Question

You buy a 75-W lightbulb in Europe, where electricity is delivered to homes at 240V. If you use the lightbulb in the United States at 120 V (assume its resistance does not change), how bright will it be relative to 75-W 129-V bulbs?

Answer 1

Answer:

The bulb will be $\frac{1}{4}$ times as bright as it is in Europe.

Explanation:

Data provided in the question:

Power of bulb in Europe = 75 W

Voltage provided in Europe = 240 V

Voltage provided in United Stated = 120 V

Now,

We know,

Power = Voltage² ÷ Resistance

Therefore,

75 = 240² ÷ Resistance

or

Resistance = 240² ÷ 75

or

Resistance = 768 Ω

Therefore,

Power in United States = Voltage² ÷ Resistance

= 120² ÷ 768

= 18.75 W

Therefore,

Ratio of powers

$\frac{\text{Power in united states}}{\text{Power in Europe}}=\frac{18.75}{75}$

= $\frac{1}{4}$

Hence,

The bulb will be $\frac{1}{4}$ times as bright as it is in Europe.