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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
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 23, 2012 #2
    Mistake has been found, since ω is in rad/s, t needs to be in s, ∴

    V=V.*cos(ωt)
    0=V.*cos(0.0785*20)
    0=V.*0.00
    0=0

    ..so it was really an error in calculating and not method.

    Therefore C=5.404Farads.

    Thank you
     
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