The capacitor in its conventional form is constructed from two electrically conducting metallic plates facing each other and separated by an electrically insulating medium.

Applying DC voltage on the capacitor no conduction current flows through the capacitor if its insulating medium is perfect insulator. This is because ther are no free charge carriers in such medium. Practically the real insulator contains very few charge carriers and therefore a very small leakage current passes in the capacitor depending on the conductivity of the insulator. The ideal insulating medium is the vacuum as noted by Prof. Shmaliy above.

On the other side ,If a time varying voltage is applied on the capacitor, a displacement current passes through the capacitor irrespective of the insulating medium. This current is termed also the capacitive current. It flows because of changing electric displacement D with time. The displacement current density is = The rate of change of the displacement with time. The electric displacement itself D= epsilon *E where epsilon is the dielectric constant and E is the electric field intensity. So if the applied voltage varies with time the E will be also time varying and also D and displacement capacitive current will be existing.

I hope that i shed some light on current in the capacitors.

Thank you.

An ideal capacitor is supposed to have two plates in vacuum. There is zero conductivity in vacuum and DC thus cannot flow. In real world, there is some conductivity, so... The phase shift for AC is 90 in vacuum and it is lower than 90 due to the conductivity.

AC practically does flow from a capacitor, while most of the DC if not 100% is blocked through a cap..

For my opinion, at first a common understanding is necessary regarding the fundamental question: What is the thing called "current" ?

The capacitor in its conventional form is constructed from two electrically conducting metallic plates facing each other and separated by an electrically insulating medium.

Applying DC voltage on the capacitor no conduction current flows through the capacitor if its insulating medium is perfect insulator. This is because ther are no free charge carriers in such medium. Practically the real insulator contains very few charge carriers and therefore a very small leakage current passes in the capacitor depending on the conductivity of the insulator. The ideal insulating medium is the vacuum as noted by Prof. Shmaliy above.

On the other side ,If a time varying voltage is applied on the capacitor, a displacement current passes through the capacitor irrespective of the insulating medium. This current is termed also the capacitive current. It flows because of changing electric displacement D with time. The displacement current density is = The rate of change of the displacement with time. The electric displacement itself D= epsilon *E where epsilon is the dielectric constant and E is the electric field intensity. So if the applied voltage varies with time the E will be also time varying and also D and displacement capacitive current will be existing.

I hope that i shed some light on current in the capacitors.

Thank you.

Thank you for this contribution.

Yes - "displacement current" is the key word to understand the effect.

Thank you Professor Wangenheim for your comment,

prof Wangenheim thank you for asking such a basic question and prof Abdelhalim Zekry thanks a lot for explaining in detail thanks am feeling very lucky to register in this forum to get to know the basic and queries in detail

In the case of D.C. only charging transient current can flow through the capacitor till the voltage across the capacitor is equal to the charging voltage and afterwards no current can flow through it as the two voltages are equal and opposite. D.C current cannot flow through the capacitor under steady state.

That is why we call the coupling capacitor in amplifiers as Blocking capacitor as it blocks D.C. and allows only A.C signal to pass through it.

Also this the reason why we ask students to be careful in handling capacitors particularly if it is an Electrolytic capacitors to avoid shock if its terminals are touched as it retains the voltage even after switching off till it is discharged fully.

Only A.c can flow through it and that is also Displacement current.To prove that the current flowing through is only Displacement Current is a popular question in Field theory., as already explained by Prof.Lutz. andProf. Abdelhalim Zekry.

Leakage current of nano amps can flow through a capacitor due to lossy dielectric..

The equivalent circuit of a capacitor is a Pure Capacitor in parallel with a very high Resistance of tens or hundreds of Mega ohms.

Dr.P.S.

Sorry,The up voting is not fair!

You probably guess that I have added the DC current speculation to make the so "simple" question more intriguing:) Everybody knows that the AC current flows "through" the capacitor but only few people will muster courage to state that the DC current can flow as well. For the present, I guess at least four arrangements where it is possible:

1. If a perfect (ideal) constant current source drives (charges) a capacitor with finite capacitance, the voltage drop across the capacitor will continuously increase. But the current source will continuously increase with the same rate its internal excitation voltage; so, a constant DC current will continuously flow "through" the capacitor.

2. If an imperfect constant current source charges the capacitor with infinite capacitance, the voltage drop across the capacitor will stay constantly zero and the constant DC current will continuously flow "through" the capacitor. This "zero" can be implemented as a "virtual zero" (virtual ground) by an ideal inverting op-amp whose output voltage can increase up to infinity.

3. Of course, if an ideal current source charges the capacitor with infinite capacitance, the result will be even more perfect than above.

4. And finally, if an imperfect constant current source charges the capacitor with finite capacitance but during a limited time, some (really, decreasing but still current) DC current will flow through the capacitor (the Pisupati's explanation above). Here I exploit the fact that we have not yet specified what "current" means (Lutz) and I assume that "current" means "some current flowing during some time":)

Once explained how the DC current "flows" through a capacitor, there is nothing easier than explaining how the AC current "flows" through the capacitor. Abdelhalim has done it above in terms of electricity ("displacement current"); I will explain it here in a more general nonelectrical way. The benefit of this approach is that we can explain the phenomenon to nonspecialists (for example, I will try to explain it to my 7-year-old grandson:-)

So, this paradoxical electrical phenomenon (current flowing through an insulator) has analogical odd worldly situations where some flow like substance (water, people, cars, etc.) apparently "flows" or "passes" through... a wall?!? IMO this is a kind of a transportation problem or a data processing task in computer science... or just a circus trick that are based on storing elements.

If the flow is continuously entering a storing element, we have the feeling that the substance disappears (a "disappearing trick"). Conversely, if the flow is continuously leaving a storing element, the feeling is the substance appears (an "appearing trick"). Finally, if we attach two storing elements (the full and the empty one) back to back and then the flow begins leaving the full storing element and entering the empty one, we make an impression of passing flow ("passing-through-a-wall trick").

Here is a water example. Attach two tubular vessels back to back vertically (the upper is empty and the lower is full of water). Begin filling the upper vessel with water and emptying the lower vessel. This makes an impression of passing through a pipe water. We do not suspect of existing a "wall" standing in a flow's way; we consider the two coupled vessels as a common "pipe".

Another impressive trick - people passing through a wall. Imagine two rooms separated by a wall having doors on the opposite sides. The one room is full of people; the other is empty. Now ask the people to begin circulating between the two rooms and they will give an impression of "passing-through-a-wall people".

In a similar way, we can make cars (and whatever, including the electrical current) pass through a wall (insulator)...

More about the explaining electrical circuits by non-electrical means:

https://www.researchgate.net/post/What_does_to_understand_a_circuit_mean

Have a fun, Cyril.

Before answering this particular question, one fundamental question must be answered: what is the carrier of an electric current? I believe that most people will say electrons. Actually it is not. Consider that we have a conductor and apply a voltage across it, then a current will immediately respond. However, physicists have already measured the speed of an electron mobility inside the metal crystal lattice, and the result is surprisingly slow, about a fraction of centimeter/second. In other words, if you call your friend via a telephone line in the same city, he/she will hear your voice in at least a couple of days if the carrier of current is electrons. In fact, the real carrier is electromagnetic field that can transmit at near the light speed, instead of a physical particle: electron movement. At this time, you may argue with me that if the current carrier is really an electromagnetic field flow, then it can be transmitted wireless, why today we still need a copper wire to transport the current flow? As you all know, electromagnetic field is omnidirectional to transmit, like the Sun radiation, which cannot be controlled to let it go through and concentrate in a small narrow channel in order to deliver the majority of energy to the receiver. However, EM field can travel along the surface of a conductor and this is the main reason why we need a conducting wire to concentrate the EM energy in a narrow direction. If you agree with my explanation, then to answer this particular question becomes straightforward. In addition, if some genius in the future would invent a wireless way to concentrate the EM field, instead of relying on the skin-effect of conductor, then the electric power would be able to deliver wireless, like your cell phone. Although such a technology may have already been tried, such as an RFID, the recent status of wireless power transmission is very limited to delivering only a small amount of electric energy. Nevertheless, we should all be optimistic to see it will happen in years to come.

Based on the principle of duality lets look at this another analogous way.

Does current flow through a transformer?

Interesting... maybe two mechanically coupled pumps serve as a good analogy?

Yes as the primary and secondary are linked or coupled through the internal flux or magnetic field of the transformer core material. Thus in a transformer we are exploiting the very high internal flux density which is an inherent properties of the material.

In the same way are we not exploiting same in a capacitor except that now we exploit the very high internal electric flux density which is an inherent property of the material. This flux density is the equivalent of the Displacement Current.

Some materials have inherent sources of flux density within their atomic structure which allows us to exploit them for use in electrical circuits but the internal works are at atomic level either due to electron spin or free space charge and both work on the principle of induction. Thus polarization and magnetization are very similar except one applies to magnetic field and the other to electric fields.

in my self opinion, i dont think current flow through a capacitor either for DC or AC.

DC current cant go through it because there is no any channel for the electron to go through it.

AC current in my humble opinion(no scientific explanation) doesnt flowing through the capacitor, but when a + voltage at its terminal so the charge will then flocking together in both terminal but they wont flow through however when a - voltage is applied at its terminal the negative voltage will soon attract the flocked charges from the previous cycle, and the phenomenon continues as in flowing AC current.

I agree with you that actually the AC current does not flow through the capacitor; it is just an illusion...

My take on this question is as follows. First let us assume we are talking about a perfect capacitor, so we ignore leakage and breakdown.

The simple answer that charges do not flow through the capacitor in any circumstance!

Does current flow through? If charges don't flow through, then in a strict sense current doesn't flow through in AC or DC.

However, the reason why in a wider sense AC current is going "through" the capacitor, can be explained with a mechanical analogy. Take the example of a stretched rope and we send a wave from one end of the rope to the other. We actually see the wave moving along the rope. However, on a microscopic scale, rope atoms are only moving up and down...they are not moving in the direction of propagation! So in a sense the moving wave on the rope you see is a fiction, but in another sense it is also real because there is an actual energy transfer.

We can make a similar statement about the capacitor. The AC current "through" it is a fiction, but it is also as real as the wave along the rope in the sense that there is a real exchange of energy represented by the flow.

Cyril - are you sure?

What is current? Is it necessary that electrons can move through the capacitor?

No - it isn`t. Current is movement of charges. And changes of the charge distribution on one side of the capacitor influence the charge distribution on the opposite side.

That effect is called displacement current.

In summary - the electric phenomenon we call "current" is assumed to "flow" even through a capacitor. I think, in this context we should realize that "current" is an artificial product of the human brain with the aim to handle/calculate all the effects to be observed in an electrical circuit.

Derek and Lutz, as a result of all these sophisticated explanations, I have the feeling that I knew if the current flowed through a capacitor... but now I am not already sure-:)

Derek - I think your mechanical example is a very good one because "current" is nothing else than a movement of an "effect" rather than a movement of parts or something else. And the field within the capacitor allows such a transfer of an effect.

Cyril, Lutz, Derek,

I understand that induced currents due to very high charge density will flow within a capacitor but not pass through it. Much like a transformer with high internal flux density. Only certain materials with the relevant properties allow this.

OK - in this case, there will be no current through a series connection of a resistor and a capacitor if connected to an ac source right? (Or not?).

Correction there will be current passing through the circuit and through the resistor but not through but induced within the capacitor and being connected to either an AC or DC source matters very little. Recall resistors represent heat generated in a material. As Cyril has said elsewhere is creates the illusion of current flowing through the capacitor just as in the current flowing through a transformer. I fail to see what the big fuss is as this is a an inherent material property.

Current does not flow through a capacitor but voltage is stored in a capacitor and consequently store electrical energy across it's plates wherein these plates are separated in between (sandwhiched) by a dielectric material or insulator. By itself it can not store energy unless there's some electric field connected across it's plate however in fact if a dc electromotive force (emf) is applied across it's positive and negative plate, respectively, this outside source forces electrons to collect on the other plate making it positive whereas on the other plate electrons are collected on it making it with excess electrons. Mathematically, the amount of voltage developed across the capacitor's plates is equal to delta change of electron charges per unit of time multiplied by the amount of capacitance of the capacitor and once these charges are separated and collected on the plates potential difference exist and hence voltage in the order of 1v to 1000v or more equal to the applied input voltages. What is amazing is that even if the outside source of input voltage is removed, this output voltage (hence stored electricity) is still exist across the capacitor, provided it is kept open circuited. Now these separated charges (+ & -) can not pass through the dielectric of the capacitor, hence the answer to the question is not all. But if the terminals of the plates are shorted then current will flow and discharge with a loud bang at the point of short circuit or when a load such as resistor is connected across it, then this stored electricity is put to use to flow as current to light a bulb, run a motor, etc. However more, if an ac input voltage is then applied instead, the same principle applies and electrical energy is also stored across the capacitor and potential difference is developed across the plates as before but with alternating polarities. The same is true, current does not pass through but only alternately change polarities with the frequency of the applied ac voltage source.

Hello Mr. Sanbuenaventura,

Unfortunately, only your last sentence speaks about the current in case of ac.

However, I do not completely understand the meaning and the contents of this sentence ("...does not pass..., but change polarities..).

Does it flow - yes or not?

In this context - I like to repeat my position:

* The quantity we call "current" is - more or less - an artificial product (invented with the aim to explain some observed effects). It is a very useful "tool" for calculating voltage distribution within a network.

* However, this "current" does not consist of parts that move - rather it is only a "movement" of an "effect" (transport of charges).

* Now, because a change of the charge distribution on one side of the capacitor influences the charge distribution on (is transferred to) the other side, we have no other chance than to say: This artificial product called "current" goes through the capacitor.

* This is true for the current caused by a dc voltage step as well as the ac current.

* This is the basis for all our calculations (Kirchhoff`s voltage and current laws). Otherwise, we cannot continue to use the basic rule that a "current" does flow within a closed R-C loop - thereby treating the capacitive ac resistance 1/wC in the same way as the ohmic resistance.

Med venligg hilsen !, Good day to you Mr.Lutz!

I stand with my understanding on the capacitor and the principle behind it's function. Current is a flow of charge passing through the conductor (opposed by it's resistance) connecting both the plates of the capacitor and applied with the EMF SOURCE across it. As I have said the electrical charges are separated (work is required to separate these charges) by the application of DC-input EMF across the capacitor and once separated these electrical charges are stored on the plates of the capacitor and then a build-up of potential difference exist and there creates electric field lines of force brought about by these separated (+ & - ) charges on each plate of the capacitor. These charges CAN NOT PASS through the capacitor (thereby short circuiting itself) as both are sandwhiched by dielectric material (i.e. paper, ceramic, mica, oil, wood, graphene, air, etc...) between them as these materials have very high resistance. However, with the passage of time, the stored electrical charges across the capacitor dissapear rather slowly and somehow drifts and dissipated away neutralizing itself according to it's Time Constant equal to RC and the same is true when the AC-input voltage is applied across the capacitor, that work is also required to separate these charges between the plates, but it looks like a displacement current flows back and forth during it's charging and discharging phase, as the iput voltage continues to change polarities proportionate to the frequency of the applied AC-input voltage. As I have said earlier, current is a quantity of matter as it is in fact electron charges flowing or drifting per second (1 Ampere = 1 Coulomb per sec.) at lower than speed of light and it is not a ghost or whimper or some kind of effect, as you claim. It is this flow of charges (for example) that passes through inside a body that is electrocuted by the sadden or accidental application of high POTENTIAL DIFFERENCE (EMF) whether DC or AC in nature on this conductive body tissue and which burns it and causes death or appyxation to the person or animal or any living things. The KIRCHHOFF's VOLTAGE LAW applies as it's the V.D. across the devices such as resistor, inductor and capacitor in a closed loop in series and shunted across with an input potential voltage source whose sum total is zero around the closed loop as per this law. It's law for the current also applies since the electrical charges do not stay within a junction but move out from it and goes out and the sum total of all these currents flow is also zero. QED, the issue case ends here.

Hello again, Mr. Sanbuenaventura,

thank you for your answer. In fact, I agree with all of your explanations.

I think, the only difference between us is - more or less - only of philosophical nature.

The keyword is : Displacement current.

For my opinion, the name of this "current" was introduced only with the aim to allow a "flowing current" within a closed loop containing a capacitor.

For my understanding that means the following (based on the common convention using term "current"):

In a closed R-C-loop a charge flow (current) can be observed through the resistor (ac case). This current changes its nature while going through the capacitor (changed into a displacement current). However, it can be observed at the other node of the driving voltage.

Thus, it is logical to say: It flows through the whole loop (and therefore, also through the capacitor).

The remaining question is: What is the physical nature of the moving charges?

Are they particles? I don`t think so - as mentioned earlier: I think it is just a kind of "effect" (or property of parts) that is moving. And such a "property" can be moved across the field inside the capacitor. That`s my philosophy.

Dear Lutz,

The fact that neither a capacitor or transformer has any current flowing through it has no effect or impact on KVL or KCL. The material properties allow it to mimic any applied field.

If one puts two magnets separated by glass moving one will cause the other to move. Work is being done by the magnetic fields. There is no violation of any laws.

What is interesting though is that as both magnetic and dielectric materials exhibit hysteresis one might expect at a microscopic level or at higher frequencies there should be some observable delay or lag and which is certainly evident in transformers.

You are correct that displacement current was a mathematic tool for the purposes of continuity, but which does not mean it represents the actual physical process rather that it models it.

Oh yes - the magnetic example is a very good one.

Similar to the magnetic field that provides a kind of "connection" between both polarities, the electric field between the capacitor plates provides also a connection between both sides - allowing transport of the mentioned "effect" (change of charge) through the device (influence effect).

GENTLEMEN, GREETINGS AGAIN TO YOU AND US ALL !

This topic about capacitor is great indeed and is productive and educating as knowledge transcends all ages, races, opinions and sex and / or religion. Exchanges of knowledges and opinions are helpful but with caution, though. Conclusion, if applied correctly and based on real facts and observations and in industry practices as well , can be a guiding rule for all to avoid error and safety concern should also be applied. One physical example of capacitor charging and discharging is in fact can be seen from nature, itself. And that is the Lightning phenomenon, whose fury and intensity is real and destructive and amazing. Many enthusiasts, observers, engineers and scientists pondered about this natural phenomenon on how to harness this wayward release of pure energy to the dismay of many. However, it's in fact the nature's manifestation of the wonderous capacitance effect and/or capacitor on how electrical energy is stored and saddenly released, violently and dangerously. GOOD DAY !

POST NOTE:

Further more, going back to the topic of Lightning phenomenon, in contrast to the man made capacitor, these medium or media such as the clouds and the earth which act as two (2) plates of the Capacitor and from which Lightning phenomenon comes fort, is in real sense happening naturally when the built-up of a million voltage and over (EMF) between these clouds and the earth which in fact is separated by air (i.e. this is the Di-electric medium in between) is so great that breakdown occurs, so this lightning strike in fact is what we call now as the electric current or flow of electric charges passing through the medium or in effect as the current in a capacitor passing through it's medium as Lightning phenomenon is now manifested by nature. That's answer to the question, with the help of nature.

It seems the displacement current is another kind of current connecting, like a bridge, the "gap" between the capacitor plates. Thus the movement is unviolated - an ordinary "electron current" flows along the outer loop while an odd "electric field current" as though "flows" between the plates. The displacement "current" serves as an intermediate bus connecting two train stations...

Break down current as in the caseof Lightning or Break down of a capacitor is Conduction Current due to short Circuiting and is different from Displacement current with Dielectric being intact.

P.S.

Quote Cyril: "...an ordinary "electron current" flows along the outer loop while an odd "electric field current" as though "flows" between the plates. The displacement "current" serves as an intermediate bus connecting two train stations..."

Cyril - yes, you have found a nice wording, which I agree upon.

(Perhaps it is appropriate to replace the term "electron current" by "charge flow")

Capacitor can be explained by the eddy currents.

Let's make an imaginary experiment: Imagine a capacitor, where the two plates are far enough from each other, so that in the space between you can apply a current clamp. Now, apply an ac voltage to the capacitor. Will the current clamp indicate a current? What will happen if instead we apply a dc current? (neglecting the transients). In my opinion, in the first case the current clamp should indicate a current, but not in the second case. This does not mean that any charges are "flying" through empty space. But, one can say that there appears to exist a current (in the ac case) between the plates. This is not a conventional current, but rather a "displacement current." Still, it is a current, because it produces all of the expected effects of a conventional current.

Plate capacitor is a galvanic gap for direct current. Think of it as two plates are connected to an AC power source with two single-ended lines. Hence in the plates of the capacitor having closed alternating eddy currents.

The process in my opinion is this. In the first plate of the capacitor formed by the first eddy current. It creates its own magnetic field. It goes to the second plate of the capacitor and there is a secondary eddy current.

These eddy currents can be detected experimentally.

@ Valery Frisk: Can you backup your opinion on eddy currents by a bibliographical link? For eddy currents to occur, a change in magnetic flux density in required (dφ/dt). Therefore an ac current is neccessary! But this would be like saying a priori that there is an ac current=>eddy currents=>a current flows through the capacitor. This prerequires the assumption that there will be a current in order to prove that there will be a current! This troubles me, unless I missunderstood somethink.

All tested experimentally. Go to my page there is an article:

Researches of electric processes in a single-wire line and in the flat condenser.

You are right, of course, this is exactly what happens, but, still: In the space between the plates a magnetic field is induced as well. This can only be explained by assigning a "virtual current," which is called displacement current.

@Frisk: Nice work, I hope you will make a more elaborate paper of this. What would happen, according to your eddy current approach, if the wires to the capacitor were of Infinitesimal diameter?

Eddy currents in the plates of the parallel plate capacitor can be proved by the classic experience of Valtenhofena. The diameter of the wires does not matter.

But in the Waltenhofen pendulum there is no capacitor! Only a metal plate swinging through a magnetostatic field!

Eddy currents, in my opinion, are formed in the plates of the capacitor.

I have done the following experience: 1. Measured alternating current I1 flowing through this capacitor. Experience 2. Sliced the capacitor plates, as in the experiment with the pendulum. Measured by passing an alternating current through this capacitor I2. The area of the capacitor plates have not changed, but the current I2 dropped significantly. Condenser stopped working.

Oh! This is a very interesting experimental result! And rather unexpected indeed!

All these "electrical" speculations about the nature of the capacitor are very interesting for professionals in the fields of physics and electricity. But I would like to return to my idea above to find more general non-electrical explanations of this phenomenon suitable for ordinary human beings... So, what is a capacitor? How does an AC current "flow" through it?

More generally speaking, the capacitor is a storing element... a kind of a reservoir... a container... But it is not a single container or even a simple combination of two equal containers. It is a system of two coupled interacting containers; it is a DIFFERENTIAL CONTAINER. The respective hydraulic analogies can be the single vessel and the communication vessels (or the more correct Bill Beaty's "water capacitor" in the attached picture below). The difference between this "differential pair of plates" and the simple combination of two distant plates (spheres) is similar to the difference between the differential transistor pair (two combined common-emitter stages with a common emitter resistor) and the simple pair of two separate common-emitter stages. In the differential pair, each of the stages influences the other stage while, in the separated pair, each stage operates independently...

Here is a link to the impressive Bill Beaty's story about the capacitor:

http://amasci.com/emotor/cap1.html

Now let's return to the main question, "Does the current flow through the capacitor?" It is interesting that I have managed to explain this phenomenon above (how the AC current "flows" through the capacitor) for the case of a "non-differential container" (two separate containers attached back to back). For your convenience, I have copied this text below:

"So, this paradoxical electrical phenomenon (current flowing through an insulator) has analogical odd worldly situations where some flow like substance (water, people, cars, etc.) apparently "flows" or "passes" through... a wall?!? IMO this is a kind of a transportation problem or a data processing task in computer science... or just a circus trick that are based on storing elements.

If the flow is continuously entering a storing element, we have the feeling that the substance disappears (a "disappearing trick"). Conversely, if the flow is continuously leaving a storing element, the feeling is the substance appears (an "appearing trick"). Finally, if we attach two storing elements (full and empty) back to back and then the flow begins leaving the full storing element and entering the empty one, we make an impression of passing flow ("passing-through-a-wall trick")."

It seems, this phenomenon does not require a differential system of interacting containers; it is valid in the simpler case of two separate but closely located containers. So, in every example of a transmission line, if we break it and insert two containers in the "gap", we create an illusion of a passing AC flow. Another example of this trick can be a loop of a tape: cut the tape and place two boxes in the gap so that the one end of the tape enters the first box while, at the same time, the other end of the tape leaves the other box. Thus you will make an impression of "passing-through-a-box tape".

Regards, Cyril

I agree with you. The idea of ​​"eddy currents" in the planar capacitor shocked by our physicists.

@Mechkov: Actually this is the way I always explain it to my students. I start wit the transient charging of a capacitor by a DC voltage source. Then I reverse the polarity of the voltage source. Thus, first the capacitor charges and then discharges and charges again with opposite polarity. During all this process a current flows through the source, first in one direction and then in the opposite. Then, if we reverse the polarity again, the phenomenon goes on and on... So, we have a continuous state of transients on the capacitor, because we reverse the polarity periodically. The next step is to substitute the DC source with an AC source and explain that the capacitor will always be in a charging/decharging state and therefore it appears that a current flows through the capacitor, although no charges actually fly through empty space!

Сложность в том, как электроны достигают обкладок конденсатора. Скорость их передвижения очень низкая.

The difficulty is that the electrons reach the capacitor plates. The speed of movement is very low.

Dimitrios, I completely second your step-by-step approach. Like you, at the initial stage of understanding, I replace the AC sources by variable and switchable DC sources (batteries). It is worth even to carry out not only mental but real experiments in the laboratory. Capacitive circuits are very impressive for students. You can see, for example, some of the movies below where the process of charging is intentionally slowed up with the purpose to be commensurable with the human speed of thinking:

http://www.circuit-fantasia.com/Deboo/P5160037.AVI - an RC integrator mounted on the middle part of the Microlab system (a Deboo integrator without a positive feedback connected) and its exponential curve on the screen

http://www.circuit-fantasia.com/Deboo/P5160035.AVI - drawing an exponential curve of an RC integrator on the screen

http://www.circuit-fantasia.com/Deboo/P5160036.AVI - a Deboo integrator mounted on the middle part of the Microlab system and its linear curve on the screen

http://www.circuit-fantasia.com/Deboo/P5160034.AVI - drawing a linear curve of a Deboo integrator on the screen

Regards, Cyril

Vinicius I fully agree as mentioned earlier. It is strange how some see the capacitor as a such a mystery but not the transformer and the principle of duality.

Once discussed how the AC current "passes" through a capacitor, it is interesting to show at least one manifestation of this phenomenon - e.g., to see what coupling capacitors really do in AC amplifiers (the most widely known application of this phenomenon). For this purpose, I have asked a special question about the capacitive coupling technique:

https://www.researchgate.net/post/What_do_coupling_capacitors_really_do_in_AC_amplifiers_Are_they_rechargable_batteries_conveying_voltage_variations_or_diverting_biasing_currents?

I hope you will join one of the so interesting discussions about the legendary, eternal and immortal circuit ideas.

Regards, Cyril

As already discussed earlier,the coupling capacitor connected between the output of the previous stage to the input of the next stage of the amplifier passes only the A.C. signals and blocks D.C.It is connected in Series. The current through the capacitor is A.C. only and it is the displacement,The Capacitor tht blocks D.C. is also known as Blocking Capacitor.

The Bypass Capacitor is connected across a Resistor and allows the A.C. Signal to pass through it to avoid drop in the signal Voltage.This current in the Capacitor is also A.C. and Displacement Current.

The other type of current passing through the Capacitor is known as Leakage Current and can be A.C. or D.C depending on the type of Voltage applied across the Capacitor and is Conduction Current,because the Di-electric Material of the Capacitor is not perfect and is a Lossy Di-electric,causing some Real Power Loss in the Capacitor.

The Lossy Capacitor can be represented by means of an Equivalent Circuit with a Pure Capacitor that has no Power Loss and a Very High Resistance in Parallel.The Real Power Loss is caused in this High Resistance.This can be A.C or D.C. Current depending upon the type of Voltage applied to the Capacitor.That is why we have a Loss Angle(Phase Angle) defined for a Lossy Capacitor.

When the Capacitor is connected to D.C.Supply we have a Transient D.C.Current flowing through it till the Capacitor is Charged fully to the Voltage appearing across it. This transient current is due to the Time Constant of the circuit RC where R is the external Resistance in the Circuit.Similarly the Discharging Current is also a Transient one with Time Constant RC.

If R =0. then Charging or Discharging will be instantaneous.Here the Capacitor considered i a Pure Capacitor.

I think the Discussion is about this Transient Current and it is automatically Displacement Current because the Capacitor Current i = C ( dv / dt ).

During charging or discharging time, the Capacitor voltage changes between Zero and V.

For A.C.Supply the current passing through a Pure Capacitor is only Displacement Current and no Conduction Current can pass through it.

P.S.

Yes - I agree. I think, the invention of a displacement current explains everything.

FELIX M.S.Jr. Comment / 15-JULY-2013:

Conservation of charges states that the summation of charges entering a junction is zero (also as per KIRCHHOFF CURRENT LAW) meaning no charge remains at the junction point as each one among all these charges should eventually come out of that junction at any given time each going each own way and none is retained at the junction point. Therefore, for the capacitor the stored charges can not pass through the insulating medium at any given time but should find it's way (i.e. current flow) via the connecting wires between it's two plates to discharge to the positive plate of the capacitor and thru the load resistor if such is connected across the terminals thereby forming a closed circuit loop. Otherwise, how can an electricity be stored on a capacitor if the current can pass thru the insulating medium (dielectric) of this capacitor. It is this medium that divides/separates the different opposite charges of electricity that with the application of working DC voltage (input) across it's plates that storing of electrical energy is achieved in a short time. However, since there's again no perfect capacitor (even for a so-called Supercapacitor with 1000 farads or more) at the passage of time the stored electrical energy on the capacitor will eventually be diminished or discharge (NOT SHORT CIRCUITED) as these electrical charges will eventually be neutralized by each other when due to imperfection of the di-electric medium and/or by some mechanism, the electric fields across the capacitor subsides or go back in neutral state. In the case of an AC circuit, when a capacitor is charged with AC voltage, the same principle applies as again an electrical energy is stored on a capacitor at half cycle phase of alternation and returns back or discharges back to the source after the next half cycle and so on indefinitely at frequency rate but this charges or current does not penetrate the insulation medium (di-electric) of the capacitor but alternately charge/discharge the plates of the capacitor and returns to the AC source, respectively, like that of displacement current (per MAXWELL law).

Very interesting thoughts... Would you join the discussions below as well?

https://www.researchgate.net/post/What_do_coupling_capacitors_really_do_in_AC_amplifiers_Are_they_rechargable_batteries_conveying_voltage_variations_or_diverting_biasing_currents?

https://www.researchgate.net/post/What_does_biasing_mean_and_how_is_it_implemented_in_electronic_circuits?

Regards, Cyril

Hi Cyril,

A capacitor definitely takes in a dc current until it is saturates. Now if there is no resistance within the circuit, the flow will take the form of a delta function. Otherwise, it is slows down exponential. For the ac case, before the slow-down is complete the current changes direction and the same charging(flow of charges) will reverse direction until it slows down again. The rate of slow-down determine the freq. response. An experiment shows the concept: A square-wave voltage source across a series connection of a capacitor and a low resistor(to sample the current by an oscilloscope), As the frequency increases, the charging impulses become narrower and vice versa. One has to note that If it does not pass current, it cannot deliver energy to a load either!

"Crazy capacitor." Recently, I spent the next experiment. I believe that to alternating current "flows" in the condenser in the form of an eddy current. Therefore, a flat capacitor between the plates of a variable magnetic field arises. Consequently, its gain between the capacitor plates to place the transformer steel plate. The capacitance is increased by about 16 times. Maybe there will be willing to repeat the experience? Compare the results.

Valery, what do you think about the Fabrizio's speculations above? IMO they resemble yours...

The observation of Prof. Valery Frisk is quite interesting and also stands to reason. If A.C. Voltage is applied across the Capacitor,displcement Current (A.C.) passes through it and this A.C. Current sets up a Time Varying Magnetic Field which induces Eddy Emf and causes up Eddy Currents in the Capacitor Plates.This also causes some Power Loss in the Capacitor.

The fact that the Capacitance increased when Transformer Steel Plates are used, as stated by Prof. Valery Frisk, needs to be studied.Transforme plate is made of Cold Rolled Grain oriented Silicon Steel which has the property of reducing the Hysterisis Loss.

P.S.

Hi cyril, yes ofcourse both types of current flows in capacitor. But the current that is flowing in capacitor is a displacement current, not conduction current and is always 90 degrees out of phase with conduction current. Even though dielectric material is present in between the parallel plates of the capacitor, on application of the voltage the dipoles in the dielectric medium arrange themselves such that they assist the flow of electrons from one plate to another, following law of conservation of charge.

In case of insulator, that is not the case, the dipoles dont arrange themselves and hence there would be no flow of electrons.

The dipoles also help in storing the energy in form of electric field.

No electric charges flow through an ideal capacitor, whether AC or DC voltage is applied, so the direct answer to your questions is NO (current is defined as I=dq/dt - the electric charge flow per unit of time). In a real capacitor there are some charges that might pass through the dielectric part but they are so few they could be easily neglected.

Nevertheless it is said that when there is an AC current or during the transient phase of DC current, current flows through the capacitor, but in fact the electric charges simply stack on the capacitor's plates and do not pass through it.

As for Fabrizio's answer, he's talking about energy transfer, not about currents.

Concept of displacement currents is very useful for explaining the reason for current flowing through the capacitor. When the voltage is applied across the electrodes of the capacitor, the dielectric material gets polarized and hence displacement current comes into picture without the actual flow of charge carriers.

Cyril, this experiment was a real capacitor. Fabrizios may be advisable to measure the high voltage with a voltmeter spark.

Prof. Pisupati Subramanyam totally agree with you.

Prof.Valeri Frisk,

Referring back to my statement on Reduction of Hysterisis Loss due to the use of Transformer Steel Plates for the Capacitor,I think the following explanation may help.

Reduction of Hysterisis Loss means Reduction of Real Power Loss and Reduction in Wattful Component of the current.

The Practical Capacitor is represented by the equivalent circuit consisting of a Pure Capacitor in Parallel with a High Resistance to take care of the Real Power Loss.Less Power Loss implies More Resistance,causing more Wattless Component of Current through the Pure Capacitance.

Current through the Capacitance Ic = V / Xc.

For Ic to be more Xc = 1 / wC should be less for which with constant w , the Capacitance C has to be more.

Thus the statement of Prof.Valeri Frisk that use of Transformer Steel Plate increases the Value of the Capacitance is justified.

A small Requuest: When you agree you may please give an Upvote to increase the Research Score of the person with whom you agree.

P.S.

So far we are of the concept that the Inductance of a Coil or the Capacitance depend on the Geometry and for a given Geometry ithey are constant.But,this concept is for Pure Inductance or for Pure Capacitance.

The coil also has a Resistace which depends on the length,area of cross section and the Specific Resistance of the coil wire and a Pure Iductance in Series with it.

If the Specific Resistance changes the Resistance of the coil changes for the same legth and area of cross section and changes the current through the coil and hence the Flux linkages and the Inductance of the Pure Inductance Component.

Similarly,the Capacitance being Dual of the Inductance,is represented by a large Resitance causing some Real Power Loss in Parallel with a Pure Capacitance.

Just as the Spefific Resistance of the conductor used for the coil affecting the Magnetic Flux linkages and hence the Inductance,it may be possible for the Composition of the Plates of the capacitor to change the value of the Capacitance as guessed by me earlier.

Detailed experimens with Precise Measurement of the Capacitance,and also the Electric Field,with Plates of different Conducting Materials may be necessary to establish this fact of Increase of Capacitance with Transformer Steel Plates as mentioned by Prof.Valery Frisk. This is a quite interesting and surprise observation.

Also Prof.Fabricio Riccilia Relli's reply in this connection is to be taken note of.

P.S.

Vasile Surducan, I suggested you did an experiment with a capacitor. After removing the short-circuit voltage meter began to show a slight voltage.

On a historical note, this is the very question that led James Clerk Maxwell to conclude that there was a current term missing from Ampere's law. And of course, the introduction of the displacement current leads to the wave equation.

So for anyone having trouble visualizing how an insulator could "conduct" a current in AC, just keep in mind that displacement current isn't a flow of electrons (as we typically think of current in DC), but rather a transfer of energy through electromagnetic waves.

@ Richard Grote: Many teachers "circuit theory" there is some doubt as to the correctness of description of the capacitor in the book "The Feynman Lectures on Physics. Electricity and Magnetism."

:-(

This topic about capacitor is now entering into a new greenfield hitherto unknown to students and professional engineers but known earlier by nikola tesla. The free energy he was advocating may indeed become the oasis of applications for so called free energy devices as against what the 19th and 20th century technologies have done to the world and where capitalists vested interests have fluorished and controlled us all up to where it is now. Where oil and gas have dominated the scene of energy generations and the free energy was put in the back burner. On the other hand, there's good outcome that came out of it though as many people benefited to it as well but however the same is true about the negative impact that co2 emmisssion and air pollution it has brought to our mother earth.

yes, but the current flows to the capacitor or from the capacitor. the capacitor is a charge storage element and it has a capacity to store it. When the capacity is full it cannot store more and the current flow stops to the capacitor. But at the same time if the capacitor is connected to a low voltage element it will emit charges or discharging starts till the voltage of both the elements become same. In this way it can have an incoming current (called as charging the capacitor) or outgoing current (called discharging current).

Bill Beaty here. Two points:

First, this topic seems to be about VACUUM CAPACITORS. Modern capacitors are quite different, and there exists a large electron current in their dielectric. Relative Permittivity can be seen as a ratio between Maxwell's displacement current in the dielectric, versus dielectric polarization current (electron flow.) Modern ceramic capacitors' dielectric constant is above 2,000, so the vast majority of the current is carried by electrons in the ferroelectric ceramic.

Second: it might help to ask whether, down within any conductor, is there a current BETWEEN the flowing charge carriers? If there is, then there's certainly a current between the carrier-filled plates of any capacitor. Or said differently: if we have a current-sensor, and a charged particle approaches and passes it, does it indicate an extremely brief pulse, where the pulse-width is associated with the diameter of the charged particle? Or, does our sensor see each moving particle as "fuzzy," with the measured current extending forwards and back from the particle location? Clamp-on inductive sensors (Rogowski coils) don't detect charges or their motions, instead they detect changing flux-linkage. A clamp-on sensor would say that the current exists between the flowing charges, not just on the particles' surfaces where the charge actually resides. A clamp-on sensor would 'see' currents in the capacitor dielectric.

Third point (I lied!), suppose we construct a capacitor where the dielectric is much wider than the diameter of the capacitor plates. Use a long narrow PZT rod with plates attached to its circular ends. Now apply some 27MHz amperes. Is the current within the rod zero? Really? Suppose we obtain a coil-shaped spiral rod. If we apply some amperes, we'll certainly detect a strong radio-frequency b-field surrounding the rod. If the current is supposedly zero within capacitor dielectrics, how can we explain this?

Bill Beaty,

Welcome to our discussion! It is a great pleasure for us to see such a famous web author with outspoken creative thinking here... I only regret that your interests are more in the area of ​​physical phenomena than circuitry ... but I hope that you will take also part in discussions about unique circuit (and to some extent physical) phenomena, e.g., negative impedance (resistance)

https://www.researchgate.net/post/What_is_negative_impedance_Does_can_it_exist_If_so_how_can_elements_with_negative_impedance_be_implemented_Are_they_passive_or_active

...its implementations - negative impedance converters

https://www.researchgate.net/post/What_is_negative_impedance_Does_can_it_exist_If_so_how_can_elements_with_negative_impedance_be_implemented_Are_they_passive_or_active,

... also about the negative differential resistance

https://www.researchgate.net/post/What_is_negative_differential_resistance_How_is_it_implemented_How_does_it_operate_What_is_its_relationship_with_the_true_negative_resistance,

... and especially about the existence of "apparent negative resistance"

https://www.researchgate.net/post/What_is_the_truth_about_the_Deborah_Chungs_apparent_negative_resistance_Was_it_a_reliable_scientific_experiment_or_only_a_scientific_sensation

Regards, Cyril

It certainly does, just connect a high sensitive ampermeter to a ~nF capacitor and you will measure fA scale current due to thermal noise ( Johnson noise, or Nyquist noise). This can be considered as a fundamental :) current. But even more exciting is a possible current due to Casimir effect (not measured directly so far to my knowledge, though electrical force was measured: http://web.mit.edu/kardar/www/research/seminars/Casimir/PRL-Lamoreaux.pdf)

Intuitively, the best way to think about what 1) a capacitor is, and b) an inductor is ... is through their DC behavior. And INDUCTOR is a WIRE when it comes to DC behavior., A capacitor is an OPEN CIRCUIT when it comes to DC behavior. So, When there is no change in voltage (i.e., dV/dt is=0), NO CURRENT FLOWS through a capacitor. ALL OF THE CURRENT flows through an inductor. This is of course, ignoring the non-idealities of these elements.

Ironically, nothing changes when the C are exposed to AC voltage and AC currents. the NET CURRENT FLOW through a capacitor is ZERO. Why so ?

Simple, the capacitor doesn't really FLOW the current, but, rather, allows the second terminal BORROW electrons, only to give it back later ... When the other side DOES GIVE IT BACK, the net flow is zero. You can borrow MORE, which gives the temporary illusion that, the current is FLOWING, but, all that is happening is that, the second terminal is borrowing MORE electrons (dQ is higher) from the first terminal. This is a situation that cannot be sustained forever, so, the first terminal eventually has to GET BACK ITS ELECTRONS. Otherwise, we will be in a deadlock. How much voltage change is induced (dV) based on how many electrons borrowed (dQ) is called the CAPACITANCE (i.e., C=dQ/dV). But, in the long term, NO NET ELECTRONS FLEW from one side to the other. They went back and forth ... and the NET FLOW is zero.

Of course, this discussion changes slightly when there is LEAKAGE in the capacitor, which doesn't make electrons FLOW, but rather LEAK to the other side unintentionally. Leakage is caused by the Equivalent Parallel Resistance (EPR) of the capacitor.

Cyril, I love these fundamental questions you are bringing up, and inspired by you, I asked the same question, except the INDUCTOR version.

Tolga - what is the "net current flow" through an ohmic resistor in case of AC?

excellent question ! To re-phrase your question: In terms of my "current flow" theory, is there any difference between an R and a C ? It is very clear in terms of DC, but, in terms of AC, it almost looks like, there is no difference. THERE IS ! Here is my answer:

I think it is a lot easier to visualize my answer by comparing two super-simple circuits. In both circuits, terminal 2 of the R (or C) is connected to GND.

CIRCUIT 1 : An AC source connected to an R, terminal 1.

CIRCUIT 2 : An AC source connected to a C, terminal 1.

COMPARISON TEST CASE: Assume a departing electron, whose name is JOE :) He departs from the AC source, and arrives at the terminal 1 of the passive element.

CIRCUIT 1 CASE: passive element is an R. JOE goes THROUGH the RESISTOR and gets dumped into the GND in the up cycle of the AC. In the down cycle, JOE is already back in the BATTERY, and that electron is WASTED. JOE is gone !!! so, we have to pull some other electron, JIM from the battery back into the other terminal.

NET FLOW : 2 ELECTRONS ...

CIRCUIT 2 CASE: passive element is a C. JOE arrives at the first terminal of C. He never GOES THROUGH C and never gets dumped into the GND. He gets stored as ENERGY in the Capacitor in the UP CYCLE of the AC. In the DOWN CYCLE, well, we have JOE sitting in the capacitor, when the down cycle comes, we send JOE back to the battery. So, JOE visited the capacitor for a quick while, and went back to the battery. HE never DIED !

NET FLOW OF ELECTRONS: ZERO.

In other words, R wasted energy in both cycles, C never did ! Storing and retrieving energy in the capacitor never wastes energy (ignoring leakage and other non-idealities). On the other hand, a resistor wastes energy whenever current is FLOWING THROUGH it.

Makes sense ?

Hi Tolga - nice story. However, I think it was known from the beginning that a resistor dissipates energy.

However - what about the "net current flow" as used in your previous posting?

didn't I answer it ?

let's define FLOW : an electron departs at the power supply, and ends up in the GND.

This is an irreversible action, since that electron got wasted, and cannot be used again.

In the case of C, the C never really completes this flow in NET terms. it gets STORED in C, and is given back to the supply in the next cycle.

In the case of R, the electron completes this flow, and returns to GND. In the next cycle, another one flows THROUGH the R in the other direction.

In other words, if you unplug the capacitor after only the UP cycle, the electron never really FLEW THROUGH the capacitor. It is still inside the capacitor. You can, then, plug it back in, and send the electron back to the supply.

In the case of R, if you UNPLUG the resistor after the UP cycle, there is nothing on the resistor, i.e., the electron completed the cycle and returned back to GND THROUGH the resistor already. When you plug the resistor back in, another complete different electron has to start a cycle in the reverse direction and complete the cycle, GND back up to Vcc.

Makes sense ?

Tolga, I dedicate my new question about the meaning of "positive" and "negative" (in respect to the impedance)

https://www.researchgate.net/post/What_does_negative_impedance_mean_in_electricity_and_electronics_Has_the_capacitor_a_negative_impedance_How_do_we_create_a_negative_capacitor

to your expressive explanations below:

"Intuitively, the best way to think about what 1) a capacitor is, and b) an inductor is ... is through their DC behavior. And INDUCTOR is a WIRE when it comes to DC behavior., A capacitor is an OPEN CIRCUIT when it comes to DC behavior. So, When there is no change in voltage (i.e., dV/dt is=0), NO CURRENT FLOWS through a capacitor. ALL OF THE CURRENT flows through an inductor."

Interesting and exciting discussions... I only regret that I will be absent from 5 to 15 September...

Regards, Cyril

@Tolga: Thank you - I got it.

(Your definition of "net flow" is somewhat different than mine. However, no problem).

I would love to hear your definition. Here is my simple view: Imagine the battery, capacitor, and GND circuit. If you put an AMPMETER right between the capacitor's bottom terminal and the GND, does the AMPMETER record any current flowing during CHARGING ? If my theory is right in that, the current is NOT FLOWING through the BOTTOM TERMINAL, the AMPMETER should record ZERO CURRENT during CHARGING. This means that, the I=CdV/dT only happened on the UPPER TERMINAL. In other words, the electron that entered the upper terminal never really reached the lower terminal (i.e., went into the GND). If it did, I could capture it, and store it in another capacitor, doubling my electron effectively ! NOT POSSIBLE !

On the DOWN cycle (other cycle), the electron that I just captured is going back to the battery, never EVER making its way to GND. So, nothing FLEW from the battery into the GND. Electrons just got STORED in the C, and UNSTORED on the next cycle.

In the case of a resistor. clearly, the electron flows through, and reaches GND, and hence, it is GONE.

If you agree with me, this means that, you are agreeing that, the electron is not really FLOWING into the GND, but, rather, getting CAPTURED (i.e., STORED) by the capacitor and never reaching the GND.

Tolga - didn`t we speak about the "net current flow" in case of AC?

Here comes my example:

take an ac voltage source and an R-C series connection across it.

I suppose, the current through both parts will be identical. Thus, if the net current flow through the capacitor is zero - what is the net current flow through the resistor?

Hi Lutz, I don't think we are agreeing on one thing.

In the case of a resistor, if an electron goes into terminal1, it comes out of terminal2. NET FLOW=1 electron.

In the case of a capacitor, if an electron goes into terminal1, NOTHING comes out of terminal2.

Do you agree ?

Yes - of course I agree.

As I have mentioned already, I think both of use different definitions.

What is this thing called "electrical current"?

According to my knowledge it is movement of charges (NOT of electrons, which move rather slow) .

As far as I understood your explanations, you only speak of electrons and their movements.

Therefore, I think that your previous statement about "net current flow" should read "net electron flow", which is something different, is it not?

Ok. Sounds good. This makes both of us happy ! Done.

My friends, it is time to reveal to you a little secret:) - for the purposes of understanding, explaining and inventing new circuits no matter the type of carriers (charges, electrons, holes, etc...). The only essential thing is that there is a transfer (flow, movement, current...) of energy... of "something"... This is the essential - we transfer energy by some carrier... So, there are three substantial quantities in the most elementary "circuit": pressure-like (voltage), flow-like (current) and impediment-like (resistance) quantity...

Cyril no doubt about this.

However, it was YOU who has asked: "Does a current flow through a capacitor"?

And now you ask us not to be too specific - because everything is energy?

Agreement is worth little: "let the experiment be made."

Go and actually measure the current in each lead of a capacitor. Try a 400V 2.0uF mylar, plugged right into 120VAC. It should draw around 50mA; easily detected with a DVM. (For safety, perhaps include a 75W incandescent lamp.)

Lutz, perhaps I should ask a question, "Can something flow through a capacitor"? or even the more impressive, "Can a man pass through a wall?":)