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RC Circuit with alternating voltage source

  1. Sep 27, 2014 #1
    1. The problem statement, all variables and given/known data
    I'm supposed to find the current in a circuit with a voltage source, capacitor, and resistor in series. The voltage source is described by V=V0ejwt.
    Here, j is the complex number j2=-1, and i is the current

    2. Relevant equations
    I=C*dv/dt

    3. The attempt at a solution
    I have several sources of confusion with this question. First, in the equation I=C*dv/dt, does that v refer to the voltage source, or specifically the voltage drop across the capacitor? Can I use Kirchoff's voltage law with this type of circuit? I tried this and got:

    V0ejwt - iR - q/c = 0
    Then taking the time derivative of the equation:

    V0jwejwt - R*di/dt - i/c = 0
    I then have no idea how to solve this differential equation. Even rewriting with euler's identity:
    V0jw[cos(wt)+jsin(wt)]=R*di/dt+i/c

    Any help would be greatly appreciated.
     
  2. jcsd
  3. Sep 27, 2014 #2

    gneill

    User Avatar

    Staff: Mentor

    I suspect that the ##V = V_o e^{j \omega t}## is meant to be a phasor representation for the input. Have you covered phasors yet? If so you're meant to deal with the real portion of the resulting voltage, which in this case would be ##V_o cos(\omega t)##.

    Yes, the v in I = C*dv/dt represents the voltage across the capacitor.

    Yes, Kirchhoff's Voltage Law (KVL) can be applied as you have done.
     
  4. Sep 28, 2014 #3
    We haven't covered phasors yet but I read ahead and it makes sense now.
    Thank you for the response.
     
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