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Natural and step response RLC find iL(t)

  1. May 31, 2013 #1
    1. The problem statement, all variables and given/known data


    The switch in the circuit in the figure has been open a long time before closing at t=0.
    Find iL(t) t>0
    Express your answer in terms of t, where t is in milliseconds.

    https://www.flickr.com/photos/84781786@N03/8899251427/

    3. The attempt at a solution

    We simplify to circuit to get

    4A current , 2kohms,62.5H,2.5uF (All in parallel with each other).

    iL(0-)= -15/3000 =-5mA ,
    Vc(0-)=0,
    iL(∞)= 4mA,

    wo^2= 1/LC=10^6/62.5*.5 =6400
    wo=80 rad/s

    a= 1/2RC =10^6/4000*2.5 =100

    s1,s2=-100±√100^2-80^2=-100±60
    s1=-40 , s2=-160

    iL=If+A'1e^-40t + A'2e^-160t

    iL(∞)=If=4mA
    iL(0)=A'1+A'2+If=-5mA

    so A'1+A'2=-9mA

    diL/dt(0) =0=-40A1 - 160A'2

    A'1=12mA A'2=3mA

    iL=4-12e^-40t+3e^-160t t≥0
     

    Attached Files:

    Last edited: May 31, 2013
  2. jcsd
  3. May 31, 2013 #2

    gneill

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    Staff: Mentor

    Your diagram doesn't appear to match your problem statement.
     
  4. Jun 1, 2013 #3

    rude man

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    Homework Helper
    Gold Member

    What switch?
     
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