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RLC with extra resistors

  1. May 4, 2014 #1

    Maylis

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    Gold Member

    Hello, I am working on this problem
    ImageUploadedByPhysics Forums1399243402.897536.jpg

    I am having some difficulty finding the right answer. A few points I'd like to expand on so that one can understand my thought process. First off, there is a standard table with the solution to series RLC circuits. I don't think I can use that table with what I have in this circuit. So one idea I have us to modify the circuit to look like what I want with a thevenin equivalent.

    If the thevenin idea is wrong, I did nodal analysis and this is what my attempt looks like.
    ImageUploadedByPhysics Forums1399243617.704557.jpg

    I get an expression but the initial current is Zero, which proves troubling to integrate. I also can't tell the nature of damping in this circuit either
     
  2. jcsd
  3. May 4, 2014 #2

    Maylis

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    I tried again with the thevenin, which brings me closer to the answer, but their value is

    -13.33e^(-.5t)sin(.375t)

    Mine is almost the same, but I have that extra -7.5 term that they don't. I get -20.83e^(-.5t)sin(.375t)

    ImageUploadedByPhysics Forums1399245106.145250.jpg

    ImageUploadedByPhysics Forums1399245125.039762.jpg
     
  4. May 9, 2014 #3

    NascentOxygen

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    At t=0 the capacitor is, presumably, fully charged, so the inductor current and voltage at this time will both be 0.

    It's a second order system, so the response will be a decaying sinusoid. Where did you copy the general solution from?

    What is alpha described as?
     
  5. May 9, 2014 #4

    Maylis

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    Here is the table

    Alpha is the damping coefficient

    ImageUploadedByPhysics Forums1399689560.199109.jpg
     
  6. May 11, 2014 #5

    NascentOxygen

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    Possibly not. Coefficients are usually dimensionless. Your alpha has units of sec⁻¹.

    Your method looks right, but you haven't finished. To determine ic you now have to multiply that derivative by C.
     
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