What is the power dissipated by a bulb of 100 W - 220 V connected to a 110 V supply:

Options

A. 50 MW
B. 0.5 W
C. 50 W
D. 5 MW

Explanation

To find the power dissipated by a bulb rated at 100 W - 220 V when connected to a 110 V supply, we can follow these steps:

### Step 1: Determine 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 (220 V) and \( P \) is the rated power (100 W).

Substituting the values:
\[ R = \frac{(220)^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

### Step 2: Calculate the power dissipated at the new voltage
Now, we need to calculate the power \( P' \) dissipated when the bulb is connected to a 110 V supply. The formula for power in terms of resistance and voltage is:
\[ P' = \frac{V'^2}{R} \]
where \( V' \) is the new voltage (110 V).

Substituting the values:
\[ P' = \frac{(110)^2}{484} \]
Calculating \( (110)^2 \):
\[ (110)^2 = 12100 \]
Now substituting this back into the power equation:
\[ P' = \frac{12100}{484} \approx 25 \, W \]

### Conclusion
The power dissipated by the bulb when connected to a 110 V supply is approximately **25 W**.

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