The Capacitor Dielectric

[crashsite]

This might be more of a physics question than an electronic one but...

The usual first-year electronics theory refers to the charge on a capacitor being stored on the plates. But, even a fairly cursory look at the formula for determining a capacitor's capacitance indicates that the dielectric constant of the insulator plays as big a role as the plate area and spacing.

The explanation then given is that the charge is actually stored in the dielectric (by essentially stressing and distorting the atoms) and the plates are merely used to provide conductive surfaces to distribute the charge between the dielectric and the campacitor's leads.

Okay, good enough. But, I guess the part I don't get (assuming I "got" the other part right) is how the atoms in the dielectric distort. It can't be that electrons are drawn through the dielectric because the better insulator the dielectric is the more capacitance it can give. Are the orbits of the electrons somehow distorted? Is there some sort of quantum action going on? Is the stress concentrated on the surfaces of the dielectric or is it distributed across the thickness of the dielectric?

An ancilary question might be: What is it about a good insulator (atomically speaking) that makes it a good dielectric in the first place (beyond the obvious, "because it effectively resists the flow of electrons").

My math is lousy and you'll notice I've used no formulas or equations and hopefully there's a reasonable explanation to this that doesn't need them...otherwise, to be quite frank, I'll be lost.

 

[Mihindu_gajaba]

hm... well i dont know much about this , all i know is , when we power the Capacitor it store some electric current which is toooo small , thats because if there more power it's unstable so we can't store much power on a Capacitor so that we are using small amount of Current i mean it's some kind of a static and when it dielectric it convertes to current but it's only for like 1ms thats the thing.
anyway there are some Formullas to be study..

 

[Mihindu_gajaba]

Capacitance

The capacitor's capacitance (C) is a measure of the amount of charge (Q) stored on each plate for a given potential difference or voltage (V) which appears between the plates:
**broken link removed**

In SI units, a capacitor has a capacitance of one farad when one coulomb of charge is stored due to one volt applied potential difference across the plates. Since the farad is a very large unit, values of capacitors are usually expressed in microfarads (µF), nanofarads (nF), or picofarads (pF).

When there is a difference in electric charge between the plates, an electric field is created in the region between the plates that is proportional to the amount of charge that has been moved from one plate to the other. This electric field creates a potential difference V = E•d between the plates of this simple parallel-plate capacitor.
The capacitance is proportional to the surface area of the conducting plate and inversely proportional to the distance between the plates. It is also proportional to the permittivity of the dielectric (that is, non-conducting) substance that separates the plates.
The capacitance of a parallel-plate capacitor is given by:

**broken link removed**

where ε is the permittivity of the dielectric (see Dielectric constant), A is the area of the plates and d is the spacing between them.
In the diagram, the rotated molecules create an opposing electric field that partially cancels the field created by the plates, a process called dielectric polarization.

Stored energy

As opposite charges accumulate on the plates of a capacitor due to the separation of charge, a voltage develops across the capacitor due to the electric field of these charges. Ever-increasing work must be done against this ever-increasing electric field as more charge is separated. The energy (measured in joules, in SI) stored in a capacitor is equal to the amount of work required to establish the voltage across the capacitor, and therefore the electric field. The energy stored is given by:

**broken link removed**
where V is the voltage across the capacitor.
The maximum energy that can be (safely) stored in a particular capacitor is limited by the maximum electric field that the dielectric can withstand before it breaks down. Therefore, all capacitors made with the same dielectric have about the same maximum energy density (joules of energy per cubic meter).

Hydraulic model

Main article: Hydraulic analogy
As electrical circuitry can be modeled by fluid flow, a capacitor can be modeled as a chamber with a flexible diaphragm separating the input from the output. As can be determined intuitively as well as mathematically, this provides the correct characteristics:

•The pressure difference (voltage difference) across the unit is proportional to the integral of the flow (current)

•A steady state current cannot pass through it because the pressure will build up across the diaphragm until it equally opposes the source pressure.

•But a transient pulse or alternating current can be transmitted

•The capacitance of units connected in parallel is equivalent to the sum of their individual capacitances

 

[Mihindu_gajaba]

Refer - Capacitors

 

[Mihindu_gajaba]

Definition

**broken link removed**

Electric field interaction with an atom under the classical dielectric model.
In the classical approach to the dielectric model a material is made up of atoms. The atoms consist of a positive point charge at the centre surrounded by a cloud of negative charge. The cloud of negative charge is bound to the positive point charge. The atoms are separated by enough distance such that they do not interact with one another. This is represented by the top left of the figure aside. Note: Remember the model is not attempting to say anything about the structure of matter. It is only trying to describe the interaction between an electric field and matter.
In the presence of an electric field the charge cloud is distorted, as shown the top right of the figure.
This can be reduced to a simple dipole using the superposition principle. A dipole is characterised by its dipole moment. This is a vector quantity and is shown as the blue arrow labeled M. It is the relationship between the electric field and the dipole moment that gives rise to the behaviour of the dielectric. Note: The dipole moment is shown to be pointing in the same direction as the electric field. This isn't always correct, but it is a major simplification, and it is suitable for many materials.
When the electric field is removed the atom returns to its original state.
________________________________________
This is the essence of the model. The behavior of the dielectric now depends on the situation. The more complicated the situation the more rich the model has to be in order to accurately describe the behavior. Important questions are:
• Is the electric field constant or does it vary with time?
o If the electric field does vary, does it vary quickly or slowly?
• What are the characteristics of the material?
o Is the direction of the field important (isotropy)?
o Is the material the same all the way through (homogeneous)?
o Are there any boundaries/interfaces that have to be taken into account?
• Is the system linear or do nonlinearities have to be taken into account?
The relationship between the electric field E and the dipole moment M gives rise to the behavior of the dielectric, which, for a given material, can be characterized by the function F defined by the equation:

**broken link removed**

When both the type of electric field and the type of material have been defined, one then chooses the simplest function F that correctly predicts the phenomena of interest. Examples of possible phenomena:
• Refractive index
• Group velocity dispersion
• Birefringence
• Self-focusing
• Harmonic generation
May be modeled by choosing a suitable function F.
Dielectric model applied to vacuum
From the definition it might seem strange to apply the dielectric model to a vacuum, however, it is both the simplest and the most accurate example of a dielectric.
Recall that the property which defines how a dieletric behaves is the relationship between the applied electric field and the induced dipole moment. For a vacuum the relationship is a real constant number. This constant is called the permitivity of free space, ε0.
Applications
The use of a dielectric in a capacitor presents several advantages. The simplest of these is that the conducting plates can be placed very close to one another without risk of contact. Also, if subjected to a very high electric field, any substance will ionize and become a conductor. Dielectrics are more resistant to ionization than dry air, so a capacitor containing a dielectric can be subjected to a higher operating voltage. Layers of dielectric are commonly incorporated in manufactured capacitors to provide higher capacitance in a smaller space than capacitors using only air or a vacuum between their plates, and the term dielectric refers to this application as well as the insulation used in power and RF cables.

 

[Mihindu_gajaba]

Refer - Dielectric

 

[ericgibbs]

Look here:
https://www.madabout-kitcars.com/kitcar/kb.php?aid=353

 

[crashsite]

So, the short answer then is that the very atoms of the dielectric distort to store the charge. Which brings up the question of what distorts when there is no matter (vacuum)?

 

[Pommie]

When we apply a voltage to a capacitor, the negative plate gets extra electrons that repel the electrons in the positive plate and a current flows until the forces balance out and we have a charged capacitor.

Mike.

 

[Papabravo]

What distinguishes an insulator from a semiconductor or a metal is the energy gap between the electrons in the outermost shell and any free electrons that may be present. In a metal there is no gap, and valence electrons and free electrons have allowed energy levels that overlap. In semiconductors like silicon and germanium the gap between the valence electrons and the free electrons is like 0.7 to 1.2 electron volts. In an insulator this gap is like 6 electron volts. So what is the point of all this? The point is that it takes a very large potential generated by an electric field to yank a valence electron out of its shell. As the field intensity increases there is a fight between the nucleus and the electric field for control of the electron.

Dielectics are useful but not essential to creating a capacitor. Tell your little friends that a parallel plate capacitor will work just fine in the cold vacuum of interstellar space. The reason we use them is because we can reduce the separation of the plates without creating a discharge. A discharge between the plates is the equivalent of shorting the plates together. In fact that is the principle behind a particle detector called a "spark chamber".

 

[crashsite]

...the negative plate gets extra electrons that repel the electrons in the positive plate and a current flows until the forces balance out and we have a charged capacitor

Unfortunately, that doesn't address the dielectric question. It's only a generalized description of what a capacitor does and not how it does it.

What distinguishes an insulator from a semiconductor or a metal is the energy gap between the electrons in the outermost shell and any free electrons that may be present

While this discussion may be accurate, it too does not address the question of how a dielectric material acts as an integral part of a capacitor for stroing the charge.

Dielectics are useful but not essential to creating a capacitor.

By this logic, the dielectric constant is trivial and could simply be deleted from the capacitor formula. You could argue that leaving it out is the same as making it, 1. That isn't a good way to think of it since we know that the dielectric constnat has a profound effect on a capacitor's capacitance. That thinking also does not address the question of why or how nothing (a vacuum) can have physical properties that make it a viable dielectric.

I would disagree that a dielectric is not needed. In it's simplest form the description of a capacitor is, "two conductors separated by an insulator" and can (often is) merely the presence of "us" (the so called, hand capacitance) since we tend to be more conductive than something like air between ourselves and some other conductor. But, that still does not address the question of how the dielectric part works to either store the charge or interface with the plates to store the charge, when its a vacuum.

From the definition it might seem strange to apply the dielectric model to a vacuum, however, it is both the simplest and the most accurate example of a dielectric

Yes, it does seem strange and, while I pretty much got lost in the math, didn't really see the "action" of the vacuum as a dielectric material in the description.

 

[Papabravo]

Well the dielectric constant of a vacuum is only 1 in a normalized set of coordinates. Just like we can build a consistant theory on the assumtion that the speed of light is 1. A vacuum still has a permitivity and a capacitor still works in a vacuum. Just because you don't believe it or understand it does not alter the reality. I'm done with this thread -- maybe someone else can satisfy this guy.

 

[ericgibbs]

Google ' define dielectric'

Dielectric model applied to vacuum
From the definition it might seem strange to apply the dielectric model to a vacuum, however, it is both the simplest and the most accurate example of a dielectric.

Recall that the property which defines how a dieletric behaves is the relationship between the applied electric field and the induced dipole moment. For a vacuum the relationship is a real constant number. This constant is called the permitivity of free space, ε0.

 

[crashsite]

Being really poor at math but, able to figure things out pretty well if I have some way to equate them, I have to pretty much beat things down to their most basic form and "start" from there. I was asking an engineer friend a question about modulation and he casually said, "Oh, it's sine omega t". And, that completely satisfied him. Means nothing to me because I think of AM or FM as one signal "tugging" on another with the result being a series of instantaneous results that, over time, create the sidebands. A very mechanical, non-math approach.

I can see a concept of X number of electrons flowing onto a capacitor plate and creating a charge across some insulator relative to the other plate and if only the plate area and spacing dictated the capacitance, that would satisfy me. But, there's more. Somehow the amount of charge (number or energy of the electrons) is also determined by the nature of the dielectric material.

If the dielectric material is "real" (consists of atoms), it's pretty easy to envision it as a spring, where the electrical stres distorts the atoms more and more as the charge builds up and then releases the energy by returning to an unstressed state when the capacitor discharges. And, I guess that would satisfy me.

But, if there are no atoms to be stressed (as in a vacuum), my "mechanical understanding" falters. I suppose if the answer were to be that, with a vacuum as a dielectric, the capacitance is dependent ONLY on plate area and spacing, I could accept that. In that case the electrical stress would only be dependent on the number of electrons that could flow onto a plate of a certain size and interact with the potential of another plate some distance, across the vacuum, away.

If the dielectric is a poor insulator (leaky capacitor) there's another problem, when thinking about it as a mechanical analogy. If the dielectric material is leaky, it still has atoms and, while the capacitor wont hold the charge, the stressing of the atoms, at the time the capacitor is charged, should be a different characteristic of the material than the rate the electrons will be allowed to leak through it over time (or, at least it seems like it should be a different charteristic than if there's nothing there at all).

If there's a "dynamic" to the matter (or lack thereof, in the case of a vacuum) that allows energy to be dissipated across it by some process besides the flow of electrons through it that could dissipate the charge, that's different for different materials.....well....that's just pure conjecture and I'll stop on this line of thought.

So, no I'm not satisfied with it and, maybe there is no answer to be given that doesn't state how it is, mathematically and you just have to work with it in those terms. I hope that's not the case as I would like to "understand" (at some level for which I have a comfortable frame of reference) how it works. But, I certainly don't want to feel like I'm infringing on anyone's patience or time with my ignorance or lack of understanding of this phenomena.

 

[crashsite]

The Capacitor Dielectric Revisited

The last time I posted this topic I was eventually sort of branded as someone who couldn't be satisfied. It is true that I don't feel that I got THE answer.

Let me apologize here for this being rather long but, I want to try to be specific.

The question boiled down to, "why does changing the dielectric constant of the insulator in a capacitor change the capacitance".

It's certainly easy to "quantify" the effect. To reference formulas and equations that describe how the effect affects the capacitance but, that doesn't really explain HOW it works.

One could say that it's as easy as 2+3=5. But, that equation doesn't really explain anything. It merely states that the squiggle, 2 (which by agreement equates to this many of something of which I'll use asterisks, **). Then, the squiggle, 2 is acted on by a mathematical operation (by agreement, to mean aggregation) denoted by a plus sign (+), in conjunction with another squiggle, 3 (which represents this many, ***). The result is that you get an aggregate amount of this many, ***** which, itself is denoted, by agreement, by the squiggle, 5. While the math gives a result it doesn't really describe what's happening. Only if you already know the meanings...how it works AND the nomenclature...can you solve and understand the math.

The capacitor formulas are like that. They quantify things. But, to understand how the capacitor works you need to understand that matter consists of atoms and that atoms are comprised of light electrons and much heavier protons and that electrons are orbiting the protons and carry an electrical charge (referred to as negative by convention) and that electrons can be accumulated (which increases the negative electrical charge) and that those elctrons came from atoms which leaves those atoms less negatively charged (by convention referred to as positively charged). We also need to know that like charges attract and unlike charges repel.

Related to a capacitor, we can envision a fairly simple action of electrons trying to equalize things via that attractive force. If a battery (one of the devices which can accumulte electrons to create a charge imbalance) across two conductive plates which are separated by an insulating material, it's easy to envistion that some lectrons will flow onto one of the plates and, being attracted to a deficiency of electrons on the opposing plate find themselves attracted to it (unlike charges attracting). But, the insulating material prevents the electrons from actually flowing to the other plate.

Fine. We have basic capacitor action grounded in reality. What we don't have is numeric values to quantify it. We need the math for that but, not for underdstanding the action itself.

If the insulating material between the plates is a vacuum, that's fine. The electrical attraction is still there and thus, some number of electrons will be pulled onto the negatively charged plate before the circuit stabilizes. If the battery is then removed, the electrons on the plates have no way to go anywhere and thus just stay where they are and the electrical attraction between the plates is still there. By convention that attractive force is called, voltage.

If the plate area increases, it's easy to envision that more electrons can flow onto them (creating a larger capacitor value). It's not quite as intuitve that putting the plates closer together will also increase the capacitaance (in fact, it's almost counter-intuitive) but, with a little thought it makes sense. If the plates are closer the strength of the electrical field is greater and so it takes more electrons to balance things out. In fact, charging up a capacitor and then moving the plates will actually vary the voltage on the capacitor (the principle behind the condenser microphone and varactor diode amplifier).

Which brings us to the dielectric. Increasing the dielectric constant has the same effect as moving the capacitor's plates closer together. There is something about the properties of the dielectric that makes that happen. Somehow, increasing the dielectric constant increases the electrical interaction of the plates such that it takes more electrons to balance out the charges when a voltage is applied across the c apacitor.

THAT is my question! What is the property (are the properties?) of the dielectric that makes it increase the capacitance of a capacitor as the dielectric constant of it increases.

One post suggested that electron band gaps were the explanation and maybe it is but...if so, I'm not sure how that works. Or how it relates to a vacuum as the dielectric.

 

[henrybot]

The way that it makes sense to me (Your mileage vary)...

If you leave everything else constant, and only change the dielectric, a higher value makes higher capacitance. No charge ever moves through the dielectric. But the more insulative the gap between the plates, the larger the potential to store the charge. The capacitance in Farads, C, is equal to the area in square meters multiplied by the dielectric constant, multiplied by the permittivity of free space (8.854x10^-12 Farads/Meter), multiplied by the area in square meters of the plates, divided by the distance between the plates in meters. The units of distance cancel out, leaving a number, and the Farads unit. So,

C=k * (8.854 * 10^-12) F/m * A m^2 / D m

By increasing the dielectric constant (k), you will increase the capacitance directly. Does that help? I'm not quite sure that I am quite grasping your question.

EDIT: I re-read your question. Moving the plates closer together increases the capacitance, as well as increasing the dielectric constant. Less distance between the plates makes it easier for the charges to interact. A higher-k dielectric makes for a higher potential to be stored before the dielectric breaks down. I think that I might be oversimplifying your question, but I think that you might be obfuscating the problem.

-Mike

 

[crashsite]

but I think that you might be obfuscating the problem.

I don't know if I'm obfuscating the problem...

I did repost this same question earlier today with a slightly different slant (as a new thread).

Your post does clearly state how the change in the dielectric constant acts, in a quantitative way, but I still don't get a sense of "why" it works as it does.

I've used capacitors on a pretty regular basis all my life and have even made a few of them (rolling up tin foil and paper, etching plates in opposite sides of double-sided pc board, even made a capacitor bridge to measure fluid level once that used the variation of capacitance due to the change in the dielectric, etc.) and have often figured out the values from the formula in my little Radio Shack Electronic Data Handbook.

20 years ago I felt like I had a pretty good handle on it but, I guess I'm getting more introspective because I realize I really don't have a good feel for what's actually happening at all (and, I don'[t like it).

 

[Papabravo]

The difference between "free space" and a dielectric is that for free space charges on one plate act only on the charges on the other plate. With the dielectric in between the charges on the plate can act on the electrons of the dielectric, which are not normally free to move about. At least they are not free to move about at low voltages.

Now as the voltage increases to the levels of the energy gap in an insulator ( 6 eV ) electrons can potentially be ripped away from their atoms and create charge distributions that alter the fields and thus the capacitence for a capacitor with the same plate area and separation as the capacitor in free space. These charges are not mobile in the sense that they would be for a metal or a semiconductor, but you can move them around.

I don't know if this helps and I can't necessarily draw a picture, but the answer lies in this direction.

Have you read Feynman, Vol. II? I strongly suggest you take a stab at it.

 

[henrybot]

Your post does clearly state how the change in the dielectric constant acts, in a quantitative way, but I still don't get a sense of "why" it works as it does.

All the positive charge is stored on one plate, and the negative charge stored on the other. Unlike charges attract, so they are desperately trying to balance to a neutral charge. If you increase the distance between the plates too far, it simply becomes an open circuit. If you bring the plates extremely close, the attraction between the unlike charges increases. On the other hand, if you keep the small distance constant and make the dielectric higher (more insulative), then it means you can store more charge on the plates without shorting through the insulator.

As far as what's happening on the sub-atomic level, I'm not sure (Not a physicist!! )

-Mike

 

[Leftyretro]

I don't know if I'm obfuscating the problem...

I did repost this same question earlier today with a slightly different slant (as a new thread).

Your post does clearly state how the change in the dielectric constant acts, in a quantitative way, but I still don't get a sense of "why" it works as it does.

I've used capacitors on a pretty regular basis all my life and have even made a few of them (rolling up tin foil and paper, etching plates in opposite sides of double-sided pc board, even made a capacitor bridge to measure fluid level once that used the variation of capacitance due to the change in the dielectric, etc.) and have often figured out the values from the formula in my little Radio Shack Electronic Data Handbook.

20 years ago I felt like I had a pretty good handle on it but, I guess I'm getting more introspective because I realize I really don't have a good feel for what's actually happening at all (and, I don'[t like it).

As I read through this post I can understand your questioning of the magic of dielectric constant and how it actual causes a change in the value of the total capacitance. While I can't answer it, maybe I can state the question in a simpler manner and see if anyone would like to chew on it some more.

QUESTION

Given two metal plates of a given fixed area and a fixed spacing, if the spacing is filled with two different materials, say mica and Teflon, during two separate tests with the same applied voltage, what is the cause, at the electron or atomic level, for the different materials to cause the total capacitance value to be different for the two insulating materials.

And saying the materials have different dielectric constants is not a sufficient answer

Lefty