A `100W, 200V` bulb is operated on a `110V` line. The power consumed is

Options

A. 25W
B. 50W
C. 75W
D. 90W

Explanation

To solve the problem of how much power a `100W, 220V` bulb consumes when operated on a `110V` line, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Bulb Rating**:
The bulb is rated at `100W` and `220V`. This means that at `220V`, the bulb consumes `100W` of power.

2. **Calculate the Resistance of the Bulb**:
The resistance \( R \) of the bulb can be calculated using the formula:
\[ R = \frac{V^2}{P} \]
where \( V \) is the rated voltage and \( P \) is the rated power.
Substituting the values:
\[ R = \frac{220^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

3. **Calculate the Power Consumed at 110V**:
When the bulb is operated at `110V`, we can use the same resistance to find the new power consumed. The power \( P' \) consumed at a different voltage can be calculated using:
\[ P' = \frac{V'^2}{R} \]
where \( V' \) is the new voltage (110V). Substituting the values:
\[ P' = \frac{110^2}{R} = \frac{110^2}{484} \]
First, calculate \( 110^2 \):
\[ 110^2 = 12100 \]
Now substitute \( R \):
\[ P' = \frac{12100}{484} \approx 25 \, W \]

4. **Conclusion**:
The power consumed by the bulb when operated at `110V` is approximately `25W`.

### Final Answer:
The power consumed is **25W**.

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