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Series RLC circuit with source

  1. May 11, 2013 #1
    1. The problem statement, all variables and given/known data
    t2eHpiO.png
    R=50Ω
    L=5H
    C=1/125F
    vs=200.[1+u(t)] V

    Find i(t)
    2. Relevant equations

    3. The attempt at a solution
    Write the KCL equation
    -vs+Ri+L.i'+1/C.∫idt=0
    Do the derivation to get rid of the integral, replace all possibly values, we got:
    i''+10i'+25i=1/5.vs' (*)
    solve A(s)=s2+10s+25=0, we got the natural response in(t)=A1+A2.e-5t

    Replace the inductor with a short circuit, the capacitor with open circuit, so I have ip=0
    and the initial condition i(0+)=i(0-)=0. (**)

    So the solution should be i(t)=in+ip

    I thought I was wrong at (**) and maybe at (*) cause the vs' would be zero and the solution would be zero as well.
     
  2. jcsd
  3. May 11, 2013 #2

    rude man

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    i(0+) = i(0-) ≠ 0. Look at the definition of the input. What does vs=200.[1+u(t)] V mean?
     
  4. May 11, 2013 #3

    rude man

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    Even if Vs = u(t) the current i(t) would not be zero! You are ignoring Vs!
    You have to include Vs before trying to fit the initial conditions. Since this is a 2nd order ODE you know there have to be two initial conditions on i.
     
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