1. Not finding help here? Sign up for a free 30min 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!

Complex number accuracy

  1. Nov 10, 2013 #1
    1. The problem statement, all variables and given/known data
    Calculate
    Z1=5+j10
    Z2=10+j8
    Z3=10+J5
    RL=40
    V=100

    VTH=VX(Z2/Z1+Z2)
    ZTH=Z3+(Z1Z2/Z1+Z2)
    I=VTH/(ZTH+RL)

    IL=?

    2. Relevant equations
    My question is what calculation method is more accurate:

    First to convert complex numbers in polar forms, and then calculate or calculate complex number until final result and then convert in polar form?


    3. The attempt at a solution
     
    Last edited by a moderator: Nov 10, 2013
  2. jcsd
  3. Nov 10, 2013 #2

    NascentOxygen

    User Avatar

    Staff: Mentor

    You carry along sufficient significant figures so that either gives the answer to the desired accuracy. So neither can be said to be "more accurate".
     
  4. Nov 10, 2013 #3

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Ya got a little happy with the HW template.
     
  5. Nov 10, 2013 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I removed the additional copies of the homework template.

    As you have to add complex numbers, I would not convert them to polar form. This increases the number of steps a lot, probably also increasing the error. I would not worry about that, however, your initial values are given with a precision of 2-3 digits, every reasonable system will calculate that with much more than 3 digits precision.
     
  6. Nov 10, 2013 #5

    gneill

    User Avatar

    Staff: Mentor

    Staying in rectangular form it's possible to carry through the calculations exactly when the given values are all expressed with whole numbers. Here, for example, ##I_L = \frac{12176}{13121} - j\frac{4888}{13121}##.

    For practical work, though, this rarely happens, and in general all values have some uncertainty associated with them. Keep enough guard digits in all intermediate values though the calculation so that rounding and truncation doesn't introduce errors larger than your uncertainties!

    Angle conversions, in particular can be troublesome since the conversions are not linear functions: plot the tan and arctan functions and see. In some parts of the curves small errors can be magnified while in other places the conversion is practically insensitive to small changes in the function argument. My advice is to keep more digits in angles than you think is necessary and never round intermediate angle values. Round only for final result presentation.
     
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: Complex number accuracy
  1. Complex numbers (Replies: 6)

Loading...