Can a Capacitor be fully charged?

[Ratchit]

steveB,

Would anyone but the Deity be able to tell if the capacitor plates were unbalanced by one electron? Would the metal plates be stable enough to hold that state? How can anyone answer that question? What practical use is the answer?

Ratch

 

[steveB]

In answering questions like this, we make a model, and then the solution, based on the model and the included assumptions gives us an answer. Once you are convinced that the model you are using is good enough, then the answer you get is the one you accept as fact. But, the real world is never exactly what your model is, so there will always be some doubt. Inclusion of quantum limited noise and discrete electron charge are going to be more meaningful than a noiseless, continuous charge solution in a question like this.

 

[Ratchit]

I just thought that i'm not really right. When cap is energized potential difference between cap's plate and voltage source decreases, so speed of last electrons decreases to, so they will move slower and slower infinitely? Or no? Even if charge is discrete, electric force acting last electrons can vary depending on distance from charge stored on cap's plate, so last electrons will slow down infinitely while moving to cap (or from it on other side, but let's forget about other plate)? Last electron will newer get to cap? If space-time or energy is discrete itself it will stop after some time, but i don't know if it is. However this small movement will became indistinguishable from thermal noise much earlier.

The unbalancing of charges on the plates of the capacitor will occur at a slower rate as the unbalance increases. I don't know what you mean by space-time. Nor do I know if energy itself is discrete. At those small amounts, it becomes a philosophical problem rather than a physics problem.

Ratch

 

[Ratchit]

In answering questions like this, we make a model, and then the solution, based on the model and the included assumptions gives us an answer. Once you are convinced that the model you are using is good enough, then the answer you get is the one you accept as fact. But, the real world is never exactly what your model is, so there will always be some doubt. Inclusion of quantum limited noise and discrete electron charge are going to be more meaningful than a noiseless, continuous charge solution in a question like this.

In the end, all you would have is a result that only the Deity could determine is correct.

Ratch

 

[steveB]

In the end, all you would have is a result that only the Deity could determine is correct.

Ratch

Same thing with the exponential solution. Only a Deity can wait an infinite amount of time or distinguish between the solutions. Likewise, you will object and object till the end of time. This is useless.

 

[MrAl]

Hello again,

Just to be clear, i am not 100 percent against saying that a capacitor that has its voltage increasing is 'energizing' the capacitor, but i am more in favor of keeping the older terminology where we say it is 'charging'. I'd say i am about 80 percent for 'charge' and 20 percent for 'energize'. Maybe we could take a vote to see others opinions too. But even better would be to explain them both.
In fact, we are forced to explain them both, we have no choice, just as we must do here.

There's nothing wrong with saying 'energize' but i reckon the situation with the cap as being similar to a memory element versus a transistor. Let me try to show the similarity. When we store a bit in a memory element, we have to energize one transistor and de-energize the other transistor (a simple flip flop). When we turn a single transistor on, we could say we energize the transistor. We call the change in the transistor 'energize' but we call the change in the memory element an operation we call 'store', as in storing a bit in that element. If we call them both 'energize', then we cant show the difference without resorting to what kind of element it is.
So in short we are doing two different things to two different kinds of elements and we come up with a term that better explains the change we have made to the external world.
So for the cap again, if we say 'charge' we know we energized it, but if we say 'energize' we cant be sure if we charged it or not. Maybe we raised both terminals up to the same voltage level and that did nothing to the internal state. When we say 'charge' we know we did something to the internal state.

On the topic of noise bothering the determination of any experiment, who cares about noise. If we have a circuit without noise we do it one way, with noise we do it another way. We just find a way to compensate for the noise in order to determine what it is we are after. For this we resort to statistical methods, and for this particular problem we might resort to a simple average. We look at the average in order to determine what is happening. True noise is random so it averages to zero.
Many hall effect devices have lots of noise mixed with the DC output level, but we still use them with a very high success rate.

Interesting question:
What do you think future electrical engineers 200 years from now will be calling the cap with increasing voltage?
1. Charge.
2. Energize.
3. Chargize.
4. Enercharge.
5. None of the above.

Another view is what we call it depends on what we want to observe about the process. For example, we might say we "Voltize" a capacitor if we are more concerned with the voltage across the capacitor than the behavior of the charge or energy.
It would be very hard to change the terminology anyway as so many people both newbies and professionals use the term "charge".

 

[Ratchit]

Same thing with the exponential solution. Only a Deity can wait an infinite amount of time or distinguish between the solutions. Likewise, you will object and object till the end of time. This is useless.

Yes, trying to define values for infinitesimals is not profitable endeavor.

Ratch

 

[Ratchit]

MrAl,

I don't think that comparing a switch which does not store energy with an analog storage element like a cap is relevant. It does not seem right to say energize a switch instead of "turn it on". You mentioned explaining what charging a capacitor means. So far, I don't think you have explained how unbalancing the charge on its plates means charging. As I said before, that describes how you do it, not what you are doing. I am not going to speculate on what the English will sound like 200 years from now. But, except for the lack of modern words, the U.S. Constitution is readable.

Ratch

 

[MrAl]

Hi again Ratch,

Well i was not comparing a switch to a capacitor, i was comparing a memory element to a capacitor, a memory element such as a bistable latch.
When we change the state of the latch we say we have stored a bit. We dont say we energized the latch because although we did do that too, it's not descriptive enough.
To me when we say we energized a capacitor that doesnt sound descriptive enough to me either. For one thing, if we had to set up an experiment where we had to have a pulse of current for a short time and decided to use a capacitor, we might 'energize' one lead of the cap only before we start, and therefore we have not charged it yet but we have energized it. We could even energize both leads and still not charge it. It's only when we change the physical position of some of the charge that we have done what we normally refer to as having charged it. We must move the charge and that requires energy yes, but so does every other action in the universe, so should we call everything we do that requires energy 'energizing' that thing?
I energized my computer so i could write this post.
I energized my car so i could go to the store today.
I energized my legs so i could walk down the stairs.
In other words, it seems more descriptive to say what the energy accomplished IN ONE WORD than having to state both the fact that we energized and also what the energizing did for us. We know from common experience that everything we do requires energy, so we drop the common term and go with the more descriptive and to the point. In other words, we leave 'energize' as an implication since it is so familiar.

Also, energy itself as we know it in more common experience is not polarized, so a negative voltage has the same energy as a positive voltage of the same amplitude when that energy is stored. For example, we start with a horizontally oriented capacitor charged left side to +0.5v and right side to -0.5v. The energy in the cap is C/2 Joules. We then force a current through the cap so that now the left side is -0.5v and the right side is +0.5v, the energy is still C/2 Joules. The energy is the same in both cases so what did we do to the cap, can we say we energized it? Before and after it had C/2 Joules. We might be able to say we reversed the charge, but we sure can not say we reversed the energy

 

[steveB]

Hi all,

i know practically a cap can be fully charged (to an accuracy we take as 100%) but as the voltage goes up in a cap the current drops equally so even when the cap is 99.9999999999% charged would the current would keep lowering so the cap would never actually reach full charge? or would it eventually reach its max?

Regards

So, let's look at it another way, using numbers. I think with numbers we can show how the exponential solution reins in the infinity question very nicely.
Let's take a series RC circuit with R=1 ohm and C=1 F. The time constant is 1 second, which is a fairly long time in terms of typical electrical circuits. Typically, we would say that after 5 seconds, the cap is fully charged for all practical purposes. However, your question requires waiting a little longer. How much longer? ... Let's calculate

If we consider applying a voltage of 1 V, then we expect 1 C of charge to end up on the capacitor eventually, and this is a sizable charge. Now, the electron charge is 1.6e-19 C, so let's calculate how long the exponential should take to get within 1e-20 C of 1 C. This is calculated as minus the logarithm base "e" of 1e-20 which equal 46 seconds.

Ok, think about an answer of 46 time constants which it takes to charge to an order of magnitude less than the charge of an electron. Now, what if we wait 100 time constants? We get something around 4e-44 C of charge which is more than 24 orders of magnitude below the electron charge magnitude. Can you even fathom what 24 orders of magnitude means?

Surely we dont have to wait till infinite time to say the capacitor is charged fully. Even in this extreme case, 46 seconds will do it, and 100 seconds will do it for even the most obstinate critic (Ratch likely excluded). It's more than a practical answer, it's a theoretical one too.

 

[Ratchit]

MrAl,

" We dont say we energized the latch because although we did do that too, it's not descriptive enough."

No, a latch is not energized. It is activated. No storage involved.

"...we might 'energize' one lead of the cap only before we start"

I don't understand what you mean by energizing only one lead of a capacitor.

" so should we call everything we do that requires energy 'energizing' that thing?"

" We must move the charge and that requires energy yes, but so does every other action in the universe, so should we call everything we do that requires energy 'energizing' that thing?
I energized my computer so i could write this post.
I energized my car so i could go to the store today.
I energized my legs so i could walk down the stairs.
"
You should not, unless it stores energy. Your computer, car, and legs do not store energy

" We could even energize both leads and still not charge it."

It would be a neat trick to energize both leads of a cap. So tell me, how you would do it. Store energy, that is. In other words, everything that involves energy does not mean energized. How did you come to that conclusion, or think I did? I said many times a cap was a energy storage device. That is why I call filling it with energy, energizing.

"We might be able to say we reversed the charge, but we sure can not say we reversed the energy "

That's right. The cap is energized either way.

Ratch

 

[steveB]

" As long as there is a conduction path, a wire does not have a charge distribution.

It will typically have a surface charge distribution. I attached a pdf which discusses this in a basic way.

As I mentioned above, this is completely irrelevant to this discussion, but since you seem to say something misleading, I just pass this information on for the benefit of others.

 

[nsaspook]

It will typically have a surface charge distribution. I attached a pdf which discusses this in a basic way.

As I mentioned above, this is completely irrelevant to this discussion, but since you seem to say something misleading, I just pass this information on for the benefit of others.

I've used that same pdf to explain electron conduction and EM energy transmission in DC circuits but as you say it's not really relevant to this discussion.

The origin of the word 'charge' in electricity is archaic.
https://www.etymonline.com/index.php?term=charge

"Meaning "fill with electricity" is from 1748"

Then you have to look at the scientific meaning of electricity.

"a fundamental entity of nature consisting of negative and positive kinds."

So 'electricity' in the strict scientific meaning of charge is not a form of energy.

https://books.google.com/books?id=h... use instead of charge in electricity&f=false

 

[Ratchit]

steveB,

So, let's look at it another way, using numbers. I think with numbers we can show how the exponential solution reins in the infinity question very nicely.
Let's take a series RC circuit with R=1 ohm and C=1 F. The time constant is 1 second, which is a fairly long time in terms of typical electrical circuits. Typically, we would say that after 5 seconds, the cap is fully charged for all practical purposes. However, your question requires waiting a little longer. How much longer? ... Let's calculate

If we consider applying a voltage of 1 V, then we expect 1 C of charge to end up on the capacitor eventually, and this is a sizable charge. Now, the electron charge is 1.6e-19 C, so let's calculate how long the exponential should take to get within 1e-20 C of 1 C. This is calculated as minus the logarithm base "e" of 1e-20 which equal 46 seconds.

Ok, think about an answer of 46 time constants which it takes to charge to an order of magnitude less than the charge of an electron. Now, what if we wait 100 time constants? We get something around 4e-44 C of charge which is more than 24 orders of magnitude below the electron charge magnitude. Can you even fathom what 24 orders of magnitude means?

Surely we dont have to wait till infinite time to say the capacitor is charged fully. Even in this extreme case, 46 seconds will do it, and 100 seconds will do it for even the most obstinate critic (Ratch likely excluded). It's more than a practical answer, it's a theoretical one too.

Well, let's see. How much voltage does a difference of one electron make? v = q/C = 1.6E-19/1.0 = 1.9E-19 volts below 1 volt. How long does it take to reach that voltage? e^x = 1.6E-19 ---> x = 43.2791 seconds. So what does that prove and where do we go from here?

Ratch

 

[Ratchit]

It will typically have a surface charge distribution. I attached a pdf which discusses this in a basic way.

As I mentioned above, this is completely irrelevant to this discussion, but since you seem to say something misleading, I just pass this information on for the benefit of others.

Thanks for the paper. It looks interesting. I should have qualified my statement to say that as long as the conductor is symmetrical, which a wire is, it should not matter too much what the charge distribution is.

Ratch

 

[steveB]

Thanks for the paper. It looks interesting. I should have qualified my statement to say that as long as the conductor is symmetrical, which a wire is, it should not matter too much what the charge distribution is.

Ratch

The conductor can be symmetrical and still have a charge distribution. Perhaps you mean symmetrical and straight, but real circuits must eventually curve to form a closed circuit, so there will always be a charge in reality.

Indeed, the charge is small and not something we typically need to think about. It was just a passing comment of interest.

 

[steveB]

steveB,



Well, let's see. How much voltage does a difference of one electron make? v = q/C = 1.6E-19/1.0 = 1.9E-19 volts below 1 volt. How long does it take to reach that voltage? e^x = 1.6E-19 ---> x = 43.2791 seconds. So what does that prove and where do we go from here?

Ratch

I'm not really sure what you are saying here.

Personally, I'm not trying to prove anything to you, but I am trying to give the OP insight into his question.

We dont need to go anywhere from here if the OP is satisfied with the various comments that have been made and his curiosity is sufficiently satiated.

 

[MrAl]

Hello there Steve,

I appreciated your view of the charge process where we take the quantum view and more or less count the electrons. For your example of 1v and 1 Farad we can put 6250000 trillion (6.25 million trillion or just 6.25 e+18) electrons into the cap. Since current is the flow of these electrons per unit time, and there will be some finite resistance in series with the cap, we might argue whether or not that last electron gets to go into the cap or ends up staying in the source, or perhaps how long it takes that last electron to travel to the cap, but that's about it i think. In fact, maybe we should look at that because when we take the quantum view for the charge itself we end up taking a quantum view of the voltage too, and at some point the voltage will be too low to force another electron through the resistance in a finite amount of time.
So i think your explanation best fit the case of the cap charging through a resistance from a voltage source and if it ever gets fully charged, and i think it would be interesting to look into it further too.

 

[steveB]

So i think your explanation best fit the case of the cap charging through a resistance from a voltage source and if it ever gets fully charged, and i think it would be interesting to look into it further too.

I think it is a reasonable way to look at it too, but keep in mind I was just reiterating what nyaknyan was saying.

I agree a proper model of it would be interesting. Of course the continuum model makes things very easy to derive and use and a proper discrete model might get unwieldy and harder to interpret. I haven't tried it though, so who knows.

 

[MrAl]

Hi again,

It looks like it takes longer and longer to get any electrons from the source to the cap through a resistor. Eventually the cap will be one electron short i guess, so that means the voltage differential will be about 1.6e-19 volts, and with a resistance of 1 ohm that means the current will be 1.6e-19 amps, so it will take 1 second for that last electron to get to the cap. If the resistance is 10 ohm though then it should take 10 seconds for that last electron to get to the cap, 100 ohms 100 seconds, etc.
I havent went through the entire calculation yet, which i believe can be represented by a series but may even be simpler than that.

LATER:
It looks like it simplifies to:
digamma(Ka+1)+Kb

which for this problem might simplify to:
ln(Ka)+Kb

where
Ka is equal to 6.25e18 and
Kb is the Euler-Mascheroni constant

which comes out to approximately:
43.2791131376+0.5772156649

which is approximately:
43.856 seconds.

That is the time to get all the electrons into the capacitor using a 1 ohm resistor. Note the only difference between this and the classic exponential solution is the addition of the Euler-Mascheroni constant. This extra constant comes in as a result of the simplified quantum nature rather than the continuous nature of the electron, which added about 1.3 percent more time here.

Also note that this like many other calculations like this has to rely on certain ideal behaviors of the parts involved.