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Need help finding the Max Power in a math/EE problem please

  1. Mar 25, 2016 #1
    1. The problem statement, all variables and given/known data
    The voltage across the inductor is given by v(t)=L(di(t)/dt).
    Determine:

    (1.) Tthe voltage v(t)
    (2.) The power p(t)=v(t)*i(t).
    (3.) The maximum power transferred ( t = ??? (in seconds) when power is at maximum).

    if the inductance is L=2 and the current i(t) is given by:

    (a.) i(t)=13e-200t A.
    (b.) i(t)=20cos(2π60t) A.

    It's the formula/steps to get pmax that I am stuck on.

    Thank you so much!
    media%2F941%2F9419074d-70c8-4f5d-98f8-71788a501cc1%2Fphpx6alCG.png
    media%2Ff6e%2Ff6ea84a2-7f92-40ce-b36a-632ea0860cac%2FphpKdwV8D.png

    2. Relevant equations
    See above.

    3. The attempt at a solution

    I got as far as answering the (1.) and (2.) for each (a.) and (b.), but I do not know how to calculate the pmax.

    (a1.) v(t) = -5.2 e-200t V.
    (a2.) p(t) = -67.6 e-400t W.
    (a3.) ??? ( t = ??? when power is at maximum).

    (b1.) v(t) = -4.8 π sin(120πt) V.
    (b2.) p(t) = -48sin(240πt) W.
    (b3.) ??? ( t = ??? when power is at maximum).

    Thank you very much!!!
     
  2. jcsd
  3. Mar 25, 2016 #2

    Mark44

    Staff: Mentor

    What's the behavior of y = e-400t? This is a decaying exponential function, which tells you something about where its maximum value is.

    The negative sign on -67.6 looks wrong to me. Power should be nonnegative, I believe.
    What does the graph of y = sin(240πt) look like? What is its maximum value, and where does it attain this maximum? Also, I'm not sure about the sign you have on -48.
     
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