Question

(II) You buy a 75-W lightbulb in Europe, where electricity is delivered at 240 V. If you use the bulb 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? [Hint: Assume roughly that brightness is proportional to power consumed.]

Answer 1

The brightness of the 75-W 240 V bulb relative to the 75-W 120 V bulb is 50%.

Step-by-step explanation:

When comparing the brightness of a 75-W lightbulb operating at 240 V in Europe to a 75-W lightbulb operating at 120 V in the United States, we can use the fact that brightness is proportional to power consumed. Since power is equal to voltage multiplied by current, we can calculate the current for each bulb using the formula P = IV. For the 75-W 240 V bulb, the current is 0.3125 A, and for the 75-W 120 V bulb, the current is 0.625 A. The brightness of the European bulb relative to the US bulb can be calculated by dividing the current of the European bulb by the current of the US bulb: 0.3125 A / 0.625 A = 0.5, or 50%.

Answer 2

Step-by-step explanation:

You are looking for the resistance to start with

W = E * E/R

75 = 240 * 240 / R

75 * R = 240 * 240

R = 240 * 240 / 75

R = 57600 / 75

R = 768

Now let's see what happens when you try putting this into 110

W = E^2 / R

W = 120^2 / 768

W = 18.75

So the wattage is rated at 75. 18.75 is a far cry from that. I think they intend you to set up a ratio of

18.75 / 75 = 0.25

This is the long sure way of solving it. The quick way is to realize that the voltage is the only thing that is going to change. 120 * 120 / (240 * 240) = 1/2*1/2 = 1/4 = 0.25