- #1

anizet

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## Homework Statement

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

## Homework Equations

The damped oscillator equation is:

second_derivative(q)+R/L*first_derivative(q)+q/LC=0

## The Attempt at a Solution

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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?