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The filament of 60W and 100 W bulbs are ...

The filament of 60W and 100 W bulbs are of the same length. Which filament will be thicker ?

A

100 W bulb has thicker filament

B

60 W bulb has thicker filament

C

Both filaments are of same thickness

D

It is impossible to get different wattage unless lengths are different

Text Solution

AI Generated Solution

The correct Answer is:
To determine which filament is thicker between the 60W and 100W bulbs, we can analyze the relationship between power, resistance, and cross-sectional area of the filament. ### Step-by-Step Solution: 1. **Understanding Power and Resistance**: - The power (P) consumed by a bulb is given by the formula: \[ P = \frac{V^2}{R} \] where \( V \) is the voltage and \( R \) is the resistance of the filament. 2. **Relating Power to Resistance**: - Rearranging the formula gives: \[ R = \frac{V^2}{P} \] - This shows that for a constant voltage, the resistance is inversely proportional to the power. Therefore, a bulb with higher power will have lower resistance. 3. **Comparing the Two Bulbs**: - For the 60W bulb: \[ R_{60} = \frac{V^2}{60} \] - For the 100W bulb: \[ R_{100} = \frac{V^2}{100} \] - Since \( R_{60} > R_{100} \), the 60W bulb has a higher resistance than the 100W bulb. 4. **Understanding Resistance and Area**: - The resistance of a wire (or filament) is also given by: \[ R = \rho \frac{L}{A} \] where \( \rho \) is the resistivity of the material, \( L \) is the length, and \( A \) is the cross-sectional area. - Since the length of both filaments is the same (as given in the problem), we can conclude that: \[ R \propto \frac{1}{A} \] - This means that if the resistance increases, the cross-sectional area must decrease. 5. **Conclusion**: - Since the 60W bulb has a higher resistance than the 100W bulb, it must have a smaller cross-sectional area. Therefore, the filament of the 100W bulb, which has lower resistance, must be thicker. ### Final Answer: The filament of the 100W bulb is thicker than the filament of the 60W bulb. ---
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