Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Second order ODE for RLC circuit
  1. RLC circuits (Replies: 4)

  2. RLC oscillator circuit (Replies: 8)

Loading...