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Critically damped current in this network

  1. Jul 31, 2011 #1
    1. The problem statement, all variables and given/known data
    I'm supposed to find whether the current in the following network is

    a) under-damped
    b) critically damped
    c) undamped
    c) over-damped

    69a41e90b3645d9e7114cb87b7e00ab2.png

    2. Relevant equations
    According to Kirchoff's laws
    c14ee8367ddccabff780a7275dd9f322.png

    3. The attempt at a solution

    The answer given by my professor for this question is supposed to be "b) critically damped" so I just converted the given values into SI values
    R = 1kilo-ohm = 1000 ohm
    L = 10mH = 0,01H
    C = 40nF = 4 * 10^(-8)

    and then I tried relating them to

    3e2c036273361ac3e5a5bc528b59cc44.png

    But I do not find two real roots that are equal for it to be critically damped.

    What did I do wrong?
     
  2. jcsd
  3. Jul 31, 2011 #2
    Critical damping will occur when [itex]\alpha[/itex][itex]^{2}[/itex]-4[itex]\omega^{2}_{o}[/itex]=0. Another way to write it is: R=sqrt(4*L/C). If you plug in your values for R, L and C, you'll find that it is indeed critically damped.
     
  4. Jul 31, 2011 #3
    Thank you. I see that my silly mistake was that I substracted the 10 instead of leaving it homogenous.

    Though, when exactly is a circuit undamped? I know when it's critically, overdamped or underdamped but when would it be undamped?
     
  5. Jul 31, 2011 #4
    If there's a resistor, there will always be energy lost, hence the damping.
    An LC circuit (no resistor) will oscillate without damping.
     
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