The tungsten filaments of two electric bulbs are of the same length. If one of them gives 25 W power and the other 60 W power, then

Options

A. Both the filaments are of same thickness
B. 25 W bulb has thicker filament
C. 60 W bulb has thicker filament
D. Both the filaments have same cross-sectional area

Answer

To solve the problem, we need to compare the thickness of the filaments in two electric bulbs based on their power ratings. The bulbs have the same length, but different power outputs.

### Step 1: Understand the relationship between power, voltage, and resistance
The power \( P \) consumed by an electrical device can be expressed using the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage across the device and \( R \) is its resistance.

### Step 2: Identify the power ratings of the bulbs
Let’s denote:
- \( P_1 = 60 \, W \) (for the first bulb)
- \( P_2 = 25 \, W \) (for the second bulb)

### Step 3: Compare the resistances of the two bulbs
Since both bulbs are connected to the same voltage source, we can compare their resistances using the power formula:
\[ R_1 = \frac{V^2}{P_1} \quad \text{and} \quad R_2 = \frac{V^2}{P_2} \]
Since \( P_1 > P_2 \), it follows that:
\[ R_1 < R_2 \]
This means the resistance of the 60 W bulb is less than the resistance of the 25 W bulb.

### Step 4: Relate resistance to the physical properties of the filament
Resistance \( R \) can also be expressed in terms of resistivity \( \rho \), length \( L \), and cross-sectional area \( A \) of the filament:
\[ R = \frac{\rho L}{A} \]
Since both filaments are of the same length and made of the same material (tungsten), we can say:
\[ R \propto \frac{1}{A} \]
Thus, if \( R_1 < R_2 \), it implies:
\[ A_1 > A_2 \]
This means the cross-sectional area of the filament in the 60 W bulb is greater than that of the 25 W bulb.

### Step 5: Conclusion
Since the cross-sectional area \( A \) is directly related to the thickness of the filament, we conclude that:
- The 60 W bulb has a thicker filament than the 25 W bulb.

### Final Answer
The bulb that gives 60 W power has a thicker filament.

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