A cylindrical copper wire of resistance R is uniformly stretched until its length is doubled (l' = 2l) while keeping its volume constant. What is the new electrical resistance of the wire?
Answer and explanation
Correct answer: B. 4R
- Step 1: The original resistance of the wire is: .
- Step 2: When stretched, the volume of the wire remains constant: .
- Step 3: Given , the new cross-sectional area becomes: .
- Step 4: The new resistance is: .
Answer
4 R
Why not the others: '2 R' accounts only for the length increase while forgetting the simultaneous halving of cross-sectional area; 'R / 2' and 'R / 4' mistakenly assume resistance decreases upon stretching.
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