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If a copper wire is stretched to make it 0.1% longer. The percentage change in its resistance is ?

If a copper wire is stretched to make it 0.1% longer. The percentage change in its resistance is ? 
 

Grade:12

4 Answers

Vikas TU
14149 Points
9 years ago
Resistance is directly proportional to square of length.
think
Siddharth Singh
22 Points
9 years ago
I am not quite satisfied with you
But thanks anyway..
As far as I know
R= ρ(l/A)
So, as length increases by 0.1% the area of cross section that wil eventually decrease since the volume is
constant so, it will also decrease by 0.1% so both will contribute to increase in resistance and that is by 0.2%.
Yashwant
12 Points
6 years ago
As resistance is directly proportional to the square of the length keeping its volume constant then by diffrentiating partially on both side we gey dR/R= 2*dL/L. But given dL/L=0.1 so persentage change in the resistance dR/R=2*0.1=0.2
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem.
 
Since the wire gets stretched, its length increases while its cross sectional area decreases keeping the volume constant.
Hence, V = Al
Differentiating,
dV/V = 0 = dA/A + dl/l
Hence, dA/A = – dl/l
 
Now, R = ρ(l/A)
Hence, dR/R = dl/l – dA/A
= dl/l – ( – dl/l)
= 2 dl/l
 
Hence, dR/R x 100 = 2 dl/l x 100 = 2 x 0.1 = 0.2 %
 
Hence, the resistance increases by 0.2 %
 
Thanks and regards,
Kushagra

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