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Determining steady state current from phasor current?

  1. Jun 15, 2013 #1
    1. The problem statement, all variables and given/known data


    [Broken]



    a) Determine the phasor current and impedance of the circuit

    b) Determine the steady-state current i(t).



    2. Relevant equations

    impedance conversion:

    ZL = ωLj

    ZC = -1j/ωC

    ZR = R


    Polar form conversion:

    rectangular form = R + jX

    Zmag = (j2 + r2)1/2

    Zangle = arctan(j/r)


    V = IR

    I=V/R




    3. The attempt at a solution

    ω = 100

    Zr = 9Ω


    ZC = -1j/(100*(1x10-3))

    ZC = -10Ωj


    ZL = 100 * (10 x 10-3)

    ZL = 1Ωj

    Ztotal = 9Ω - 9Ωj


    In polar form:

    Zmag = (81 + 81)1/2

    Zmag = 12.7

    Zangle = arctan(-9/9)

    Zangle = -45°

    So

    Z = 12.7∠-45°

    and

    V = 100∠0°


    I = V/R

    I = (100∠0°)/(12.7∠-45°)


    Phasor current I = (7.87∠45°)A


    Now, I am actually stuck how to get the steady state current but I think it's something in waveform like


    i(t) = 7.87cos(100t + 45) ?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jun 15, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    Yes, that's fine. Be sure to specify the units on the answer.

    Also remember to hang onto a few more decimal places in intermediate steps to prevent rounding error from creeping into your values as calculations progress.
     
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