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Where does the phi come from in the charge of a capacitor in an LC circuit?

  1. Jul 22, 2012 #1
    I'm reading University Physics 13e by Young and Freedman and we're given this equation:

    -L(di/dt)-q/C=0

    So we know that i, current, is, i=dq/dt. So the first equation can be read, after some simplification, as

    q''+(1/LC)q=0

    where q prime means the derivative of q (charge) with respect to time.

    This is a homogeneous system so I figure solve it like anything else. So

    s^2 = -(1/LC)
    =>
    s=i*(1/LC)^1/2..... the i here is imaginary

    let: a=(1/LC)^1/2

    thus q=k1*cos(at) + k2*sin(at)

    Yet in the formula in the book we end up with the formula:
    q=Q*cos(at + phi)

    with no sine...

    Any help?
     
  2. jcsd
  3. Jul 22, 2012 #2
    Figured it out:

    s48fb6.jpg

    This was inspired by the youtube video I found here.
     
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