Differential Ecuation simple circuit

Discussion in 'Homework Help' started by omar-rodriguez, Mar 29, 2016.

  1. omar-rodriguez

    Thread Starter Member

    Jun 24, 2015
    51
    2
    Hello, I'm trying to find the differential equation of this circuit

    [​IMG]

    but I got an Integro differential equation, I don't know what's next because the current function is on terms of tao and t at the same time

    [​IMG]
     
  2. anhnha

    Active Member

    Apr 19, 2012
    774
    48
    You could take derivative with t of both sides and then there is only one variable t.
     
  3. omar-rodriguez

    Thread Starter Member

    Jun 24, 2015
    51
    2
    Ok I did it and it looks like that
    [​IMG]

    But I have one more quesion, why when I am finding the differential equation, I said that in this case
    [​IMG]

    but when I apply laplace for example to a derivative, I have to replace the real values of the initial conditions derivative
    [​IMG]
     
  4. anhnha

    Active Member

    Apr 19, 2012
    774
    48
    The first case Vc(0) is a constant while the second case it is the value of capacitor derivative at the time t equals to 0 (first you derivative Vc and get dVc/dt then you evaluate it at t=0).
     
    omar-rodriguez likes this.
  5. omar-rodriguez

    Thread Starter Member

    Jun 24, 2015
    51
    2
    mmmmm..... It all makes sense now, thank you so much
     
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