The resistance of a wire of uniform diameter D and length L is R. The resistance of another wire of the same material but diameter 2D and length 4L will be:
Correct answer: C. R
- A. 2R
- B. R/2
- C. R
- D. R/4
Explanation
Resistance R is proportional to L/A, and area A is proportional to D². The new resistance R' will have a factor of 4 from the length and a factor of (1/2)²=1/4 from the diameter. The net effect is R' ∝ (4L)/(2D)² = 4L/4D² = L/D², so the resistance remains the same.
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