When does the limit become quantized?

[Physics_Kid]

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?

 

[axmls]

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.

 

[Physics_Kid]

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?

 

[Nugatory]

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.

 

[Physics_Kid]

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

 

[bhobba]

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

 

[Nugatory]

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".