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Error Propagation Question

  1. May 13, 2014 #1
    My goal is to find the uncertainty [itex]δd[/itex] in the following equation.

    [itex]d=C_1 \frac{1}{\sqrt{V}} \frac{1}{D}[/itex]

    • [itex]C_1[/itex] is the collection of constants [itex]\frac{2Lhc}{\sqrt{2m_e c^2 }}[/itex]
    • [itex]D[/itex] is a value measured in meters with an uncertainty [itex]δD = 0.001 m[/itex]
    • and [itex]V[/itex] is a value measured in volts with an uncertainty [itex]δV = 100 V[/itex]

    My best guess on how to calculate [itex]δd[/itex] is

    [itex]\frac{δd}{d}=|C_1| \sqrt{(\frac{δV}{V})^2+(\frac{δD}{D})^2 }[/itex]
    ... then plug in all the known values and solve for [itex]δd[/itex]

    ...Unfortunately I have no resources to tell me if I'm doing this right. I appreciate any helpful pointers any of you may have, I'm a big time noob when it comes to error analysis.

    For those of you who are curious, this is from a Bragg Scattering lab and [itex]d[/itex] represents the distance between atoms in a polycrystalline graphite crystal.
     
    Last edited: May 13, 2014
  2. jcsd
  3. May 13, 2014 #2

    SammyS

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    d is inversely prop. to √(V) , not V itself.

    You should have something like:
    [itex]\displaystyle \frac{δd}{d}=|C_1| \sqrt{\left(\frac{δ(\sqrt{V})}{\sqrt{V}}\right)^2+\left(\frac{δD}{D} \right)^2 }[/itex]​
     
  4. May 13, 2014 #3
    Awesome, thank you!

    Quick side question: is it true that both of these equations have the same δd formula?

    Equation 1. [itex]d = \sqrt{V}D[/itex]
    Equation 2. [itex]d = \frac{1}{\sqrt{V}D}[/itex]

    Error for either equation:
    [itex]\frac{δd}{d} = \sqrt{(\frac{δ(\sqrt{V})}{\sqrt{V}})^2 + (\frac{δD}{D})^2}[/itex]
     
  5. May 13, 2014 #4

    SammyS

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    Yes, for reasonably small relative error.
     
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