An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be:

Question

Accepted Answer

To determine the power consumed by the electric bulb when operated at a different voltage, we need to use the relationship between power, voltage, and resistance. The power consumed by an electrical device is given by the formula:

$$ P = \frac{V^2}{R} $$

where $ P $ is the power, $ V $ is the voltage, and $ R $ is the resistance.

1. **Calculate the resistance of the bulb:**

The bulb is rated at 220 V and 100 W. Using the formula for power:

$$ 100 = \frac{220^2}{R} $$

Solving for $ R $:

$$ R = \frac{220^2}{100} = \frac{48400}{100} = 484 \, \Omega $$

2. **Calculate the power consumed at 110 V:**

Now, using the resistance calculated, we find the power consumed when the bulb is operated at 110 V:

$$ P = \frac{110^2}{484} $$

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

Thus, when the bulb is operated at 110 V, the power consumed is approximately 25 W, which corresponds to Option 4.

**Explanation for why other options are incorrect:**

- **Option 1 (100 W):** This option is incorrect because 100 W is the power consumed at the rated voltage of 220 V, not at 110 V. The power decreases when the voltage is reduced.

- **Option 2 (75 W):** This option is incorrect because the power consumed at 110 V is significantly lower than 75 W. The calculation shows that the power is approximately 25 W.

- **Option 3 (50 W):** This option is incorrect because, although it is closer to the correct answer than the previous options, it still overestimates the power consumed at 110 V. The correct calculation yields approximately 25 W.

In conclusion, the correct answer is Option 4, as the power consumed by the bulb when operated at 110 V is approximately 25 W.