100 W,220V bulb is connected to 110V source. Calculate the power consumed by the bulb.

Answer

To solve the problem of calculating the power consumed by a 100 W, 220 V bulb when connected to a 110 V source, we can follow these steps:

### Step 1: Calculate the Resistance of the Bulb
The power rating of the bulb at its rated voltage can be used to find its resistance. The formula for power is given by:

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

From this, we can rearrange the formula to find the resistance \( R \):

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

Substituting the values for the rated voltage (220 V) and power (100 W):

\[ R = \frac{220^2}{100} \]

Calculating this gives:

\[ R = \frac{48400}{100} = 484 \, \Omega \]

### Step 2: Calculate the Power Consumed at 110 V
Now that we have the resistance of the bulb, we can find the power consumed when the bulb is connected to a 110 V source. We will use the power formula again:

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

Substituting the new voltage (110 V) and the resistance we calculated (484 Ω):

\[ P = \frac{110^2}{484} \]

Calculating this gives:

\[ P = \frac{12100}{484} \approx 25 \, W \]

### Final Answer
The power consumed by the bulb when connected to a 110 V source is approximately **25 W**.

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