60W-220V and 100W-220V bulbs are connected in series to 220V mains. The power consumption is more in the bulb of :

Options

A. 60W
B. 100W
C. same for both the bulbs
D. none

Answer

To solve the problem of determining which bulb consumes more power when a 60W-220V bulb and a 100W-220V bulb are connected in series to a 220V mains supply, we can follow these steps:

### Step 1: Calculate the resistance of each bulb

The resistance \( R \) of a bulb can be calculated using the formula:
\[ R = \frac{V^2}{P} \]
where \( V \) is the voltage and \( P \) is the power rating of the bulb.

**For the 60W bulb:**
\[ R_1 = \frac{220^2}{60} = \frac{48400}{60} \approx 806.67 \, \Omega \]

**For the 100W bulb:**
\[ R_2 = \frac{220^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

### Step 2: Compare the resistances

From the calculations:
- \( R_1 \approx 806.67 \, \Omega \) (for the 60W bulb)
- \( R_2 = 484 \, \Omega \) (for the 100W bulb)

Since \( R_1 > R_2 \), the resistance of the 60W bulb is greater than that of the 100W bulb.

### Step 3: Determine the power consumption in series

In a series circuit, the same current flows through both bulbs. The power consumed by each bulb can be expressed as:
\[ P = I^2 R \]
where \( I \) is the current flowing through the circuit.

Since the current \( I \) is the same for both bulbs, we can conclude that the power consumed by each bulb is directly proportional to its resistance.

### Step 4: Conclusion

Since \( R_1 > R_2 \), it follows that:
\[ P_1 > P_2 \]
Thus, the power consumption is greater in the 60W bulb.

### Final Answer:
The power consumption is more in the 60W bulb.

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