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First order Transient Circuit

  1. Jun 9, 2007 #1
    I'm having serious trouble understanding how to solve this problem using the differential equation method ( I MUST use this method). I provided the answer but my solution attempts are not producing the same result.

    Here is the problem. [​IMG]

    The first thing I need to do is find the voltage across the capacitor at time [tex]t_{0^-}[/tex]. By combining the 4k and 6k resistors and using voltage division I see that the voltage across the capacitor for [tex]t_(0^-)= 8V[/tex]

    Now I'm confused here, should I also find the current in the circuit for [tex]t_(0^-)[/tex]?

    Let me assume that I don't need this parameter and then I go on the analyze this circuit for [tex]t_(0^+)[/tex]

    For this circuit all we have is one loop consisting of the capacitor and the 4k and 6k resistors.
    Now I can write and equation for the current around this loop:
    [tex]C\frac{dV_c(t)}{dt} + 6ki(t)=0[/tex]
    Last edited: Jun 9, 2007
  2. jcsd
  3. Jun 9, 2007 #2
    Have you tried using a combination of Kirchoff's voltage and current laws? I tried it and got three equations and three unknowns. But its crazy to solve. I doubt its the right way, but maybe you can give it a shot?

    How about Laplace transformations? Find the transfer function for capacitor and output, and then inverse laplace it for the final answer.
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