When a piece of aluminium wire of finite length is drawn through a series of dies to reduce its diameter to half its original value, its resistance will become
Correct answer: D. Sixteen times
- A. Two times
- B. Four times
- C. Eight times
- D. Sixteen times
Explanation
The resistance of a wire is calculated using the formula R = ρ(L/A), where ρ is resistivity, L is length, and A is the cross-sectional area. If the diameter is halved, the cross-sectional area becomes one-fourth of its original value. To conserve volume, the length of the wire must double. This results in the resistance increasing by a factor of 2 (from length) × 4 (from area reduction), which equals 16. Therefore, the correct option is D: Sixteen times. Other options do not fully take into account both the change in area and the resulting change in length.
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