Two electric bulbs have tungsten filament of same length. If one of them gives `60 W` and the other `100 W` , then

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 not possible to get different wattage unless the lengths are different

Answer

To solve the problem, we need to analyze the relationship between power, resistance, and the physical properties of the bulbs. Here’s a step-by-step solution:

### Step 1: Understand the relationship between power and resistance
The power \( P \) consumed by an electrical device can be expressed in terms of voltage \( V \) and resistance \( R \):
\[ P = \frac{V^2}{R} \]
From this equation, we can see that power is inversely proportional to resistance when the voltage is constant.

### Step 2: Relate resistance to physical properties
The resistance \( R \) of a conductor (in this case, the filament of the bulb) can be calculated using the formula:
\[ R = \frac{\rho l}{A} \]
where:
- \( \rho \) is the resistivity of the material (constant for tungsten),
- \( l \) is the length of the filament,
- \( A \) is the cross-sectional area of the filament.

### Step 3: Analyze the given information
We are given that both bulbs have the same length of filament and are made of the same material (tungsten). Therefore, the resistivity \( \rho \) and length \( l \) are constant for both bulbs.

### Step 4: Establish the relationship between power and area
Since the length \( l \) is constant, we can say:
\[ R \propto \frac{1}{A} \]
Thus, if power is inversely proportional to resistance, we can conclude:
\[ P \propto A \]
This means that the power of the bulb is directly proportional to the cross-sectional area of the filament.

### Step 5: Compare the two bulbs
Given that one bulb has a power of 60 W and the other has a power of 100 W:
- The 100 W bulb has a greater power, which means it must have a greater cross-sectional area.
- Therefore, the filament of the 100 W bulb is thicker than that of the 60 W bulb.

### Conclusion
From the analysis, we can conclude that the 100 W bulb has a thicker filament than the 60 W bulb.

### Final Answer
The 100 W bulb has a thicker filament.

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