impedance of a capacitor

Discussion in 'Math' started by mentaaal, Nov 7, 2008.

  1. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
    451
    0
    Hey guys, this may seem a bit strange but I am trying to prove to myself that the impedance of a capacitor to a sinusoidal input signal is 1/ωC using the complex exponential form of cos(θ) and sin(θ) but i cannot solve it. Could someone tell me where i am going wrong or what i must do to complete it.

    Let Vin be sin(ωt) = (e^(jωt)-e^(-jωt))/2j

    Due to the formula I = Cdv/dt
    Iin will be Cωcos(ωt) = Cjω(e^(jωt)+e^(-jωt))/2

    Xc is then Vin/Iin

    = ((e^(jωt)-e^-(jωt))/2j) / Cjω(e^(jωt)+e^-(jωt))/2)

    it is here that i get bogged down and am not sure how to arrive at the expected result of 1/JωC

    I have tried looking this up and and i can only find solutions using Cos and sin (which makes perfect sense)
     
  2. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
    451
    0
    Its ok guys i found my mistake, when i differentiated vin the js would cancel.

    tut tut
     
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