A 220 volt, 1000 watt bulb is connected across a 110 volt mains supply. The power consumed will be

Options

A. 750 watt
B. 500 watt
C. 250 watt
D. 1000 watt

Explanation

To solve the problem of finding the power consumed by a 220V, 1000W bulb when connected to a 110V mains supply, we can follow these steps:

### Step 1: Determine the resistance of the bulb
The power rating of the bulb is given as 1000W when it operates at 220V. We can use the formula for power to find the resistance (R) of the bulb.

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

Rearranging the formula to find R gives us:

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

Substituting the values:

\[ R = \frac{(220V)^2}{1000W} \]

### Step 2: Calculate the resistance
Calculating the resistance:

\[ R = \frac{48400}{1000} = 48.4 \, \Omega \]

### Step 3: Calculate the power consumed at 110V
Now that we have the resistance, we can find the power consumed when the bulb is connected to a 110V supply using the same power formula:

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

Where \(V' = 110V\). Substituting the values:

\[ P' = \frac{(110V)^2}{48.4 \, \Omega} \]

### Step 4: Calculate the power consumed
Calculating the power consumed:

\[ P' = \frac{12100}{48.4} \approx 250W \]

### Conclusion
The power consumed by the bulb when connected to a 110V mains supply is approximately **250W**.

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