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Second order ODE for RLC circuit

  1. Nov 24, 2014 #1
    if I consider a circuit consisting of a capacitor, an inductor and a resistor and using kirchoffs voltage rule for the circuit i come up with the following

    L(Q''(t)) + R(Q'(t)) + (Q(t))/C = 0 I solve for the roots using a characteristic equation of the form
    LM2 +MR +(1/C) = 0
    solving this for m I obtain
    m = [-R/L +/- sqrt((r/l2) - 4(1)(1/LC))]/2
    i'm expecting an equation using both decaying exponentials and sinusoids so that the energy will tend towards zero after a long time. But this depends on the values of R, C and L. I'm having trouble moving forward from this point in deriving the equation for the charge on the capacitor as a function of time.
    Q(t) = Ae-Btcos(w't+θ)
    B = R/2L
    Last edited: Nov 24, 2014
  2. jcsd
  3. Nov 24, 2014 #2
  4. Nov 24, 2014 #3
    so obviously the characteristic equation doesn't directly lead to that damped charge motion then, it depends on the discriminant. I thought I was SUPPOSED to get the decaying exponential out of it. Anyways, thanks.
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