, $\text{Brightness}\propto V_{rated}^2$

Therefore, option $\left(c\right)$ is right.

Why this question ? Caution: While solving this type of question, focus on what data is constant like power, voltage or current, and use this knowledge in the equation to find proportional or inverse proportional relation.