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Question

If a wire is stretched, so that its length 20% more than its initial length, the percentage increase in the resistance of the wire is-

A
40%
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B
10%
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C
44%
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D
25%
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Solution

The correct option is C 44%
Given, the wire is stretched, but its volume remains the same.

Vi=Vf

A1l1=A2l2 l1l2=A2A1

Resistance of a wire is, R=(ρlA)

RlA

R1R2=(l1l2)×(A2A1)

R1R2=(l1l2)2

Here, l1=l and l2=1.2l

R2=R1(l1l2)2=1.44R1

Percentage increase in the reistance is,

% increase=R2R1R1×100

=(1.441)R1R1×100=44%

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (C) is the correct answer.

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