Talk:Capacitor

Permittivity symbol is confusing

The symbol used for the permitivity in equations in the text seems to be different than the symbol used in the larger equations. Maybe it's just italicized but it looks like a different symbol. I changed the symbols in the "parallel plate model" section to be consistent, but I did not continue to the rest of the article as I am not familiar with the topics.

The usual mistake(s)

An electric field in a capacitor does NOT contain energy. The energy of a capacitor is in the electrons on the plates. In loading a capacitor a battery does work on the electrons (not on some field). The electric field is only the result of a created potential difference. So yes, a capacitor contains energy, but not its field but its electrons. Please, change the first sentence of this article. By the way, for a parallel-plate capacitor the E-field does NOT depend on z. Therefore, the equation is not consistent with the text. So change the equation too, please. — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 15:59, 24 February 2021 (UTC)

Well, when talking potential energy, there is always an object, and a field that exerts force on that object. In nearly all situation it's common to picture the force as being a property of the field, and the energy as being a property of the object. The kinetic energy is a function of the object's mass and speed, while the potential energy is a function of its mass and position in the object/field system. But this is strictly a matter of convention, as one could just as easily assign the energy to the field, since both the field and the object are needed to store the energy. Thus, when talking about a fighter plane, we tend to assign the force to the gravitational field, and the energy to the aircraft.

Electricity is a little different, because in this case it works almost opposite of things like gravity. Not only do the objects (electrons) carry a charge of their own, but it is also a negative charge, so things work quite backwards in a very literal sense. The electrons move from the negative charge to the positive, but the power or the energy moves from the positive to the negative. The real potential is on the side of the battery that has fewer electrons; the positive terminal. It's hard to visualize until you see it in action. For example, in a semiconductor, the electrons move from negative to positive, but the power moves from positive to negative via "holes" that move through the crystalline lattice. Likewise, in a gas discharge lamp, the power is carried by the positive ions in the plasma rather than the electrons. So in this case, it's more natural to assign the energy to the potential field (the positive charge) rather than the object. But still it is just a matter of convention, as both are needed for any kind of potential energy to exist, so in reality the energy exists in the object/field system. Zaereth (talk) 18:51, 24 February 2021 (UTC)

You can read what Feynman says about field energy here: [1] In sec 27-4: "Anyway, everyone always accepts the simple expressions we have found for the location of electromagnetic energy ... nobody has ever found anything wrong with them ... we believe that it is probably perfectly right." Constant314 (talk) 19:49, 24 February 2021 (UTC)

Is this the equation that you are questioning?

$V=\int _{0}^{d}E(z)\,\mathrm {d} z=Ed={\sigma \over \varepsilon }d={Qd \over \varepsilon A}$

It is correct even if E(z) is independent of z. I think that the explanation of $\sigma \over \varepsilon$ could use a better explanaton. Constant314 (talk) 20:12, 24 February 2021 (UTC)

There might be fringing field at the edges, so it might not be constant with z, but usually close enough. Less constant if the spacing is comparable or larger than the plate dimensions. And yes I agree with Feynman.Gah4 (talk) 21:14, 24 February 2021 (UTC)

You can't argue with Feynman, nor beat a good Feynman quote. One of my favorites is: "It is important to realize that in physics today, we have no knowledge what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way." At best, energy is more of a function of variables rather than anything you can put your finger on. If you start adding light into the equation, now your talking a "massless" particle (may be a particle, or may be a wave; sometimes one, the other, or both; and in reality most likely neither) whose energy is solely a function of its wavelength. Quantum physics, huh? Just when you think you got it all figured out, that's the moment you realize you were never more wrong. Zaereth (talk) 21:38, 24 February 2021 (UTC)

@Constant314: Yeah, I wrote that section, and I didn't explain $E={\sigma \over \varepsilon }$ adequately. Thanks for bringing that up. For anyone else who is wondering, it comes from Gauss's law applied to a cylindrical volume intersecting one plate, with one end between the plates and the other end outside the plates. There is no flux through the side of the cylinder or the end outside the plates, all the flux passes through the end surface between the plates, and the electric field through that end is perpendicular to the surface. If the cross sectional area of the cylinder is $A$, the flux through the inside end is $EA$ and the charge inside the cylinder is $\sigma A$, where $\sigma$ is the surface charge density on the plate. So from Gauss's law $EA=\sigma A/\varepsilon$. I guess a brief explanation of this should be added. --Chetvorno^TALK 22:11, 24 February 2021 (UTC)

I was thinking of going at it from the equation for the E field above an infinite charged plane of constant surface charge density, but that is the same as what you are saying. Constant314 (talk) 22:33, 24 February 2021 (UTC)

Yes, that would be a good way too. Less math. --Chetvorno^TALK 19:51, 28 February 2021 (UTC)

@Koitus~nlwiki: If the electric field doesn't contain energy, why does it take work (energy) to pull the plates of a charged capacitor apart, which doesn't change the number of electrons on the plates but only changes the volume of field? Why does a capacitor with a dielectric between the plates contain more energy than a capacitor charged to the same voltage with vacuum between the plates? In the section "Energy stored in a capacitor" it is proved that the total energy stored by a capacitor is equal to the energy density in the electric field times the volume of the field. In electromagnetics it is shown that an electrostatic field contains an energy density of ${1 \over 2}\varepsilon E^{2}$ joules per cubic meter. There are many examples showing that electric fields and magnetic fields themselves have energy independent of their source charges. An electromagnetic wave like light, which just consists of electric and magnetic fields, carries energy itself, independent of its source. We can still see light from a star (which means that our eyes respond to the energy) that was emitted thousands of years ago, even if the source of the fields, the electron in the star which emitted the light, or the whole star, has long ago ceased to exist. --Chetvorno^TALK 21:18, 24 February 2021 (UTC)

By the way, you can sign your posts by typing ~~~~ after your text, which will insert your username. --Chetvorno^TALK 21:18, 24 February 2021 (UTC)

Capacitor

What type of capacitor do I need? I'm running a 120v generator that seems to have a voltage drop when the refrigerator comes on. This causes my stereo to shut off (automatic surge protection). I would like to end this problem. Thank you. 2001:5B0:4FDE:AE98:ADBD:2F77:5C4B:BAEF (talk) 16:40, 4 February 2022 (UTC)

A motor-start capacitor. Zaereth (talk) 18:17, 4 February 2022 (UTC)

Hydraulic analogy issue

"This is just as when water flow moves the rubber membrane, it increases the amount of water on one side of the membrane, and decreases the amount of water on the other side."

I believe this is inaccurate. Water is basically incompressible, so there isn't an accumulation of the amount of water. I think the analogous mechanic is probably the deformation of the membrane. The curvature increases positively on one side and negatively on the other. BennyWahWah (talk) 15:40, 15 October 2022 (UTC)

Well, no analogy is going to be completely accurate. It's just a way to help visualize it. Some people hate hydraulic analogies because of this, but personally I find them very helpful, because the way my mind works I have to be able to understand it from a mechanical standpoint. A pneumatic analogy would also work just as well.

In learning about capacitors, the analogy of a hydraulic accumulator was very helpful to me in helping to explain the mysterious capacitor, at least as they are used in DC circuits. In AC circuits, the membrane described would be analogous to the dielectric in the capacitor, yet the dielectric doesn't actually move like a membrane would. Still, it helps explain how the dielectric can separate two sides of a circuit and still have them behave as if they are linked. In this analogy, the fluid doesn't have to be compressible. You add more fluid into the pipe on one side and it pushes fluid out of the pipe on the other side. The energy does not come from the membrane (elasicity). It's simply a matter of creating a pressure (voltage) differential. Zaereth (talk) 19:47, 15 October 2022 (UTC)

Ok, I'm convinced. Not an issue, thanks! BennyWahWah (talk) 13:20, 18 October 2022 (UTC)

Well, don't get me wrong. You may just have a point, in that there may be a better way to rephrase it to make the analogy clearer. I'm not sure what that would be yet, but that's why these discussions are helpful. They're especially helpful to me, because it's a way to help work through the thought process. I'll let it stew in my subconscious for a while, but any input you want to give is always welcome.

For example, the more I think about it, if anything electricity is analogous to an incompressible fluid than a compressible one. You can imagine a pump (generator) on one side of the pipe and a hydraulic cylinder (solenoid) on the other. We can make this analogy because many of the variables involved are also analogous. We have flow (amps), pressure (volts), volume (coulombs), etc... There is a huge difference, though, in that electricity flows backwards, against the direction of pressure rather than with it, so there is a limit to how far you can take the hydraulic analogy before it breaks down. I'll give it some more thought. Zaereth (talk) 19:21, 18 October 2022 (UTC)

Non-ideal Behavior

The non-ideal behavior section is over simplified to the point of being misleading, especially since it neglects parasitic inductance (ESL). The diagram on the Capacitor types page is much better:

A more complete model of a non-ideal capacitor.

Mentioning ESL is critical for understanding capacitor self-resonance. Neglecting self-resonance is a major conceptual omission that is common in discussions of capacitors, yet it dominates the high frequency behavior of capacitors and often dominates how they are used in filters. Speaking of which, capacitor self resonance is not mentioned on this page! It is discussed on the Capacitor types page, along with a much more complete discussion of non-ideal electrical behavior of capacitors. The detailed discussion of the electrical characteristics of capacitors doesn't belong on the Capacitor types page and should be merged into the main Capacitor page.