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Homework Help: Calculating Capacitance of LC Circuit

  1. Sep 23, 2012 #1
    1. The problem statement, all variables and given/known data

    Calculate capacitance of LC Circuit where:

    Inductor - 30H
    Capacitance voltage fully charged goes to zero in 20 seconds

    2. Relevant equations

    Main Eq: V=V. *cost(ωt) where V is final Voltage, V. = Voltage initial, ω = resonant angular frequency

    ω = 1/√(LC) = 2∏f

    f. = 1/2∏√(LC) --> resonance frequency

    3. The attempt at a solution

    Calculated f=1/80 =0.0125Hz as voltage of capacitor takes 20s to deplete 1/4 cycle
    ∴ ω = 2∏*0.0125=0.0785

    Rearranged angular frequency equation to solve for C
    ∴C=1/(ω^2 * L) = 5.404F

    Since Voltage = 0 after t = 20s = 1/3min,

    V=V. *cost(ωt)
    0=V.*cos(0.0785*(1/3))

    Since the whole equation is multiplication, calculating V. would not be required since if cos equaled 0 then so would the whole right hand side of the equation. However cos equals close to 1 and therefore i'm stuck.

    Please help

    Thank you

    Edit: Thread has been answered and I'm correcting my mistake for those reading this post as a reference on how to answer this type of question. Mistake was in the calculation of main equation:

    V=V.*cost(ωt)
    0=V.*cos(0.0785rad/s*20s) --> Calculate using radian mode on calculator
    0=V.*0.00
    0=0 --> as anything multiplied by 0 is equal to 0

    Answering main question of this thread...

    Capacitance = 5.404 Farards
     
    Last edited: Sep 23, 2012
  2. jcsd
  3. Sep 23, 2012 #2

    gneill

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    Staff: Mentor

    Check your calculator for degrees versus radians setting.
     
  4. Sep 23, 2012 #3
    Hi,

    I checked by calculating cos in radians and degrees but both equal a figure close to one but i need it to equal zero.

    Thank you
     
  5. Sep 23, 2012 #4

    gneill

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    Staff: Mentor

    Your ω is in units of radians per second. Your time should be specified in seconds, not fractions of a minute.
     
  6. Sep 23, 2012 #5
    Alright I got it.

    V=V.*cos(ωt)
    0=V.cos(0.0785rad/s * 20s)
    0=V.*0.001=V.*0
    0=0

    Thanks for the help gneill, I suppose the above therefore is correct.

    Answering the main question of this thread;

    Capacitance = 5.404 Farads

    Thank you
     
    Last edited: Sep 23, 2012
  7. Sep 23, 2012 #6

    gneill

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    Staff: Mentor

    Yes, that looks good :smile:
     
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