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Simple Electrical Modeling Question (w/ only C and L)

  1. Jan 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Find a differential equation that describes the circuit that includes only vin and vout as variables.

    2. Relevant equations
    C(dvin - dvout)/dt = i
    vin - vout = L(di/dt)

    3. The attempt at a solution
    So the answer I got was:

    C(d2vout/dt2) + vout = LC(d2vin/dt2)

    My question is, is it allowable to break up the capacitor derivate like that? After substituting in for i, I got:

    vout = Ld/dt(C(dvin - dvout)/dt)

    Then I broke up the capacitor into vin and vout terms and just rearranged. But I'm not 100% sure if that's legal.

    Attached Files:

  2. jcsd
  3. Jan 24, 2016 #2


    User Avatar

    Staff: Mentor

    That first C should be LC.

    A rule of the Calculus says that the derivative of a sum equals the sum of the separate derivatives, so your approach is correct.
  4. Jan 24, 2016 #3
    Woopsie, right. LC

    Ok sweet, thanks. I just can't remember something we might have glossed over a few years ago . . . and no one recently has said "You can do this to a derivative". They just sorta do it on their own.
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