An electric bulb, marked `40 W` and `200 V`, is used in a circuit of supply voltage `100 V`. Now its power is

Options

A. 10w
B. 20W
C. 40W
D. 100W

Answer

To solve the problem, we need to determine the power consumed by the electric bulb when it is supplied with a voltage of 100 V, given that it is rated at 40 W and 200 V.

### Step-by-Step Solution:

1. **Understand the given values**:
- Rated Power (P1) = 40 W
- Rated Voltage (V1) = 200 V
- Supply Voltage (V2) = 100 V

2. **Calculate the resistance of the bulb**:
The resistance (R) of the bulb can be calculated using the rated power and voltage:
\[ P1 = \frac{V1^2}{R} \implies R = \frac{V1^2}{P1} \]
Substituting the values:
\[ R = \frac{(200)^2}{40} = \frac{40000}{40} = 1000 \, \Omega \]

3. **Calculate the power at the new voltage (V2 = 100 V)**:
Using the formula for power:
\[ P2 = \frac{V2^2}{R} \]
Substituting the values:
\[ P2 = \frac{(100)^2}{1000} = \frac{10000}{1000} = 10 \, W \]

4. **Conclusion**:
The power consumed by the bulb when supplied with 100 V is 10 W.

### Final Answer:
The power of the bulb when used in a circuit with a supply voltage of 100 V is **10 W**.

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