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Error progrigation

  1. Jan 21, 2008 #1
    Error propagation

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

    [tex] \frac{ - \frac{R_{2}}{R_{1}}}{1 + \frac{1}{A} + \frac{R_{2}}{A R_{1}}}[/tex]



    2. Relevant equations

    [tex] R_{1} = 10000 \pm 5 \% [/tex]
    [tex] R_{2} = 10000 \pm 5 \% [/tex]
    [tex] A = 1000 [/tex]

    3. The attempt at a solution

    I try to follow the example of at the website http://www.rit.edu/~uphysics/uncertainties/Uncertaintiespart1.html and in there example
    [tex] x = ( 2.0 \pm 0.2) [/tex]
    [tex] y = (3.0 \pm 0.6) [/tex]
    [tex] z = \frac{x}{y} [/tex]

    This is what they do in their example:
    [tex] z = \frac{2.0}{3.0} = 0.6667 [/tex]
    [tex] \Delta z = 0.3 (0.6667 ) = 0.2 [/tex]
    [tex] z = (0.7 \pm 0.2) [/tex]

    Now what i dont realy understand is where they get [tex] 0.3 [/tex] from?
    It seems that they just divide the uncertainty [tex] \frac{0.2}{0.6} = .33 [/tex].

    But, if i do this in my example i get [tex] \frac{500}{500} = 1[/tex]. Then when i multiply this agianst [tex] \frac{10000}{10000} = 1 [/tex] i get 100% error. Yikes!

    I kind of feel embarrassed asking this because i should have learned this a long time ago in physics but it was one of those things i never really took the time to actually understand.
     
    Last edited: Jan 21, 2008
  2. jcsd
  3. Jan 21, 2008 #2

    hage567

    User Avatar
    Homework Helper

    The 0.3 comes from the addition of the relative errors of x and y. Find equation 2a on that page.
     
  4. Jan 22, 2008 #3
    Thank you sir
     
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