When does the limit become quantized?

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Discussion Overview

The discussion revolves around the behavior of a charging capacitor, specifically questioning whether the final state of charge can be considered quantized as time approaches infinity. Participants explore the implications of charging dynamics, equilibrium states, and the definitions of quantization in this context.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions if the charging of a capacitor reaches a quantized state as time approaches infinity, suggesting that equilibrium may imply a form of quantization.
  • Another participant challenges the use of the term "quantized," stating that charge cannot be infinite and that the term has a specific meaning in physics.
  • A participant proposes that while the mathematical model indicates a capacitor never fully charges, the physical process suggests that electron migration eventually ceases, leading to a state of equilibrium.
  • It is argued that the equilibrium state can be explained using classical physics, where random thermal fluctuations dominate electron motion, rather than invoking quantum mechanics.
  • Some participants discuss the implications of different models, noting that using electromagnetic theory suggests the capacitor never fully charges, while statistical physics might indicate it eventually does.
  • Clarification is provided that the statement about capacitors not fully charging refers to the predictive nature of the mathematical model rather than an absolute physical limitation.

Areas of Agreement / Disagreement

Participants express differing views on the concept of quantization in relation to charging capacitors, with no consensus reached on whether the final state can be considered quantized. The discussion remains unresolved regarding the implications of different models on the charging process.

Contextual Notes

Participants highlight the limitations of the mathematical models used to describe capacitor behavior, including the dependence on definitions of charge and equilibrium, and the unresolved nature of how these models relate to physical reality.

Physics_Kid
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so a quick Q. the equation for charging a capacitor seems to indicate that charge (watts) will always be charging the capacitor, but is it true that as t⇒∞ the charging actually stops and the state of equilibrium is quantized?
 
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Could you possibly rephrase the question? A capacitor can't have an infinite amount of charge on it. Also, quantized has a specific meaning in physics, and I don't believe you're using it in that sense. Also, charge is not measured in watts.
 
if i know my volts and watts at any given t≥0 where at t=0 v=0 watts=0, then i know the charge at any given time.

my Q is that the RC circuit for charging never reaches 100% by the math, but we know at some point the electrons will stop migrating, thus no amps. isn't this final state quantized in some way?
 
Physics_Kid said:
but we know at some point the electrons will stop migrating, thus no amps. isn't this final state quantized in some way?

No, it can be explained in completely classical terms, no quantum mechanics needed.

When the potential difference becomes small compared to the energy in random thermal and environmental fluctuations, these fluctuations will start to dominate the motion of the electrons and they are as likely to push an electron away from the capacitor as towards it. The system reaches equilibrium when we get to the point where the number of electrons moving towards the capacitor at any given moment is statistically indistinguishable from the number moving away.

Plenty of other systems will display similar behavior: connect two vessels containg gases at different pressure so gas flows until the pressure equalizes, put two objects at different temperatures in contact with one another so heat flows until the temperature equalizes... In all of these cases equilibrium is a statistical phenomenon.
 
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ok, sounds right. so why do we say charging a cap never fully charges the cap? at some point the charging is done.
 
Physics_Kid said:
ok, sounds right. so why do we say charging a cap never fully charges the cap? at some point the charging is done.

Its the model you use. Using EM it never charges. Using some kind of model incorporating statistical physics it will eventually charge, but whether creating such a model is of any value is another matter.

Thanks
Bill
 
Physics_Kid said:
ok, sounds right. so why do we say charging a cap never fully charges the cap? at some point the charging is done.

If your teacher is not cutting corners in the explanation (which is a different problem), the statement is not "the capacitor never fully charges", it is "the equation that describes the behavior of the capacitor throughout its interesting operational range predicts that it never fully charges".
 
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