Question

A $25\;{\text{W}}$and $100\;{\text{W}}$ bulb are joined in series and connected to the mains. Which bulb will glow brighter?
A. $25\;{\text{W}}$ bulb
B. $100\;{\text{W}}$ bulb
C. Both bulb will glow brighter
D. None will glow brighter

Answer 1

The calculation of power is essential since the bulb will glow brighter and it will dissipate more power. And each bulb is manufactured such that they operate in particular voltage range and have particular power output. The brightness will vary according to the series or parallel connection.

Complete step-by-step solution:
Given the bulbs are connected to the mains. Thus the voltage will be $220\;{\text{V}}$ .
The electrical power is measured in Watts. The expression for power is given as,
$P = \dfrac{{{V^2}}}{R}$
Where, $V$ is the voltage and $R$ is the resistance.
From the above equation it is clear that more resistance will be for low power output.
The $25\;{\text{W}}$ bulb will be having more resistance than $100\;{\text{W}}$.
The expression for power is given as,
$P = {I^2}R$
Where, $I$ is the current, $R$ is the resistance.
Since the bulbs are connected in series, the current through each bulb will be the same. Thus the power dissipated will be proportional to the resistance of each bulb. The bulb having more resistance will dissipate more power. Thus $25\;{\text{W}}$ bulb having more power will glow brighter.
The answer is option A.

Note:- If the bulbs are connected in parallel, the current will be different for each bulb. The current will be more than the bulb having low resistance. Since the power is proportional to square of the current, the low resistance bulb will glow brighter.