You buy a 75-W lightbulb in Europe, where electricity is delivered to homes at 240 V. Part A 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 120-V bulbs

The European bulb would be (1/4) less bright than the standard 75 W US bulbs.

Explanation:

The brightness of the bulb depends upon the power consumed by the bulb.

Electric power consumed in Europe = 75 W

But to calculate the power the same bulb would consume in the US,

Electric Power = IV

where I = current and V = voltage

From Ohm's law, V = IR; I = (V/R)

Electric power can be rewritten as

P = IV = (V/R) V = (V²/R)

So, we can obtain the resistance of the light bulb as it is used in Europe (whose voltage rating is 240 V) from this relation.

75 = (240²/R)

R = (240²/75)

R = 768 Ω

In the US, voltage rating is 120 V, for the European bulb,

P = (V²/R) = (120²/768) = 18.75 W

The power consumed by the European bulb in the US = 18.75 W.

Compared to the 75 W US bulbs, 18.75 = (75/4)

Therefore,

P (European) = P (US) / 4

The European bulb would be (1/4) less bright than the standard 75 W US bulbs.