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.