A 200 W- 200 V lamp is connected to 250 V mains.it power consuption is

Options

A. 300 W
B. 312.5 W
C. 292 W
D. 250 W

Explanation

To solve the problem of how much power a 200 W - 200 V lamp consumes when connected to a 250 V mains supply, we can follow these steps:

### Step 1: Calculate the Resistance of the Lamp
The resistance of the lamp can be calculated using the formula:

\[ R = \frac{V^2}{P} \]

Where:
- \( V \) is the rated voltage of the lamp (200 V)
- \( P \) is the power rating of the lamp (200 W)

Substituting the values:

\[ R = \frac{(200)^2}{200} = \frac{40000}{200} = 200 \, \Omega \]

### Step 2: Calculate the Power Consumption When Connected to 250 V
Now we need to find the power consumption when the lamp is connected to a 250 V supply. We can use the formula for power:

\[ P' = \frac{V_s^2}{R} \]

Where:
- \( V_s \) is the supply voltage (250 V)
- \( R \) is the resistance we calculated in Step 1 (200 Ω)

Substituting the values:

\[ P' = \frac{(250)^2}{200} = \frac{62500}{200} = 312.5 \, W \]

### Conclusion
The power consumption of the lamp when connected to a 250 V mains supply is **312.5 W**.