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Inductor First order circuits

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data
    The current in a 25mH inductor is known to be - 10A for t <= 0 and (-10cos400t - 5sin400t)e^-200t A for t >= 0. Assume the passive sign convention.

    Part A: At what instant of time is the voltage across the inductor maximum?
    Part B: What is the maximum voltage?

    2. Relevant equations
    V=L*di/dt


    3. The attempt at a solution

    I took the derivative of (-10cos400t - 5sin400t)e^-200t, then took the derivative again, set to zero, and found the value of t at that point.

    5000*e^(-200t)*sin(400t)

    1000000*e^(-200t)(2cos400t - sin400t) = 0 @ t = 0.01339 s

    Where am I going wrong? Am I missing something?
     
  2. jcsd
  3. Oct 10, 2012 #2

    gneill

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    Staff: Mentor

    t = 0.01339 s doesn't look like a zero of that function to me...
     
  4. Oct 10, 2012 #3
    your right, that's way off.... looking at it again.

    I need 2cos400t - sin400t to equal 0...

    2cosx = sinx
    2 = tanx
    arctan(2) = x

    x = 1.107s

    this didn't work.. is my derivative correct? I'm pretty sure my algebra and trig were correct.
     
    Last edited: Oct 10, 2012
  5. Oct 10, 2012 #4

    gneill

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    Staff: Mentor

    You've solved for the angle, x. But the angle is not t...
     
  6. Oct 10, 2012 #5
    hahaha, what a silly mistake, I used a variable in place of 400t and didn't sub the variable out... x/400 = t so, 1.107/400 = t = .0027679s
     
  7. Oct 10, 2012 #6

    gneill

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    Staff: Mentor

    Yes, that looks much better :smile:
     
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