A 200 W and 100 W bulbs, both meant for operation at 220 V, are connected in series to 220 V. The power consumption by the combination is

Options

A. 46 W
B. 66 W
C. 56 W
D. 75 W

Explanation

To solve the problem of finding the power consumption by the combination of a 200 W and a 100 W bulb connected in series to a 220 V supply, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Power Ratings and Voltage:**
- The power ratings of the bulbs are:
- Bulb 1 (200 W)
- Bulb 2 (100 W)
- The voltage supply is \( V = 220 \, \text{V} \).

2. **Calculate the Resistance of Each Bulb:**
- The resistance \( R \) of a bulb can be calculated using the formula:
\[ R = \frac{V^2}{P} \]
- For Bulb 1 (200 W):
\[ R_1 = \frac{(220)^2}{200} = \frac{48400}{200} = 242 \, \Omega \]
- For Bulb 2 (100 W):
\[ R_2 = \frac{(220)^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

3. **Calculate the Total Resistance in Series:**
- The total resistance \( R_{\text{total}} \) when resistors are connected in series is given by:
\[ R_{\text{total}} = R_1 + R_2 \]
- Therefore:
\[ R_{\text{total}} = 242 + 484 = 726 \, \Omega \]

4. **Calculate the Power Consumption of the Combination:**
- The power consumed by the combination can be calculated using the formula:
\[ P = \frac{V^2}{R_{\text{total}}} \]
- Substituting the values:
\[ P = \frac{(220)^2}{726} = \frac{48400}{726} \approx 66.67 \, \text{W} \]

5. **Conclusion:**
- The power consumption by the combination of the two bulbs when connected in series to a 220 V supply is approximately \( 66.67 \, \text{W} \).

### Final Answer:
The power consumption by the combination is approximately **66.67 W**.

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