If R1 and R2 are respectively the filament resistance of a 100-Watt bulb and 200-Watt bulb designed to operate on the same voltage, then resistance of:
Correct answer: A. R1 is two times R2
- A. R1 is two times R2
- B. R2 is two times R1
- C. R2 is four times R1
- D. R1 is four times R2
Explanation
The power formula P = V^2/R can be rearranged to find the resistance R = V^2/P. For the same voltage V, the resistance is inversely proportional to power. Therefore, R1 (100-W bulb) = V^2/100 and R2 (200-W bulb) = V^2/200. This means R1 is twice R2 because 100 is half of 200.Option A is correct because it correctly applies the inverse relationship between power and resistance. Options B, C, and D fail to apply this relationship accurately.
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