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Circuit with both AC and DC

  1. Dec 15, 2016 #1
    IMG_1481801473.286857.jpg

    See picture, sorry that it's huge. V1 is a DC voltage and there is also an oscillating source of frequency omega. Let V be the voltage between the two resistors, I be the current exiting the cap, and I1 and I2 be the currents through the 2 resistors. Then we have: ## I_1 = (V - V_1) / R_1## , ## I_2 = V / R_2##, ##I_1 + I = I_2 ##, and ## I = - C \frac{d}{dt} (V - V_0 \cos (\omega t)) ##. Combining gives ## -C \frac{d}{dt} (V - V_0 \cos (\omega t )) = V / R_2 - (V - V_1)/ R_1 = V( 1/R_2 - 1/R_1) + V_1 / R_1##. The constant term can be eliminated with a substitution, and then the sign on the right hand side can be chosen to give a homogenous solution of the form ##e^{ax} ## with ##a > 0##, by choosing ##R_1## accordingly. This obviously makes no sense. Can someone see where I am setting this up wrong?
     
    Last edited: Dec 15, 2016
  2. jcsd
  3. Dec 15, 2016 #2

    mfb

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    The sign or direction of I1 looks inconsistent.
     
  4. Dec 17, 2016 #3
    Sorry for not updating. The current across R1 is inconsistent. Thanks.
     
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