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Question

If a copper wire is stretched to make it 0.1% longer, the percentage change in its resistance is

A
0.2% increase
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B
0.2% decrease
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C
0.1% increase
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D
0.1% decrease
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Solution

The correct option is A 0.2% increase
Step 1: New Area of the wire
The volume of the wire remains the same even after stretching.
Vi=Vf
Al=Al
Given that , l=l+0.1%l=l+0.1100l=1.001l
A=11.001A

Step 2: Resistance of wire
R=ρlA .....(2)
R=ρlA .....(3)
Dividing equation (3) by (2)
RR=lAlA
RR=(1.001)2

Using Binomial approximation
(1+x)a=(1+ax) when ax<<1
(1.001)2=(1+0.001)2=(1+2×0.001)=1.002

R=1.002R

Step 4: Percentage increase in resistance of wire
Thus percentage increase in resistance=RRR×100 % =(1.0021)×100 %
=0.2%
Hence option(A) is correct.


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