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LC circuit current of inductor

  1. Jan 11, 2017 #1
    1. The problem statement, all variables and given/known data
    In the figure given, find i(t) for the inductor
    My problem is though when we found i(t) with a source we find the transient response and the steady state response...
    I know how to do the transient response of an RLC circuit not an LC one.... do i just consider R to be 0

    2. Relevant equations
    the damping factor is given as (1/RC) for a parallel RLC circuit
    the frequency is given as 1/(√LC) which in this case is 1/2 am I right?
    3. The attempt at a solution
    There obviously is no damping factor therefore α = 0, however if R = 0 and we substitute for R in the damping factor equation we get infinity??
    and for some reason the book says the frequency is 1/4... where did I go wrong??
    Thank you
     

    Attached Files:

  2. jcsd
  3. Jan 11, 2017 #2

    NascentOxygen

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    Staff: Mentor

    Is this the damping factor ζ or is it the Quality factor Q?

    The frequency of ½ looks right, though you need to specify its units.
     
  4. Jan 11, 2017 #3
    In my textbook it's the damping factor which is R/2L for series RLC circuits and 1/RC for parallel RLC circuits
     
  5. Jan 11, 2017 #4

    NascentOxygen

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    Staff: Mentor

    More commonly known as the attenuation factor, ##\alpha##. Are you sure the last one isn't ##\mathsf {\frac 1{2RC}}##?

    wikipedia is a good resource for this, along with myriad others
     
  6. Jan 11, 2017 #5

    gneill

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    Staff: Mentor

    Since the circuit in question does not contain any resistance it is unwise to apply the "standard" RLC circuit formulas. With R = 0, any derivations of quantities or terms that rely on a division by R will be undefined or infinite (in other words, nonsense).

    A better approach might be to start from the beginning, writing the differential equation for the given circuit.
     
  7. Jan 11, 2017 #6
    Thank you
     
  8. Jan 11, 2017 #7
    Never mind, I found it
    thanks ;)
     
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