# Calculating total error

1. ### Acuben

61
1. The problem statement, all variables and given/known data

First of all, I do not know if I am asking a complex question or easy question... since I haven't covered this in detail, but my physics teacher requires the class to use it in the lab

1. When you have one value value how do you calculate for total error?
Here I find the R, the Resistance of Manganin wire with has
$$\rho$$=44x10^-8 (neglecting error)

l=30.30 $$\pm$$ 0.05 inches
r= 0.02185 $$\pm$$ 0.00005 cm
R=$$\rho$$l/A

A= $$\pi$$$$r^{2}$$

2. Must this final error be in percentage?

2. Relevant equations
R=$$\rho$$l/A
A= area so pi times radius squared
so...
R=$$\frac{\rho l}{\pi r^{2}}$$

$$\Delta$$f = $$\frac{\partial f}{\partial x}$$*$$\Delta$$t + $$\frac{\partial f}{\partial y}$$*$$\Delta$$y

I never used this formula and I have no idea how to use it partial x and delta x?

3. The attempt at a solution

since for $$\pm$$ errors are multiplied, squared, divided, etc...
I can try changing to percent error so..

since R=$$\frac{\rho l}{\pi r^{2}}$$

and let's say I converted to % error
a= percent error of l
b= percent error of r
would total % error be a-2b ?

or must I get partial derivatives involved?
treat me like I don't know anything xD

edit1: give me time to edit my post, the symbols are not coming out as I wanted to it to be
edit2: done editing!

Last edited: Sep 23, 2010
2. ### Stonebridge

648
Find the % error in each of your measurements.
Rule 1
If the quantities are multiplied or divided (as is the case in your equation) add the percentage errors to get the total % error in the answer.
Rule 2
If a number is squared take 2 times the % error. (This is the case with the radius)
From the total % error, convert this back to an actual error in the final result.