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Homework Help: Complex Circuit Analysis Simplification

  1. Feb 9, 2012 #1
    I have the following circuit....

    I have managed to derive an equation for U2:


    Now I want to substitute U2 into U1, in order to derive equation for U1

    I have defined U1 as:


    Now I substitute U2 into the above equation. This is how far I get.....I am stuck...

    My circuit simulator is saying that U1 is equal to:


    However I cannot simplify to get this equation. Can someone please help I have spent hours trying to get U1 to look like the U1 that the simulator produces.

    I thank you in advance.
  2. jcsd
  3. Feb 9, 2012 #2
    Have you try to replace R1, R2 and E2 with his Thevenine equivalent circuit ?
    Eth = R2/ ( R1 + R2 ) * E1 and Rth = R1||R2


    V3 = I * R3

    [tex] I = \frac{Eth}{\sqrt{(Rth + R3)^2 + Xc^2)}} = \frac{E1*\frac{R2}{R1+R2}}{\sqrt{(R1||R2 + R3)^2 + Xc^2)}} [/tex]


    [tex] V3 = \frac{E1*R2*R3}{(R1+R2)\sqrt{(R1||R2 + R3)^2 + Xc^2)}} [/tex]

    Attached Files:

    Last edited: Feb 9, 2012
  4. Feb 9, 2012 #3
    No I haven't tried this before, but I did just try it and I still can't derive U1. Perhaps I am being stupid...
  5. Feb 9, 2012 #4
    A made a small error instead of V3 I should write U1

    What is the name of your simulation program?
  6. Feb 9, 2012 #5
    Thanks for your help Jony, the simulator is giving me this equation:


    I haven't derived that myself^. When I expand out the equation you derived:

    [tex] V3 = \frac{E1*R2*R3}{(R1+R2)\sqrt{(R1||R2 + R3)^2 + Xc^2)}} [/tex]

    I still not can get a the equation looking like the simulator one.

    BTW the simulator is called Solve Elec, you can download it for free.

    [URL="http://www.physicsbox.com/indexsolveelec2en.html[/URL] [Broken]
    Last edited by a moderator: May 5, 2017
  7. Feb 9, 2012 #6
    Ah done it! you are right I was being stupid. I am upset with myself that I never thought to do a thevin equivalent :( thanks alot for your help. I can sleep peacefully tonight.
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