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Impedance and Admittance: Find the current given an RLC circuit w/ Vs = 50cos(200t) V

  1. Apr 3, 2007 #1
    Impedance and Admittance: Find Vs given Io in a circuit with 2 caps,2 inductors,2res

    1. The problem statement, all variables and given/known data

    Find [itex]V_s[/itex] if [itex]I_0\,=\,2\angle0\deg[/itex] A.

    [​IMG]



    2. Relevant equations

    KCL, KVL



    3. The attempt at a solution

    I made a new diagram:

    [​IMG]

    But how do I combine the left hand equivalent impedance, so that the final circuit to work on would be this:

    [​IMG]


    [tex]\frac{1}{Z_3}\,=\,\frac{1}{Z_1}\,+\,\frac{1}{j4\Omega}\,=\,\frac{1}{2\,+\,2j}\,+\,\frac{1}{4j}[/tex]

    Figuring [itex]V_o[/itex]:

    [tex]V_o\,=\,I_o\,Z_2\,=\,\left(2\angle0\right)\left(2\angle45\right)\,=\,4\angle45[/tex]

    [tex]I_L\,=\,\frac{V_0}{j2}\,=\,\frac{4\angle45}{\sqrt{2}\angle63.43}\,=\,\frac{4}{\sqrt{2}}\angle-18.43[/tex]

    [tex]I_1\,=\,-\left(I_L\,+\,I_0\right)\,=-\left[\,\left(\frac{4}{\sqrt{2}}\angle-18.43\right)\,+\,\left(2\angle0\right)\right][/tex]

    [tex]V_1\,=\,I_1\,Z_1[/tex]

    I need this to find [itex]V_s[/itex].

    [tex]V_s\,=\,V_1\,-\,V_0[/tex]

    How do I finish? Please help!!!
     
    Last edited: Apr 4, 2007
  2. jcsd
  3. Apr 4, 2007 #2
    I did the calculations and conversions of complex rectangular to polar and got this as a final answer:

    [tex]V_S\,=\,9.581\,cos\left(t\,+\,29.70)[/tex]

    Does that look right?
     
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