LC Circuit: Initial Conditions and Switch

[AiRAVATA]

Hello guys. I have a simple question regarding an LC circuit.

Imagine a voltage source V_0, a capacitor C and an inductor L, all hooked up in series. I know that the equation governing the behvior of the system is

V_0=\frac{1}{C}q(t)+L\ddot{q}(t),

and hence

q(t)=A\cos \omega t + B\sin \omega t + CV_0.

What I'm having trouble with is the initial conditions. Is it fair to assume that in t=0 there is no charge nor current in the system?

If I put a switch in the system, how would the initial conditions change (assuming is open in t=0 and closed in t>0)?

 

[John Creighto]

Hello guys. I have a simple question regarding an LC circuit.

Imagine a voltage source V_0, a capacitor C and an inductor L, all hooked up in series. I know that the equation governing the behvior of the system is

V_0=\frac{1}{C}q(t)+L\ddot{q}(t),

and hence

q(t)=A\cos \omega t + B\sin \omega t + CV_0.

What I'm having trouble with is the initial conditions. Is it fair to assume that in t=0 there is no charge nor current in the system?

If I put a switch in the system, how would the initial conditions change (assuming is open in t=0 and closed in t>0)?

Yes because the voltage across a capacitor cannot change instantaneously and then current though an inductor cannot change instantaneously.

 

[AiRAVATA]

So the answer is

q(t)=CV_0 (1-\cos \omega t)

no matter if I have a switch or not?

 

[AiRAVATA]

Well, in case you have been wondering, It's all wrong!

What I have to do is imagine a RLC ciruit, solve it with conditions i(0)=V_0/R, \, i'(0)=0, integrate in t, divide by C and then take the limit as R \rightarrow 0. Then I'll know what's the voltage passing trough the capacitor on my original LC circuit!

Yeah!

 

[John Creighto]

Well, in case you have been wondering, It's all wrong!

What I have to do is imagine a RLC ciruit, solve it with conditions i(0)=V_0/R, \, i'(0)=0, integrate in t, divide by C and then take the limit as R \rightarrow 0. Then I'll know what's the voltage passing trough the capacitor on my original LC circuit!

Yeah!

Well, you didn't give us that initial set of conditions.

 

[AiRAVATA]

I know, I know. It was exactly that what made me realize my minstake. Thanks for the input tough, you really got me thinking.