What happens when a battery is connected to an ideal LC circuit?

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Discussion Overview

The discussion revolves around the behavior of an ideal LC circuit when a DC battery is connected, particularly focusing on the time domain response and the oscillatory nature of the circuit. Participants explore the implications of connecting a battery to an initially uncharged LC circuit, the resulting current and voltage dynamics, and the concept of energy conservation within the circuit.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the intuitive understanding of the LC circuit's response to a battery connection, seeking a non-mathematical explanation of the current and voltage behavior.
  • Another participant asserts that connecting an ideal DC battery to an ideal de-energized LC circuit results in an ideal sine current oscillating indefinitely, with specific amplitude and frequency derived from the circuit parameters.
  • It is noted that the voltage across the capacitor oscillates between 0 and 2V, and this behavior is linked to the solution of differential equations governing the circuit.
  • A participant describes the initial voltage appearing across the inductor, followed by a ramp-up of capacitor voltage as current builds, leading to an overshoot and reversal of the cycle, indicating a continuous oscillation at the resonant frequency.
  • Another participant expresses confusion regarding the relationship between capacitor charging to the step voltage and the inductor current, questioning the occurrence of overshoot when the inductor current should be zero.
  • A participant emphasizes the conservation of energy in the system, explaining how energy transfers between the capacitor and inductor, leading to oscillatory behavior.

Areas of Agreement / Disagreement

Participants express various viewpoints on the behavior of the LC circuit, with some agreeing on the oscillatory nature and energy transfer concepts, while others raise questions and challenges regarding specific aspects of the response, indicating that the discussion remains unresolved.

Contextual Notes

Some participants highlight the difficulty of explaining the circuit's behavior without mathematical formulations, and there are unresolved questions about the conditions under which certain behaviors occur, such as the relationship between capacitor voltage and inductor current during oscillation.

k_rlc
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Hi All ,

I was thinking about the time domain unit step response of ideal series LC crcuit. If both cap and inductor are ideal and unchrged initially and I am looking at voltage across capacitor.
Connecting a battery to LC circuit at t=t1 , would the circuit oscillate ?
I am not able to imagine this situation in terms of current and voltages of inductor /capacitor.I would be greatful if someone could intutively expain (without math and analogies) what exactly would happen.
My another question is, in case of underdamped response of RLC . I am again not able to think what causes the ringing behaviour with respect to inductor / capacitor current and voltage.
 
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If an ideal DC battery gets connected to ideal de-energized LC circuit, transient is an ideal sine current. Sinnce there's no damping, it will oscillate forever with amplitude I=V/√(L/C) and angular frequency ω=1/√(LC). Voltage on the capacitor will oscillate between 0 and 2V. The process is hard to explain without any math becouse this is the result obtained from solving differential equation.
 
A voltage step applied to an LC series pair will initially appear across the inductor. As current starts to build up through the inductor, (because VL = L * di/dt), the voltage across the capacitor will begin to ramp up. The inductor current will reach a maximum when the capacitor voltage reaches the step voltage, where the inductor voltage passes through zero. The capacitor voltage will overshoot and the cycle will reverse and repeat. The LC pair will ring at the resonant frequency, (at which XL + XC = zero), and because the circuit resistance is zero, it will continue ring forever.
 
zoki85 said:
If an ideal DC battery gets connected to ideal de-energized LC circuit, transient is an ideal sine current. Sinnce there's no damping, it will oscillate forever with amplitude I=V/√(L/C) and angular frequency ω=1/√(LC). Voltage on the capacitor will oscillate between 0 and 2V. The process is hard to explain without any math becouse this is the result obtained from solving differential equation.

Baluncore said:
A voltage step applied to an LC series pair will initially appear across the inductor. As current starts to build up through the inductor, (because VL = L * di/dt), the voltage across the capacitor will begin to ramp up. The inductor current will reach a maximum when the capacitor voltage reaches the step voltage, where the inductor voltage passes through zero. The capacitor voltage will overshoot and the cycle will reverse and repeat. The LC pair will ring at the resonant frequency, (at which XL + XC = zero), and because the circuit resistance is zero, it will continue ring forever.

Thanks Zoki85

Thanks Baluncore. I had also thought on the same lines. However , one question that was challenging my thought process was that when capacitor charges to step voltage then there should will not be any current flowing in inductor so there should not be any overshoot. Hence , I was confused . Let me know if you have any explanation.
 
k_rlc said:
I am not able to imagine this situation in terms of current and voltages of inductor /capacitor.I would be greatful if someone could intutively expain (without math and analogies) what exactly would happen.
Why do you insist on tying your hands behind your back?

When voltage appears across the capacitor it stores energy, simply EC = ½ C V2
When current flows through the inductor it stores energy, simply EL = ½ L I2

Conservation of energy requires that when the capacitor voltage is zero, the inductor current must be at a maximum. Likewise, when the inductor current is zero the capacitor voltage must be at a maximum.

Rather than considering a voltage step applied to an LC series pair, consider the parallel connection of an open circuit inductor with a charged capacitor. The energy flows from the capacitor to the inductor until the capacitor reaches zero voltage, when all the energy is stored in the inductor at maximum current. The energy then passes from the inductor to the capacitor until the capacitor voltage is the negative of it's starting voltage, when the inductor current has fallen again zero. At that point half a cycle has occurred. In effect the capacitor voltage has been reversed. It will reverse again to return the initial situation.
 
Thanks a lot baluncore for all the explanations
 

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