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Calculating capacitive reactance

  1. Feb 7, 2013 #1

    Apologies if this has been posted/answered else where but I could not find it.

    I am trying to develop a model in matlab for a simple (short cylindrical coil) air cored transformer. So far I am capable of defining the coil such as core diameter, turns, length etc.., calculate the coil resistance, input current, magnetic field produced, flux density at a given distance along the central axis, and potential emf for the secondary coil.

    The next thing I need to work out is the impedance Z.

    Z = sqrt(R^2 + X^2)

    where X = XL - XC

    I can calculate XL because I have found an equation to work out the inductance of the coil, L.

    L = (r^2 * N^2)/(9r + 10l)
    *from the wiki inductor page

    so XL = 2πfL.

    I run in to problems with capacitive reactance XC. I cannot find anywhere online explaining how to work out the capacitance of a coil so I can calculate the capacitive reactance XC.

    XC = 1/(2πFC)

    Does anyone here know how to calculate the capacitance of a coil, or even if my understanding is completely off?
  2. jcsd
  3. Feb 7, 2013 #2

    jim hardy

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    Here's a fellow experimenter who gives a formula for self-resonant frequency, and some references:

    more at the link

    maybe you could back into capacitance...
    Last edited: Feb 7, 2013
  4. Feb 13, 2013 #3
    Thanks for a reply, its been useful, but seems to be for coils greater in length than I am dealing with. I tried using the suggestions anyway but they maths doesnt seem very dependable. I think I am best off just measuring it from a physical coil, then compare it back to the maths.
  5. Feb 13, 2013 #4


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    If you have one available then that is certainly worth doing. Just find the self resonant frequency and the inductance at a very low frequency. That will give you the self capacitance more accurately than you are likely to be able to calculate it. You can alter things a lot by squashing or stretching the coil just a bit.
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