Power Consumption and Resistance Ratio of Incandescent Light Bulbs
What is the ratio of the resistance of a 75-W incandescent light bulb to the resistance of a 50-W incandescent light bulb?
Answer:
The ratio is 0.667.
The ratio of the resistance of a 75-W incandescent light bulb to the resistance of a 50-W incandescent light bulb is 0.667. But why and how do we calculate this ratio?
When comparing the resistance of two incandescent light bulbs with power ratings of 75 W and 50 W, we can determine the ratio by using the formula for power consumption:
- For 75-W bulb: \(R = \frac{V^2}{75}\)
- For 50-W bulb: \(R = \frac{V^2}{50}\)
Therefore, the ratio of the resistance of the 75-W bulb to the 50-W bulb is:
\[ \frac{\frac{V^2}{75}}{\frac{V^2}{50}} = \frac{V^2}{75} \times \frac{50}{V^2} = \frac{50}{75} = 0.667 \]So, the ratio of the resistance between these two bulbs is indeed 0.667.