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Deriving v(t) from i(t)

  1. Nov 16, 2011 #1
    1. The problem statement, all variables and given/known data

    I've been given a series circuit with a .5H inductor .01F cap, .5H inductor and 10Ω resistor in series.

    This circuit is connected to a source i(t) = 10cos(10t) and I need to find v(t) across Z

    2. Relevant equations
    From the givens I've found the Z(s) to be s+100/s+10 and Z(jω) to be j((ω^2-100)/ω)+10

    3. The attempt at a solution

    I believe I need to use Ohm's law V=IR to find V. So if I multiply j((ω^2-100)/ω)+10 by 10cos(10t) I should get a v(t) but I think I'm doing something wrong with this.
  2. jcsd
  3. Nov 17, 2011 #2


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    Gold Member

    what you need to do is make sure you are in the s-domain, so V(s) = I(s)Z(s), you need to perform laplace transform to the current output to obtain I(s), then you can multiply that with the frequency dependent impedance, then finally get your answer from the inverse laplace of the product
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