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Partial RL Circuit Help.

  1. Nov 4, 2008 #1
    1. The problem statement, all variables and given/known data
    A current pulse is fed to the partial circuit shown in Figure P32.25. The current begins at zero, then becomes Imax = 7.0 A between t = 0 and t = 200 µs, and then is zero once again. Determine the current in the inductor as a function of time. Let L = 1.0 mH and R = 100 . (Use t as appropriate.)


    Figure

    2. Relevant equations
    ...


    3. The attempt at a solution

    I know I need to use Kirchhoff's rules for this. I am not quite sure how to go about setting this up...I know I will have:

    Emf - IR - L(dI/dt) = 0

    Since there is no Emf this becomes:
    L(dI/dt) = - IR

    I am not sure where to go from here. I have the correct answer for [tex]0\leq[/tex] [tex]t[/tex] [tex]\leq200\mu s[/tex] being:

    [tex]I(t) = 7(1 - e^{-100000t}) [/tex]

    I also am not sure how to proceed with finding the current for t > 200 microseconds.
     
    Last edited: Nov 4, 2008
  2. jcsd
  3. Nov 4, 2008 #2
    I know that Iresistor must be:

    Iresistor (I2) = Iinitial(I1) - Iinductor(I3).

    However, whenever I use that I can't ever seem to get the actually statement they are getting for Iinductor. I get this DE:

    L(dI3/dt) = -I2*R.

    When I solve that I get:

    I3 = I1 + e^(-Rt/L)

    That expression doesn't seem right, and is not right.
     
  4. Nov 5, 2008 #3
    This is the DE you need. The boundary condition is just continuity with the earlier function you found.
     
  5. Nov 5, 2008 #4
    I am not sure I follow what you mean about the earlier function. Are you talking about Kirchhoffs rule with the Emf in it?
     
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