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

Options

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

Answer

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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