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Homework Help: Help with Second Order Circuits

  1. Dec 16, 2009 #1
    1. The problem statement, all variables and given/known data
    I have a RLC circuit in series. I am trying to find the current i(t) passing through this RCL circuit. When solving the RCL circuit, it happened to be critically damped. And simplified i ended up with:
    i(t) = A2te-20t
    Where i need to find what is the cosntant A2

    2. Relevant equations
    R = 100Ohm
    L = 2.5H
    C = 1mF
    i(0) = 0A
    vC(0) = 24V
    vL = L di/dt
    vR = iR
    di/dt = -20A2te-20t

    3. The attempt at a solution
    I apply KVL to the closed RCL loop and get:
    vC + vL + vR = 0
    vC(0) + L di(0)/dt + i(0)R = 0
    24V + 2.5H di(0)/dt + 0 = 0
    di(0)/dt = -24V/2.5H = -9.4A

    But di/dt is also -20A2te-20t so
    di(0)/dt = -9.4 = -20A2(0)e-20(0)
    -9.4 = 0
    which is fallacy

    but according to the book:
    A2 = -9.4
    so,
    i(t) = -9.4te-20t

    Where did i go wrong?
     
  2. jcsd
  3. Dec 22, 2009 #2
    Dear Friend

    di/dt = A2 * t * (-20 * e (-20t) ) + A2 * e(-20t)

    The derivative of multiplied terms.
     
  4. Dec 22, 2009 #3
    Rgiht! How could i make such a basic mistake. The product rule! Thanks a bunch. T^T
     
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