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RLC circuit

  1. Dec 4, 2013 #1
    The circuit and questions are attached.
    1. The problem statement, all variables and given/known data
    First: Calculate the complex impedance of the circuit.
    Second:Limiting cases
    Third:Imax
    Lastly: Phase

    2. Relevant equations



    3. The attempt at a solution

    I've never had any ac circuits and the DC circuits I did before transferring were extremely simple and more than a couple years ago. So, I'm lost.

    I asked a friend for help and he indicated that the initial equation should look something like:

    ##Z=(\frac{1}{R} -\frac{1}{wCi})^{-1}+iwL##

    If this is correct then I believe I have a,b,c covered. Can someone comment to let me know?

    Once I have that squared away then for part D am I understanding it correctly that they want that I do this with the real equation instead of the complex one?
     

    Attached Files:

    • RLC.jpg
      RLC.jpg
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  2. jcsd
  3. Dec 4, 2013 #2
    I've tried figuring this out myself and I get a different impedance than my friend.

    ##Z=(\frac{1}{R} +\frac{1}{X_C})^{-1}+X_L##
    So for the complex impedance I got:
    ##Z=(\frac{1}{R} +wCi)^{-1}+iwL##

    This is where I'm stuck. I'm just not sure which (if either) is correct! If mine is correct I have a lot of algebra to do in order to get it to the form they want.
     
  4. Dec 4, 2013 #3
    You have a resistor in parallel with a capacitor. The node connecting these two is in series with the inductor.

    [itex]Z_{total} = Z_{C}||Z_R + Z_L[/itex]

    You have to be careful when determining the impedance of the parallel network due to the imaginary number associated with the capacitor.
     
  5. Dec 4, 2013 #4
    I've calculated impedance using the first equation I was told was correct and now the one I've come up with. I don't understand what you're trying to tell me though. Like I said, I've done only RC circuits and years ago so I'm entirely lost with this.
     
  6. Dec 4, 2013 #5
    The bottom one is correct.
     
  7. Dec 4, 2013 #6
    Thank goodness! Glad I didn't waste my time redoing it. I thought the first one looked fishy. I separated the equation so that its in the format they asked for. It's messy but wolfram got the same:

    ##Z=\frac{1}{C^2Rw^2+\frac{1}{R}}+i(Lw-\frac{Cw}{C^2w^2+\frac{1}{R^2}}) ##

    You asked in the other thread setting up the complex impedance for figuring out the phase. I do not know what the relationship is between the two.

    Thank you for your help. Wish I could have started school here instead of transferring. I'm behind in every class it seems.
     
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