Question

Two bulbs of  \((40W,\ 200V)\) and \((100 W,\ 200V)\). Then correct relation for their resistance:

• A. \(R_{40}<R_{100}\)
• B. \(R_{40}>R_{100}\)
• C. \(R_{40}=R_{100}\)
• D. \(No\  relation\  can\  be\  predicted\)

Answer 1

The Correct Option is B

To determine the correct relation between the resistances of the two bulbs, we use the formula for power in terms of resistance and voltage:

\(P = \frac{V^2}{R}\) 

Where \(P\) is the power, \(V\) is the voltage, and \(R\) is the resistance.

We have two bulbs:

• Bulb 1: \(40W,\ 200V\)
• Bulb 2: \(100W,\ 200V\)

Let's calculate their resistances:

1. Resistance of 40W bulb:
   Using \(R = \frac{V^2}{P}\), we substitute the values:
   • \(R_{40} = \frac{200^2}{40} = \frac{40000}{40} = 1000 \, \Omega\)
2. Resistance of 100W bulb:
   Again, using \(R = \frac{V^2}{P}\), we substitute the values:
   • \(R_{100} = \frac{200^2}{100} = \frac{40000}{100} = 400 \, \Omega\)

Now, comparing the resistances:

• \(R_{40} = 1000 \, \Omega\)
• \(R_{100} = 400 \, \Omega\)

Clearly, \(R_{40} > R_{100}\).

Therefore, the correct relation is: \(R_{40} > R_{100}\).