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

1. Jan 23, 2013

### anban

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

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

3. 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....

Last edited: Jan 24, 2013
2. Jan 24, 2013

### ehild

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

3. Jan 24, 2013

### anban

Typo, thank you!

Big help!!! Turns out I was off by a decimal point. My answer makes a lot more sense now. Thank you very, very much.

4. Jan 24, 2013

### anban

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

5. Jan 24, 2013

### ehild

What is your result at all?

ehild