Question

Two electric bulbs A and B are marked 220V , 40W and 220V 60W respectively. Which one has a higher resistance?

Answer 1

The 40W bulb (Bulb A) has a higher resistance.

Here's the detailed explanation of why:

The Relationship

The relationship between Power (P), Voltage (V), and Resistance (R) is given by the formula:

$P = V^2 / R$

To find the resistance, we can rearrange this formula:

$R = V^2 / P$

The Logic

1. Constant Voltage: Both bulbs are designed to work on the same voltage, which is 220V. So, the 'V' in the formula is the same for both bulbs.
2. Inverse Proportionality: From the rearranged formula ($R = V^2 / P$), you can see that resistance (R) is inversely proportional to power (P).
3. Conclusion: This means that for the same voltage, the bulb with the lower power rating will have the higher resistance.

The Calculation

Let's calculate the resistance for each bulb to prove it:

For Bulb A (220V, 40W):
$R_A = V^2 / P_A$
$R_A = (220)^2 / 40$
$R_A = 48400 / 40$
$R_A = \textbf{1210 Ω}$

For Bulb B (220V, 60W):
$R_B = V^2 / P_B$
$R_B = (220)^2 / 60$
$R_B = 48400 / 60$
$R_B \approx \textbf{806.7 Ω}$

As you can see from the calculation, 1210 Ω is greater than 806.7 Ω.

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Intuitive Way to Think About It

Think of what "power" means. A 60W bulb is brighter than a 40W bulb, meaning it consumes more energy and lets more electric current flow through it. For more current to flow at the same voltage (electrical "push"), the resistance must be lower. It's like trying to get more water through a pipe; you need a wider pipe (less resistance) to increase the flow rate.