A wire with a resistance R is lengthened to 1.25

[discoverer02]

My answer for this problem doesn't agree with the answer in the back of my textbook book:

A wire with a resistance R is lengthened to 1.25 times its original length by being pulled through a small hole. Find the resistance of the wire after it has been stretched.

R = pL/A

p = resistivity
L = length
A = area of a cross section perpendicular to the length
r = radius

R1 = pL1/A1

L2 = 1.25L1 so r1/r2 should equal 1.25 right.

The decrease in radius should be proportional to the increase in length.

So r2 = r1/1.25

Therefore R2 = p(1.25L1)/[pi](r1/1.25)^2 = R1(1.25*1.56) = 1.95R1

The answer in the back of my textbook is R2 = 1.56R1

Where have I gone wrong?

Thanks

 

[Hurkyl]

The decrease in radius should be proportional to the increase in length.

Should it? How would you go about proving this?

 

[discoverer02]

I'm assuming it's proportional. If it's not then I'm lost

 

[enigma]

Originally posted by discoverer02

L2 = 1.25L1 so r1/r2 should equal 1.25 right.

Volume is constant, and volume is L*A, not L*r

 

[discoverer02]

You're right. Stupid me!

The area would have to shrink proportionally: A2 = A1/1.25 so R2 = 1.25*1.25R1 = 1.56R1.

Thank you very much for the help.