R through a wire: What's the max error in diameter if your R has 1% uncertainty?

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anban
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Homework Statement



I have a wire of some resistance, resistivity, and length.

What is the maximum error in measuring the diameter that you can have if the resistance is to have 1% uncertainty?


Homework Equations



R = [itex]\frac{ρ*l}{\pi*r^{2}}[/itex] for which I substituted the area as [itex]\pi[/itex](.5 D) ^{2}.


The Attempt at a Solution



I picked an arbitrary R and found the corresponding D. Then, I took 1% of that arbitrary R and found the corresponding D. The issue is that D's were basically the same number. I'm not sure if I could just go out to more decimal places or if I'm just wrong...
 
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anban said:

Homework Statement



I have a wire of some resistance, resistivity, and length.

What is the maximum error in measuring the diameter that you can have if the resistance is to have 1% uncertainty?

Homework Equations



R = [itex]\frac{Rρl}{\pi*r^{2}}[/itex] .

The Attempt at a Solution



I picked an arbitrary R and found the corresponding D. Then, I took 1% of that arbitrary R and found the corresponding D. The issue is that D's were basically the same number. I'm not sure if I could just go out to more decimal places or if I'm just wrong...

You meant R = [itex]\frac{ρl}{\pi*r^{2}}[/itex] , didn't you?

Solve the problem symbolically. If the resistance can differ from R by one percent it can be 1.01 R or 0.99 R. What are the corresponding diameters and how are they related to the original D? By what percent are they different from it? ehild
 
ehild said:
You meant R = [itex]\frac{ρl}{\pi*r^{2}}[/itex] , didn't you?

Typo, thank you!

Solve the problem symbolically. If the resistance can differ from R by one percent it can be 1.01 R or 0.99 R. What are the corresponding diameters and how are they related to the original D? By what percent are they different from it?

Big help! Turns out I was off by a decimal point. My answer makes a lot more sense now. Thank you very, very much.
 
Another clarification-- the D in the denominator is squared. Does that mean I need to take the square root of my result?