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Transient response RLC, Check my work?

  1. Oct 16, 2016 #1

    gmm

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    9121. Problem
    circuit-jpg.107526.jpg
    If we assume that the initial voltage, Vs, is equal to zero, and it rises to five volts at t = 0, derive an expression for the voltage across the capacitor as a function of time. That is, calculate Vc(t)

    2. Relevant equations
    formulas-jpg.107528.jpg
    this is a series RLC so I'm trying to calculate for Vc(t). Also I used α=R/2L

    3. Attempt at solving
    L= 120 *10^-6 H
    C=0.01 *10^-6 F
    R= 33 Ω
    ωo=1/√(120*.01*10^-12)=912,870
    α=33/(2*120*10^-6)= 137,500
    α<ωo ∴ this is under-damped
    ωd=√(912,870^2 - 137,500^2)=902,456
    D1=(0-5)V... because voltage across capacitor at t=0 is 0V
    D2=(0 + 137500[0 - 5])/902456= -0.7618... the current and the voltage through the capacitor at t=0 are both zero, because the inductor does not allow the current to change instantaneously.
    With this I built my Total Response:
    Vc(t) = e^(-137500t)*(-5cos(902456t) - .7618sin(902456t)) + 5

    I then simulated the circuit in Multisim with a square wave voltage source of 0 to 5 V.
    the transient analysis shows that when the voltage source goes from 0 to 5V the peak voltage at the capacitor goes up to about 8.5V Here is the plot, and a zoom into the first pulse. vc-png.107529.png

    vczoom-png.107533.png

    The red is the Source voltage and the blue is the capacitor voltage.
    when I plot my Vc(t) it does not resemble this, it gives a lower peak capacitor voltage, Did i mess up in some of the parameters?? Am I missing something?
    graph-png.107532.png

    Attached Files:
     
  2. jcsd
  3. Oct 16, 2016 #2

    gneill

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    Staff: Mentor

    Your calculated plot looks fine to me. I'd be more dubious abut the Multisim accuracy. Simulators are great tools but you need to be a bit careful with them when dealing with high speed transients. See if you can find a simulator menu where you can specify the maximum simulation time step size and play with the value a bit. See what effect it has on the waveform peaks.
     
  4. Oct 19, 2016 #3

    gmm

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    Ah yes. I adjusted my time step size and re-simulated now it's pretty much identical to my model. Thanks qneill
     
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