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Question

A wire of 1 Ω has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in the resistance to the nearest integer is -

A
25%
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B
12.5%
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C
76%
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D
56%
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Solution

The correct option is D 56%
We know that,
R=ρlA
So,
R1R2=l1A2A1l2 ...(1)

Also, volume remain constant. So,
A1l1=A2l2
A2A1=l1l2 ...(2)

From (1) and (2),

R1R2=l21l22

1R2=(l)2(1.25l)2

R2=1.5625 Ω

Hence, percentage change in the resistance,
=1.562511×100=56.25%56%

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