If a wire of length L and diameter d has a resistance R, then another wire of the same material but having length four times and twice the diameter has the resistance:
Correct answer: B. Same as the first wire
- A. Half of the first wire
- B. Same as the first wire
- C. Twice of the first wire
- D. Four times of the first wire
Explanation
If the length of the wire is four times and the diameter is twice, then the length becomes 4L and the diameter becomes 2d. The cross-sectional area of the wire is proportional to the square of the diameter, so the area becomes (2d)2 = 4(d2). The resistance is inversely proportional to the area, so the resistance becomes R/(4(d2)). This is the same as the resistance of the first wire (R), so option B is correct.
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