LC Circuit: Initial Conditions and Switch

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Discussion Overview

The discussion revolves around the initial conditions of an LC circuit, particularly focusing on the effects of a switch in the circuit. Participants explore the governing equations of the circuit and the implications of assuming no initial charge or current.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether it is reasonable to assume no charge or current in the system at t=0.
  • Another participant asserts that the voltage across a capacitor and the current through an inductor cannot change instantaneously, suggesting this affects initial conditions.
  • A different participant proposes a solution involving an RLC circuit and specific initial conditions, indicating that the approach to solving the problem may differ based on the circuit configuration.
  • There is a challenge to the initial assumptions made about the LC circuit, with a suggestion that the original approach may be incorrect.
  • One participant acknowledges a mistake in their reasoning and expresses appreciation for the feedback received.

Areas of Agreement / Disagreement

Participants express differing views on the initial conditions and the appropriateness of the assumptions made. The discussion remains unresolved regarding the correct approach to analyzing the circuit with or without the switch.

Contextual Notes

Participants did not provide a complete set of initial conditions, which may affect the analysis and conclusions drawn about the circuit's behavior.

AiRAVATA
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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)?
 
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AiRAVATA said:
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.
 
So the answer is

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

no matter if I have a switch or not?
 
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!
 
AiRAVATA said:
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.
 
I know, I know. It was exactly that what made me realize my minstake. Thanks for the input tough, you really got me thinking.
 

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