The Ratio of Resistance of 100-W and 60-W Light Bulbs

What is the ratio of the resistance of the 100-W bulb to the resistance of the 60-W bulb?

1.2

0.75

2.5

4.0

0.6

Final Answer:

The ratio of the resistance of the 100-W bulb to the resistance of the 60-W bulb is 0.6.

In this scenario, we are comparing the resistance of a 100-W light bulb to a 60-W light bulb designed for use with the same voltage. The ratio of their resistances is 0.6.

Explanation:

The power of a light bulb is the measure of how quickly it converts electrical energy into light energy. The resistance of a light bulb is inversely proportional to its power, meaning a higher power bulb will have a lower resistance.

The formula for calculating the resistance of a light bulb is: Resistance = Voltage^2 / Power

Since the voltage is the same for both bulbs, we can directly compare their power ratings. The 100-W bulb has a power of 100 watts, and the 60-W bulb has a power of 60 watts. Therefore, the resistance of the 100-W bulb is 0.6 times the resistance of the 60-W bulb.

This means that the 100-W bulb has a lower resistance compared to the 60-W bulb, with a ratio of 0.6. This relationship is important when considering the efficiency and performance of different light bulbs in electrical systems.