Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:


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


    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:


    This was inspired by the youtube video I found here.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook