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Question

# If a wire is stretched to n times of its original length, its new resistance will be

A
1/n times
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B
n2 times
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C
n times
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D
None
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Solution

## The correct option is B n2 timesStep 1: Volume of the wireVolume of the wire remains same before and after stretching.Vi=Vf=V Step 2: Resistance of the wireInitial resistance: R=ρlA where A=V/l ⇒R=ρl2V ....(1)Final resistance : R′=ρ l′2V ....(2)Step 3: Dividing equation (2) by (1)⇒ R′R=l′2l2Given l′=nl⇒R′=(nl)2Rl2=n2RHence option B is correct.

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