>studying for Physics Exam >want to know how to derive

for that circuit, the L and C part are independent

I = C.dV/dt => dI/dt = C.d^2V/dt^2
V = -L.dI/dt = -L.C.d^2V/dt^2
=> V=V0*sin(w*t+phi) where w=1/sqrt(L.C)
V0 and phi are determined by initial conditions (capacitor voltage and inductor current at t=0).

Charge is given by Q=C.V.

>>8506437
there's no source and assumed initial conditions are always 0 therefore q(t) = 0

>>8506475
Assuming there is an induced current through the circuit, and also we are trying to determine the charge at any time t

>>8506472
>V = -L.C.d^2V/dt^2
Do we plug this into Q=CV and do the integration?

>write DE of L
>write DE of C
>Kirchoff 2
>find general solution
>apply IC

Profit?

>>8506472
Okay so I solved V_0 = (Q_0)/C and plugged it back in for the V equation and used that in the derivative. I plug ω = 1/sqrt(LC) into the final result and get

Q(t) = (Q_0)sin(ωt)

I think the original V equation should be cos(ωt) to get the correct equation?

>>8506507
> I think the original V equation should be cos(ωt) to get the correct equation?
You missed out calculating phi (the phase angle), which will be pi/4 if I(0)=0.

V=V0*sin(w*t+phi)
I = C.dV/dt = C*w*V0*cos(w*t+phi)

V/I = sin(w*t+phi)/C*w*cos(w*t+phi)
= tan(w*t+phi)/(w*C)
=> phi = atan(w*C*V(0)/I(0))

If V(0)=0,I(0)=/=0, V = +/-sin, I = +/- cos
If V(0)=/=0,I(0)=0, V = +/-cos, I = +/- sin

>>8506437
Q=C*v
v=Ldi/dt=Ld^2Q/dt^2
Q/C=Ld^2Q/dt^2
Q*L/C=d^2Q/dt^2
Q*L/C=d^2Q/dt^2
Q(t)=A*cos(sqrt(L/C)t)+B*sin(sqrt(L/C)t)

File: some circuit shit.png (118KB, 2158x1205px)

118KB, 2158x1205px

I'll let you work this integral out

>>8508084
Oh wait, I'm a moron, rework those parallel impedances. That's obviously wrong. It'll only change your Z.

I think you'll have (ωL/ωC)/((1/ωC)+ωL)

How do you faggots remember this stuff after you pass the class? I fucking forgot it all the second the semester ended.

>>8506437
By any chance do you go to college in a cold place?

>>8506437
>how to derive q(t)

just talk to her, bro

>>8506437
which uni do you go to breh?

im studying for this shit as well

Also q(t) = q_0 cos(wt) is what you get when you solve the second order differential equation equation of the LRC circuit I believe.

>>8509377
I always had this problem, fuck circuits. I always had to re learn everything for those courses.

>>8510439
I don't think we go to the same uni. I had my quiz/exam on 11/30. Good luck to you /sci/bro. None of this circuit stuff was even on it