1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Error Propagation dividing

  1. Jul 13, 2014 #1
    1. The problem statement, all variables and given/known data

    So I am calculating the error for something and I am getting really weird values.
    So I know that the value for the Inductor is 24.97 +- 0.005 mH and that for the capacitor is 105.7+-0.0005 nf.

    So I am finding the value for the resonant frequency

    2. Relevant equations

    f_0 = 1/(2*pi*sqrt(LC))


    3. The attempt at a solution

    So for the f_0 I get 3097 Hz which is very close to my experimental observations. But for the error I get:

    error in LC = (2.64e-9) * sqrt((0.005/24.97)^2+(0.0005/105.7)^2) = 5.29e-13

    error in LC^-.5: (19464.95)*0.5*2.64e-8/5.29e-13 = 37994

    final error: 37994 * 1/(2*pi) = 6039.

    Now this final value is too high, what am I doing wrong? Thanks
     
    Last edited: Jul 13, 2014
  2. jcsd
  3. Jul 13, 2014 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I don't see where the 1.03e-8 comes from. LC is about 2.6e-6, no?
    What's the reason for dividing by 5.29e-13? It would be clearer if you were to write the equation in purely symbolic form, not plugging in numbers.
     
  4. Jul 13, 2014 #3
    Sure, sorry. The 1.03e-8 is the LC value and the following values in the equation are the error divided by the value. For the second equation 19464.95 is the LC^-.5 is the value and 0.5 is the exponent and 5.29e-13 is the error in LC^-0.5.

    The eqn's are:

    for multiplication (z=xy): dz = z *sqrt((dx/x)^2+(dy/y)^2)

    for exponents (z=x^y): dz = abs(y)*z*dx/x
     
  5. Jul 13, 2014 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Isn't LC = 24.97 * 105.7e-9?
    Sure, but when you plugged in the numbers you seem to have used x/dx instead of dx/x.
     
  6. Jul 13, 2014 #5
    L is in mH so there is an extra 10^-3 factor I forgot note here. I wrote down the exponent thing wrong here but the number is right, it should be:

    error in LC^-.5:
    value*exponent*error_LC/LC
    = (19464.95)*0.5*2.64e-8/5.29e-13 = 37994

    ah there are so many numbers in my sheet I get mixed up
     
  7. Jul 13, 2014 #6
    Alright I think I've got it, my data was just too ugly, I cleaned it up and did it another sheet.

    I got:

    Error in LC: 5.29E-13
    LC: 2.64E-09
    LC^-0.5: 1.95E+04
    Error in LC^-.5: 1.95E+00
    Error in final : 3.10E-01

    which ironically seems a little small but whatever.

    Thanks for the help!
     
  8. Jul 13, 2014 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I find it easier to think in terms of fractional errors. (Mistakes in the calculation usually become more obvious.)
    The fractional error in LC is 5.29E-13/2.64E-09 ~ 2E-4 (almost entirely owing to the error in L).
    The fractional error in sqrt(LC) will be half that: 1E-4.
    The fractional error in f_0 will also be 1E-4, giving an absolute error of ~ 3E3 * 1E-4 = 3E-1.
    That confirms your answer.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Error Propagation dividing
  1. Error Propagation (Replies: 3)

  2. Error propagation (Replies: 1)

  3. Error propagation (Replies: 1)

  4. Error Propagation (Replies: 0)

  5. Error propagation (Replies: 1)

Loading...