1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Phase problem in a damped RLC circuit

  1. May 25, 2016 #1
    1. The problem statement, all variables and given/known data
    The expression for electric charge on the capacitor in the series RLC circuit is as follows: q(t)=A*exp(-Rt/2L)*cos(omega*t+phi)
    where omega=square_root(1/LC-R^2/4L^2)
    What is the phase phi, if the initial conditions are:
    q(t=0)=Q
    I(t=0)=0

    2. Relevant equations
    The damped oscillator equation is:
    second_derivative(q)+R/L*first_derivative(q)+q/LC=0


    3. The attempt at a solution

    I calculated the current (as a derivative of charge):
    I(t)=A/square_root(L*C)*exp(-Rt/2L)*cos(omega*t+phi-psi)
    where tg(psi)=2*L*omega/R
    When I set the initial condtitions, I get:
    A*cos(phi)=Q
    A/square_root(L*C)*cos(phi-psi)=0
    and then I get:
    tg(phi)=-1/tg(psi)=-R/(2*L*omega)
    which seems really strange to me: shouldn't phi=0? If I start with some charge on capacitor and no current, the charge can only go down, at no moment the charge will be larger, so I think that q(t)=A*exp(-Rt/2L)*cos(omega*t)
    Or am I not right?
     
  2. jcsd
  3. May 25, 2016 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You would be right if there was no damping, and the charge was q=Acos(wt). But the exponential factor contributes to the current, so there is a phase term in the cosine.
     
  4. May 26, 2016 #3
    OK, so my result was correct. But could somebody explain to me the physical meaning of it? It is not intuitive...
     
  5. May 26, 2016 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Without damping, the time derivative of the cos(wt) function is zero at t=0. But the time derivative of the exponential factor is not.
    The charge decreases with two ways on the capacitor. One is the discharge through the inductor and resistor, shown by the exponential factor. The other way is due to the oscillation. The charge decreases faster because of the exponential. If you suppose q=e-kt cos(wt), the current would be -ke-kt cos(wt)-w e-ktsin(wt), different from zero at t=0.
     
    Last edited: May 26, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Phase problem in a damped RLC circuit
Loading...