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

In summary: Another clarification-- the D in the denominator is squared. Does that mean I need to take the square root of my result? Yes, if you solve the equation for D. In summary, the problem is to find the maximum error in measuring the diameter of a wire with given resistance, resistivity, and length, if the resistance is to have a 1% uncertainty. The equation R = \frac{ρl}{\pi*r^{2}} is used, with the area substituted as \pi(.5 D)^{2}. Symbolically solving the problem, the corresponding diameters for a 1% change in resistance are 1.01 D and 0.99 D, and they are related to the original D by
  • #1
anban
20
0

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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  • #2
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
 
  • #3
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.
 
  • #4
Another clarification-- the D in the denominator is squared. Does that mean I need to take the square root of my result?
 
  • #5
What is your result at all?

ehild
 

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

1. What is the significance of "R through a wire" in this context?

"R through a wire" refers to the resistance of a wire, which is a measure of how difficult it is for electric current to pass through the wire. In this context, we are looking at the maximum error in the wire's diameter due to uncertainty in the measurement of its resistance.

2. What does it mean to have a 1% uncertainty in R?

A 1% uncertainty in R means that the measured value of resistance could be off by up to 1% from the true value. This could be due to limitations in the measurement equipment or other factors that affect the accuracy of the measurement.

3. How does the uncertainty in R affect the diameter of the wire?

The uncertainty in R can affect the diameter of the wire because the resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. As the resistance value changes due to uncertainty, the diameter of the wire will also be affected.

4. How do you calculate the max error in diameter from the uncertainty in R?

To calculate the maximum error in diameter, you would need to know the specific formula that relates R to diameter for the type of wire being measured. Once you have this formula, you can plug in the uncertainty in R (1%) and calculate the corresponding uncertainty in diameter.

5. How can this information be applied in practical situations?

Knowing the maximum error in diameter due to uncertainty in R can be helpful when working with sensitive electrical equipment or conducting experiments where precise measurements are necessary. It can also be useful in quality control processes to ensure that wires meet the required specifications.

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