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

[anban]

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 = \frac{ρ*l}{\pi*r^{2}} for which I substituted the area as \pi(.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...

 

[ehild]

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 = \frac{Rρl}{\pi*r^{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...

You meant R = \frac{ρl}{\pi*r^{2}} , 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

 

[anban]

You meant R = \frac{ρl}{\pi*r^{2}} , 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.

 

[anban]

Another clarification-- the D in the denominator is squared. Does that mean I need to take the square root of my result?

 

[ehild]

What is your result at all?

ehild