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Series RLC Circuit

  1. May 23, 2009 #1
    1. The problem statement, all variables and given/known data
    Analyze a series RLC circuit and determine the voltage across each element due to the transient response. The circuit is powered by a square wave voltage source with a peak-to-peak voltage of 4V and frequency of 1kHz.
    R=50 kohms
    L=33mH
    C=1 nF


    2. Relevant equations
    Since this circuit turns out to be overdamped:
    I(t)=A1es1*t+A2es2*t
    Alpha=R/(2L)
    Omega_0=1/(sqrt(L*C))
    S1=-alpha+sqrt((alpha^2)-(omega_0^2))
    S2=-alpha-sqrt((alpha^2)-(omega_0^2))
    I=V/Z
    X_L=2*pi*f*L
    X_C=1/(2*pi*f*C)

    3. The attempt at a solution
    I have tried to solve this the best I can, but the results do not seem to come out right. I did an experiment using the circuit, so I'm comparing the calculated results to the experimental values and I am fairly confident in the experiment. I've summarized my work below, please let me know where I am going wrong.
    V(0)=-2V
    I(0)=-2/Z=-2/sqrt(((X_L-X_C)^2)+(R^2))=-1.20029E-5
    since I(0)=A1+A2, A1=I(0)-A2
    at T=0, di/dt=0
    di/dt=s1A1+s2A2==>s2A2+s1(I(0)-A2)
    A2=-(S1*I0))/(S2-S1)
    solving for A1 and A2 give
    I(t)=1.2169E-5e^(s1t)-1.65E-7e^(s2t)
    Vr(t)=I(t)*R
    Vc(t)=I(t)*X_C
    Vl(t)=I(t)*X_L
     
  2. jcsd
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