Electric Potential Across Capacitors

[Bashyboy]

Hello,

Suppose we have a battery, and there exists an electric potential difference between the positive and negative terminals, call it, V. When I attach a capacitor to the battery, will begin to charge, if it is initially uncharged. When the capacitor reaches its maximum charge, the phrase "the capacitor is at a same electric potential difference is used." What exactly does this mean? Does it mean that the plate of the capacitor that is connected to the negative terminal has the same amount of electrons on it as the negative terminal?

 

[mfb]

The potential energy of electrons is the same.

"Amount of electrons" is not a useful/interesting quantity in electronics.

 

[Bashyboy]

@mfb, I am not quite sure what your point is. I merely want to know what it means for the capacitor to be at the same electric potential as the battery. Does it mean that the capacitor has the same charge that the battery terminal has?

 

[mfb]

No, it does not. As I said, this is not an interesting quantity, it will just lead to misconceptions.

You can compare an electric potential (energy per charge) to the gravitational potential: Battery and capacitor would correspond to the same height difference (energy per mass).

 

[Bashyboy]

Well, doesn't electric potential depend on capacitance and the amount of charge? Wouldn't the negative terminal and the plate connected to the negative terminal have to possesses the same charge, assuming that their individual capacitances don't change?

 

[mfb]

Well, doesn't electric potential depend on capacitance and the amount of charge?

In capacitors, the amount of charge which flowed through the capacitor and the electric potential difference there have a fixed relation, right.
The battery is not a capacitor, and each capacitor has its own, different relation.

 

[DrZoidberg]

Well, doesn't electric potential depend on capacitance and the amount of charge?

Yes, exactly. V = Q/C
So if you connect a parallel plate capacitor to a battery and than change the distance of the plates, you are changing the capacity and therefore the amount of charge on the plates will change while the voltage stays constant.

 

[sophiecentaur]

@mfb, I am not quite sure what your point is. I merely want to know what it means for the capacitor to be at the same electric potential as the battery. Does it mean that the capacitor has the same charge that the battery terminal has?

I think his point was that 'numbers of electrons', by which I suppose you imply 'charge, is nothing to do with the Potential Difference across the battery terminals. If you look carefully at the actual definitions of the quantities that are involved here, the answer to your original question will become obvious.

 

[Emilyjoint]

Mfb: I think it is misleading to refer to charge that "flows through" a capacitor

 

[mfb]

Mfb: I think it is misleading to refer to charge that "flows through" a capacitor

For every amount of charge entering at one side, the same charge is leaving the capacitor at the other side (within the usual approximations of electric circuits).

 

[Emilyjoint]

The charge from one plate passes to the other plate through the external connection, not through the capacitor.
Small, but important detail

 

[sophiecentaur]

The charge from one plate passes to the other plate through the external connection, not through the capacitor.
Small, but important detail

'Sort of' correct but you have to allow current to flow in the analysis of AC circuits because Capacitors have an Impedance, defined by V/I. A (measurable) current will flow into one terminal and out of the other. By measurable, I mean that the direction of the current is appropriately described as being 'through' the capacitor due to the signs of V and I..

 

[mfb]

The charge from one plate passes to the other plate through the external connection, not through the capacitor.
Small, but important detail

In the circuit analysis, it is a circular current, flowing through the whole circular circuit (:D).
There are no electrons flying through the gap, but that does not matter.

 

[Emilyjoint]

"There are no electrons flying through the gap"...Absolutely correct.
It does matter ! explanations in these forums is supposed to comply with standard physics textbooks. For students wanting to pass exams it is essential to realize what physics is going on.
Correct terminology is part of the skills of being a physicist ("sort of") even in AC circuits.

 

[mfb]

I did not make a statistical analysis, but I would expect "current flowing through a capacitor" to be quite common in those books.

 

[sophiecentaur]

This is developing into one of those 'what is really happening?' discussions. The actual mechanism by which there is a measurable current flow 'through' a capacitor is not particularly relevant. Charge can flow in one end and charge can flow out of the other end, of course, and this is referred to as polarisation. It won't carry on for ever but this is not relevant, surely; a short term flow of current is still a flow. The true DC situation is an exception that never, theoretically, exists - as all experiments are limited in time.

The charge from one plate passes to the other plate through the external connection, not through the capacitor.

This statement gives me a problem. How would it relate to the situation of two capacitors in series? Where would an 'external connection' for one capacitor if it were not via the other capacitor?

 

[Emilyjoint]

Here is my understanding of 2 capacitors in series: 4 parallel plates numbered 1,2, 3, 4 from top to bottom.
The top capacitor is plates 1&2, the bottom capacitor is plates 3&4.
A battery (EXTERNAL supply) is connected to plates 1 and 4.
To construct a series circuit plates 2 & 3 are connected by a wire.
The only flow of charge through the battery is from plate 1 to plate 4 (or vice versa) I would say this is the external circuit.
Charge is transferred from plate 2 to plate 3 (or vice versa). I would say this is the 'internal' circuit.
NO CHARGE passes from plate 1 to plate 2 or from plate 3 to plate 4 across the gaps between these plates.
An ammeter placed in any of the wires will register a pulse of current, current flows IN the circuit but no charge passes across the gaps between the plates.
I don't think there is anything wrong with the physics of this explanation !

 

[sophiecentaur]

You seem to be implying that each electron has its own identity and it needs to make a journey through the dielectric before you will admit to a current flowing. This is why we don't talk about charges in terms of electrons. If you stick a microCoulomb of charge into one terminal of a box with the label 'Unknown' on it and a microCoulomb of charge leaves the other terminal than the convention is that one microCoulomb of charge has flowed. Whether the current has flowed in the form of mobile charges or by the atoms of the dielectric having polarised - or even by the imbalanced charges on the two plates with a vacuum between, it has still flowed.
How could you have a special form of current or charge for going into and out of a Capacitor that is somehow different from the sort of current that flows through a resistor or a piece of wire?
I think you must be still thinking in terms of electrons actually moving at a significant rate inside conductors instead of the general concept of 'Current'.
Do you not subscribe to Kirchoff's First Law? How can you reconcile what you say with K1?

Your choice of which is the 'internal' and which is the 'external' circuit is a bit arbitrary. What if both wires are the same length?

 

[Emilyjoint]

I did not mention electrons so there can be no implications about the identity of electrons!
I refer only to 'charge'.
By definition (?) a dielectric is an insulator so I would not imply that charge can pass 'through' a dielectric.
I am also aware of the common misconception held by some students that electrons have a significant speed... I know that they do not. I made no reference to the speed of charge carriers.
I used the word 'internal' within quotes to emphasise that it was a term that I was using...not necessarily an accepted term. It refers to the wire between plates 2 and3 in my description of 2 parallel plates in series.

 

[sophiecentaur]

I did not mention electrons so there can be no implications about the identity of electrons!
I refer only to 'charge'.
By definition (?) a dielectric is an insulator so I would not imply that charge can pass 'through' a dielectric.
I am also aware of the common misconception held by some students that electrons have a significant speed... I know that they do not. I made no reference to the speed of charge carriers.
I used the word 'internal' within quotes to emphasise that it was a term that I was using...not necessarily an accepted term. It refers to the wire between plates 2 and3 in my description of 2 parallel plates in series.

Why? If you insist on some sort of difference between current in different components in a circuit then how are you going to analyse it? Can you justify your approach in as far as it seems to contravene the very useful Kirchoff's Laws?

So why do charges have to pass "through" a dielectric"?

You seem to be falling into the trap of asking the "what is really happening" question yet still talking 'electronics'. Whilst there is a 'current flowing' through the dielectric in a capacitor, charges are actually being displaced in there. How is that any different from charges moving 'through' a resistor - except that it only happens until the molecular restoring forces equal the the force due to the field between plates? When AC is concerned, the physical displacement of charges can easily be the same distance in both cases.

 

[Emilyjoint]

In post 6 mfb used a phrase...charge flowing through the capacitor.
In post 9 I suggested that use of the word 'through' could be 'misleading' because it implies that charge passes across the gap between the plates.
In post 13 mfb stated that 'no electrons fly across the gap between plates'
That is all there is to it.
Nowhere will you find a description of the charging and discharging behaviour of capacitors that requires charge to cross the gap.
To suggest that there is essentially no difference between current in resistors and current in capacitor circuits is 'misleading'.
None of this is in contradiction of Kirchoffs laws, K1 is a statement regarding conservation of charge.
AC does not flow in capacitor circuits BECAUSE they have impedance (I think you mean reactance). Reactance is a quantity calculated from the voltage across a capacitor and the current in the circuit. It is special because, under normal measurement techniques, no account is taken of the phase difference between the AC current waveform and the AC voltage waveform.
We need to know what is really happening to fully understand.

 

[sophiecentaur]

I know exactly what you are getting at and I appreciate that the dielectric is an 'insulator' because its resistivity is very high. If you connect a capacitor to a DC source, then, of course, the current will soon go to zero (once the capacitor is charged) because the internal fields will balance the applied PD.
We aren't talking about the nuts and bolts of what goes on inside the package of a component. That is not really relevant. What I refer to is what happens as far as the measurer is concerned. If you apply AC to a capacitor and measure the current by looking at the volts across a series resistor, for instance. You will see that there is a current - in just the same way as if you put a resistor or an inductor in its place. You seem to be implying that a capacitor must be treated as being fundamentally different from other components. That's crazy. We use current and volts as the appropriate quantities to measure because the sums are suitable for calculating the behaviour of all combinations of RL and C.
You insist that you want to know what's really going on. Have you no comments about my point that the amount of charge movement with AC inside a dielectric can be the same or even more than the charge movement inside a resistor. If you define current as movement of charge, how can you say one is 'different' from the other - except by sticking to a very elementary appreciation of the situation. It might help if you were to describe exactly what you 'mean' when you use the word 'current' if it's not movement of charges.
Also, where does the 'displacement current', for EM waves in a vacuum (where there are no actual charges), fit in with your view?
PS 'Reactance' is a part of 'Impedance' so either word fits and real capacitors have finite resistance - either series or parallel, depending how you like it.

 

[Emilyjoint]

Posts6,9and13 have cleared up the main issue.
Your last comment is very revealing! If you are putting forward that there is no real difference between Reactance and Impedance then it explains most of your ramblings.
You do not fully understand the meanings of terms used to describe physical processes.
You are plane wrong and should check your textbooks.

 

[sophiecentaur]

Z=R+jX
I believe.

Now tell me about displacement current in a vacuum.

 

[Emilyjoint]

This thread has run its course for me.
Can I offer Z = R + j(Xl ~Xc) for completeness where the textbook definition of the terms is
Z = impedance
R = resistance
Xl = inductive reactance
Xc = capacitative reactance

I will browse for other areas of physics that interest me now

 

[sophiecentaur]

So, no comment on displacement current?
You might consider the implications when you're in the mood.