This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
"Just as two or more inductors can be magnetically coupled to make a transformer, two or more charged conductors can be electrostatically coupled to make a capacitor. The mutual capacitance of two conductors is defined as the current that flows in one when the voltage across the other changes by unit voltage in unit time."
I have reverted the edits by Machtzu for the following reasons:
(1) Reactance is the imaginary part of the impedance and as such, is real:
(2) Impedance is complex in general but capacitive impedance is pure imaginary:
Thank you. Alfred Centauri 18:04, 31 August 2005 (UTC)
All the 'electric cct' stuff in this article is really to do with practical capacitors and not with the concept of capacitance. I therefore propose moving all this stuff to the capacitor page. Any comments/objections etc? Light current 17:33, 3 September 2005 (UTC)
Thanks for your vote of confidence!! ;-) Light current 18:28, 3 September 2005 (UTC) Done it! Light current 18:42, 3 September 2005 (UTC)
Never heard of it?? No neither have I. Yet this is what we are to infer exists if we believe in back emf for inductors (since capacitors and inductors are duals of each other). If a capacitor has been charged and then the leads are short circuited, a large current will flow in the opposite direction to the original charging current. This is never called a back current yet is is the exact analogy of an open circuited inductor with a magnetic field surrounding it (due to previous current in the inductor). Note that the emf generated in an open cct inductor is caused by the collapsing magnetic field previously established (or in deed any external changing magnetic field). The fact that the mag. field may have been, in the first place, generated by the inductor is neither here nor there. The inductor is not aware of this.
Also, when a capacitor is being charged, there is no mention made of the electric field generated producing a back emf, yet this is exactly what it does do. The more voltage on the plates, the more back emf generated thus giving the expected capacitor charging response by opposing the applied voltage. Why have we not heard of this? Any comments?? Light current 04:59, 4 September 2005 (UTC)
I'm not neccesarily advocating the proposed point of view on back current. I was engaging in sarcasm trying to debunk the ideas of 'back' anything and using a capacitor as a 'dual' example of an inductor. The point is, current does flow out of the capacitor but we dont call it a back current!. Light current 21:24, 4 September 2005 (UTC)
Yes, sorry. Over here people call this 'kickback' a 'back emf'. I think it's an induced voltage due to collapsing magnetic field-- this is obviously in reverse direction to the initial applied voltage, but this is OK because it is created by an 'external' field (ie the field that the coil created before it was switched off). This obeys Amperes law of induction? I think that the direction of energy flow may help us out in terms of sign of voltage/current here-- Any thoughts? Light current 22:46, 4 September 2005 (UTC)
Yes I = Cdv/dt. I is rate of charge affected by back emf in a capacitor.Hence slowing its charge rate up. Yes?? Light current 21:24, 4 September 2005 (UTC)
Sorry, I thought I mentioned a cap charging thro' a resistor-- but I may have forgotten to mention it in the excitement! (Bear in mind I'm trying to debunk the notion of 'back emf', 'back current' by saying that it can all be explained by the simple familiar equations. So I'm not putting up bait for you, I'm simply playing Devils advocate. Light current 22:52, 4 September 2005 (UTC)
Yes, you are of course strictly correct, but I dont think we should be sidelined by considering the capacitor inductance-- its complex enough as it is! Light current 23:01, 4 September 2005 (UTC)
What I was intending to say here before my brain got addled was this:
If a capacitor is being charged from a voltage source via a resistor, the changing electric flux between the plates generates a magnetic field in opposite? direction but exactly equal in magnitude to to the magnetic field that would be caused by a real current passing between the plates of the capacitor. This real current passing between the plates we call 'displacement' current. Now the question is, is this displacement current real or is it just imagined to exist because the magnetic field between the capacitor plates indicates it does? If this current actually exists, one would assume that it was in the same direction as the conduction current and gives a complete circuit for the battery to drive charge around. If it does not really exist, then charge will stack up on the top plate with nowhere to go. Now in reality, we know that charge does indeed stack up on the top plate (assuming bottom plate is earthed/ common/ 0v etc). So what does this say about displacement current -- is it a lie? No I dont think so, but the only solution to this anomaly (that I can see) is that there must be a current generated inside the capacitor in the reverse direction to that flowing in the wires outside the capacitor. So there is current apparently flowing between the plates but its cancelled by an equal but opposite current generated by the aforementioned magnetic field. This seems to me to satisfy three apparently contradictary arguments:
a) there is currrent flowing between the plates,
b) there is no current passing between the plates and
c) charge is forced to stack up on the top plate becuase it cant pass thro the dielectric. Now my brain really hurts! Light current 00:18, 6 September 2005 (UTC)
"The induced magnetic current through a capacitor due to a changing electric flux between the capacitor plates produces an electric field that opposes the change in electric flux that induced the magnetic current".
Alfred Centauri 21:02, 4 September 2005 (UTC)
LC: Sorry, but I had to revert your statement that a physical capacitor is dual to an inductor because it is not true. This is the insight I came upon this afternoon. A physical capacitor is governed (mostly) by the divergence equations in Maxwell's equations while a physical inductor is governed (mostly) by the curl equations. Thus, they are not physical duals. They operate on different physical principles. The duality in circuit theory is a mathematical duality. The amazing (to me anyhow) duality I discovered this afternoon is that there are actually two measures of inductance - one has units of henries and the other has units of farads! Similarly, there are two measures of capacitance - one in farads and the other in, you guessed it, henries. I'm still working on the presentation of these ideas in my sandbox. Alfred Centauri 02:10, 6 September 2005 (UTC)
Here's the short version. The origin of the physical non-duality is in the nature of the fields but not in the sense you might be imagining. I'm sure you heard it said that "a capacitor stores energy in the electric field" and "and inductor stores energy in the magnetic field". So yes, the fields are different in this regard. But the difference that I'm referring to is whether the field is conservative or not. In the case of the capacitor, the electric field is conservative - that is, the field is generated by a charge density. Thus, the capacitance C = Q/V refers to charge per potential difference. Further, if you exchanged electric charge for magnetic charge, the capacitor would store energy in a magnetic field and a conservative magnetic field at that. In this case, the 'capacity' to store a given amount of magnetic charge would given by weber/amp otherwise known as the henry! Alas, magnetic charge has not been found so it might not exist.
Conversely, the inductor stores energy in a non-conservative field. A non-conservative field is not associated with charge but is instead 'induced' by a current. What we usually think of as an inductor stores energy in a non-conservative magnetic field produced by an electric current (which includes charge and displacement currents). Since the closed contour integral of this non-conservative magnetic field is not necessarily zero, we refer to this integral as the magneto-motive force (mmf) measured in amps. The inductance turns out to be the ratio of the magnetic flux integral to the magnetic field integral which gives units of weber/amp - the henry.
Now, replace electric current with magnetic current and you get energy stored in an electric field. Using the same logic as above, you get that the inductance is the ratio of the electric flux integral to the electric field integral which gives units of Coulomb per volt - the farad! But - and this is crucial - the Coulomb in the numerator is not a quantity of charge - it is the total electric flux along a closed path. Likewise, the volt in the numerator is not a potential difference - it is the total electric field along a closed path otherwise known as the emf!
This is why the capacitor and inductor are not physically dual. Despite the fact that the units work out, the meaning of the units are different, e.g., using volts to measure potential difference AND emf which are quite different ideas. Alfred Centauri 03:03, 6 September 2005 (UTC)
Isn't this guy asking for a permanent block for repeated vandalism and refusing to discuss on the talk pages? Could admins please take note?-- Light current 20:20, 24 September 2005 (UTC)
There's a contradiction in our article, and I wonder if anybody thinks it is significant.
In statement (2), where is the second conductor implied by statement (1)? I think I know the answer to this question, and it will require the article to be reworded slightly.
I've been reading articles like these two [2] and [3] by Fred Erickson, which explain the difference between the self-capacitance of a conductor and the mutual capacitance of two conductors. Perhaps we need to make this distinction in our article. The value printed on a parallel-plate capacitor is the mutual capacitance between its plates, and this is good enough for most circuit designs. However, to be precise, each plate also has its own self-capacitance, which could be thought of as the capacitance between the plate and the rest of the universe. Normally, these self-capacitances are much smaller than the mutual capacitance, so they can be ignored (although they sometimes need to be considered as parasitics). However, as you increase the plate separation, the mutual capacitance drops and the self-capacitances eventually become dominant. An example of the widely separated case is the capacitance between the Earth and the Moon, as discussed in the above-mentioned articles. Here, the mutual capacitance is small (about 3 μF) and the self-capacitances (about 680 μF for the Earth, as our article says, or 710 μF by my reckoning; and 193 μF for the Moon) dominate. The total capacitance is that of the mutual capacitance in parallel with the two self-capacitances:
(Imagine an equivalent circuit with C_mutual between the two bodies, and a C_self between each body and the universe, which acts as a ground plane.) Plugging the Earth/Moon values into this, I get a C_total of about 152 μF, which is close enough to Erickson's value of 159 μF.
I think our article blurs the difference between these two types of capacitance. Any thoughts? -- Heron 19:32, 12 November 2005 (UTC)
This article has been taken from article Capacitor to replace the former 'redirect to article Capacitor'. It has enabled the appropriate categorisation of the physical quantity capacitance, without introducing inappropriate categorisation for the physical objects, capacitors. I would hope that, in due course, it may be possible to remove the 'capacitance' aspects of the capacitor article to avoid duplication. Ian Cairns 15:03, 14 Nov 2004 (UTC)
The scope of this article is capacitance. There is a substantial amount of information on capacitors in this article that is, IMHO, outside the scope of capacitance. I propose that this information be deleted or merged with the Capacitor article. Alfred Centauri 22:49, 26 May 2005 (UTC)
I'm coming from a biological background. In neurones there is an important concept called the membrane potential. In studying the action potential a very critical determining factor is the capacitance of the membrane. Now I’m not particularly qualified to write much on the topic, but it would be good to include the biological perspective on membrane capacitance. -- Amelvin 14:53, 13 May 2006 (UTC)
c is acapacitance expressed in FARAD. 1/c is invrse of capacitance & its unit is 1/F = --------
'LC': I'm not so sure about your alternate definition of capacitance. For inductance, we find the magnetic flux by integrating (B dot dS) along a closed contour that defines a bounded surface. We find that this flux is determined by the total electric current through the surface. If we have a coil of wire, the current through the wire pierces the surface N times where N is the number of turns in the coil. Thus, for a given amount of flux, the required current through the coil divided by N. The inductance is defined as the ratio of the flux to the current through the coil:
where is the flux produced by the current i alone.
If you are trying to find an analogous equation for capacitance, you would start with finding the emf by integrating (E dot dS) along a closed contour that defines a bounded surface. Find that this emf is determined by the negative of a total current through the surface. What current? Let's call it the magnetic flux current in analogy to the electric flux current (displacement current). Now multiply this result by the permittivity of the medium and then find that the ratio of the electric flux to the magnetic flux current has units of capacitance. This is your analogous equation:
Regardless, I do feel that such and alternate and non-standard 'definition' needs to be at the end of the article as an interesting footnote. Alfred Centauri 19:49, 3 September 2005 (UTC)
Give me an example of how you would apply your formula to some physical system to calculate a capacitance. Alfred Centauri 20:31, 3 September 2005 (UTC)
I'll answer your last comment first. The numerator contains the electric flux in Coulombs. The denominator contains the time rate of change of magnetic flux which has units of weber/second. But a weber is Volt-seconds. Thus so 1 weber/second = 1 Volt. Thus, the ratio is Coulomb/Volt = farad.
Now, consider this. Imagine a parallel plate capacitor with +Q on the top plate and -Q on the bottom and separated by a distance r. The electric flux that exists between the plates depends on the value of Q but not on r. On the other hand, the voltage between the plates depends on the value of Q and r. Thus, dphi/dv = dphi/dr dr/dv = 0. So, this formula for capacitance doesn't give the correct answer. If you use C = phi/V, you get the right answer for a parallel plate capacitor if phi is the flux out of a surface containing one of the plates and V is the voltage across the plates. If you have an isolated conductor, phi is the flux through a surface enclosing the conductor and V is the potential with respect to infinity. But, it is the application of Gauss Law here that gives you the form C = Q/V, not the other way around. BTW, compare the definition of inductance I gave above to the wording in the new opening sentence for the Inductance article. Alfred Centauri 21:46, 3 September 2005 (UTC)
The alternate definition in terms of the flux is incorrect. Q is not identically equal to the flux, not in cgs units, and not in SI units. At best they differ by a factor of 4pi, and even then there would need to be an explanation of what gaussian surface was being referred to.-- 24.52.254.62 16:11, 3 November 2006 (UTC)
I think that the electrical equations should use E instead of W as well as the text should refer to Energy instead of Work. The concept electrical work is barely represented on Wikipedia, whereas electrical energy is much more detailed. But, being a Swedish engineer, I'm not confident enough about this linguistic issue to make the changes myself. Mumiemonstret ( talk) 13:27, 18 December 2007 (UTC)
Diffusion capacitance is a change in charge with voltage, but that is all that it has to do with capacitance in the normal sense. In semiconductor device with a current flowing through it (an ongoing transport of charge by diffusion) there is necessarily some charge in the process of transit. If the applied voltage changes and the current in transit chges, a different amount of charge will be in transit. This change in the transiting charge is the diffusion capacitance. I think this is a different enough phenomena that it is only confusing to merge the articles. Brews ohare 03:36, 5 November 2007 (UTC)
Also, Capacitance has nothing to do with nominal capacity and the latter should not redirect to the former. - Nathan24601 ( talk) 18:32, 25 February 2008 (UTC)
Brews, That's quite a good tidy up that you did on the capacitance and displacement current section. The only reason that I touched it last night was because it was in such a bad state. For your information, the equation in question in the 1861 paper is equation (105). That equation is also mentioned, unnumbered, in the preamble to part III. The nearest modern day equivalent is Q = CV, but as I'm sure you can see, the two equations are not exactly the same. At any rate, if we differentiate either of these two versions, we will obtain the displacement current equation, which is equation (111) in the 1861 paper. I notice that in your verison on the main article, you have used the variable capacitance version. While that is technically correct, you do need to ask yourself if it is not perhaps an unneccessary complication for the immediate purposes in hand. Anyway, as you rightly acknowledge, Maxwell did not explicitly talk about charge. To get a clearer picture on Maxwell's ideas about charge, we need to look at letters which he wrote to Lord Kelvin in the late 1860's. It would seem that he had it linked to the stress associated with linear polarization of a dielectric. Hence, for the purposes of analogy, we could probably safely link 'charge' in the modern equation, to electric displacement in the Maxwell version. Capacitance then of course links to the inverse of the dielectric constant, and voltage interestingly links to electromotive force, and indeed we nowadays consider voltage and electromative force to be equivalent, whereas Maxwell's use of electromotive force was closer to the concept of electric field E. If we have a constant capacitance, then that capacitance will bear all the hall marks of the reciprocal of dielectric constant. But when we consider that the capacitance can vary, then it's meaning switches to that of being the capacity to store charge. David Tombe ( talk) 14:47, 18 November 2008 (UTC)
Brews, I've looked at your latest edits. Here's a few points to bear in mind.
(1) Equation (105) is the beginnings of Maxwell's displacement current. But it seems that since Heaviside in 1884, the concept has got tied up with equation (138) instead.
(2) Equation (138) leads us straight down the road into Gauss's law. In fact Maxwell led us down that road straight after equation (112).
(3) When Maxwell used the displacement current in his 1864 paper to derive the EM wave equation, he only derived the H equation. If he'd tried to do the E equation too, Gauss's law would have tripped him up.
(4) The point is that Maxwell's displacement current term may only be useful in wireless telegraphy where the E term can match up with the E term in Faraday's law (the -(partial)dA/dt term). In that case div E will always equal zero. Your section contains good information. I wouldn't want to delete any of it. But ask yourself 'what is the focus?'. When you have answered that, you may wish to play around a bit with the sequencing. At least you've already debunked the myth that Maxwell invented displacement current in connection with capacitors. David Tombe ( talk) 18:59, 18 November 2008 (UTC)
Brews, does capacitance depend on voltage? Anyway, keep in mind these points. Maxwell's equation (105) is all about wireless telegraphy. However his equation (138) is all ultimately about cable telegraphy, but it was Heaviside who developed that aspect later on. For the former, you want to have div E = 0, with E = -(partial)dA/dt, because that is the term in Faraday's law (or the Lorentz force) which is needed to derive the EM wave equation. For the latter you get into the realms of Gauss's law where dive E does not equal zero in general. David Tombe ( talk) 17:36, 19 November 2008 (UTC)
Brews, You've explained Maxwell's views on the elasticity very well. As regards C being a function of V, it's OK. I personally wouldn't have bothered introducing that extra complication for that particular section, but it's OK. And yes, cable telegraphy would indeed be a bit of a digression. But do bear in mind the close connection between capacitance and cable telegraphy which doesn't appear to be so with wireless telegraphy. Maxwell's displacement current dealt with the latter, but the modern equations around Q = CV deal with the former. You're making good progress with Maxwell's 1861 paper. What do you think of the centrifugal term in equation (5)? Equation (77) is actually the Lorentz force term as per equation (D) in the 1864 paper. There is no centrifugal force term in it. But I'll be interested to hear what you make of equation (5). Between the two equations, do you not see the inverse square law attractive force, the Coriolis force, the centrifugal force, and the Euler force staring out at you? Kepler's second law gets rid of the curl bits of Faraday's law and leaves us with the radial orbital equation including centrifugal force. Maxwell uses the centrifugal force to account for magnetic repulsion between like poles. David Tombe ( talk) 18:25, 19 November 2008 (UTC)
It is actually quite incorrect to say that a capacitor blocks direct current. Consider the simple example of an ideal constant current source connected to an ideal capacitor. Clearly, the capacitor does not block this current. Instead, the voltage across the capacitor changes linearly with time at a rate given by I / C. That is, the voltage across the capacitor is unbounded. Of course, a real capacitor would eventually breakdown at some voltage. Or, a real current source would fall out of its compliance range. The phenomenon described in this article as justification for the claim that capacitors block direct current is in fact the observation that the DC steady state solution for capacitor current is identically zero.
Further, consider that a circuit that includes a capacitor or inductor is not, strictly speaking, a DC circuit! However, such a circuit may or may not possess a 'DC solution' otherwise known as the steady state solution.
All of this may seem pedantic but it is nevertheless true that capacitors do not block direct current. Alfred Centauri 15:27, 11 August 2005 (UTC)
Another problem: it is stated in the AC Circuits part of the article about capacitive reactance: "Since DC has a frequency of zero, the formula confirms that capacitors completely block direct current." This is a case of extrapolating a concept beyond the point that it is valid. The concept of reactance in AC circuits is intimately tied to the notion of AC steady state where the peak amplitudes of the sinusoidal voltages and currents are constant. Thus, setting the frequency to zero is not valid for the reactance formula. Consider letting the frequency be arbitrarily close to zero. It is evident that a small peak amplitude sinusoidal current through the capacitor produces an arbitrarily large peak sinusoidal voltage across the capacitor. In the limit as f goes to zero, the peak voltage does in fact go to infinity. What must be understood is that this peak voltage is, by definition, the voltage in AC steady state which, due to the fact that the frequency is zero, is never reached in finite time. The correct interpretation of this formula is that for an AC current of zero frequency, the voltage increases with time and is unbounded as t goes to infinity - precisely the result I described above for a constant (DC) current source. Alfred Centauri 01:44, 12 August 2005 (UTC)
So your argument is that it doesn't block dc current--it just requires infinite voltage to pass dc. Similarly an open switch or a blown fuse doesn't block current, it just requires infinite (in theory, for an ideal switch) or very large (in practice, for physical element) voltage. I don't think we need to re-write all of Wikipedia taking into account thought experiments involving non-physical infinite contingencies. Ccrrccrr ( talk) 14:26, 5 January 2008 (UTC)
The statement in the article is wrong. Capacitance is the reciprocal of inductance only in the case of parallel wires (with arbitrary cross section), see Jackson, "Classical Electrodynamics". —Preceding unsigned comment added by 88.64.74.16 ( talk) 09:06, 24 May 2009 (UTC)
A volt is one joule of energy per coulomb of charge. The energy that results from volts is volts times the number of charges () The work required to charge a capacitor equals one-half of VQ:
VQ is twice a capacitor's charging energy. Within a capacitor, Q does not seem to represent electrons and V does not seem to be energy per Q. Otherwise, the energy due to a capacitor's electrons would be V joules per coulomb of electrons, regardless of any particular value of Q or V.
Volt was originally defined as 1/1.434 of the emf of a Clark cell. This definition assumed that one electron per volt producing event occurred in a Clark cell.
In a point charge simulation of voltage, capacitors contain an equal number of plus and minus charges. Capacitor discharge converts pairs of opposite charges into other energy. Therefore, in the definition of capacitance, each Q represents a pair of charged particles. -- Vze2wgsm1 ( talk) 13:41, 24 May 2009 (UTC)
The section Capacitance#Capacitance and 'displacement current' that intervenes between the lead and the more intelligible content sections seems to be the work product of Brews ohare under the influence of David Tombe, per the discussion above. It is sourced only to Maxwell's primary writings, and is all about interpretations thereof. Can't we have a simple section, later instead of here, on a modern statement of the relevant EM theory and displacement current, with links to the main articles? Does anyone understand a reason why it would be appropriate to have the Maxwell quotes there, or why we might want a lengthy diversion about displacement current before talking about the topic of the article? Dicklyon ( talk) 05:10, 10 September 2009 (UTC)
The section is about Maxwell's work on capacitance and displacement. He's a pretty good source. How about rolling up your sleeves and looking further if you are interested? Brews ohare ( talk) 13:05, 10 September 2009 (UTC)
For now, I've taken it out. If the selection of quotes and the interpretive comments can be sourced and tied directly to capacitance, something like this could go back in. I'll put it below as a talk section for now, and tagged a few places where citations to secondary sources would be appropriate:
I firmly think that stating stray capacitance is unwanted is misleading and a biased view. There are several instances when it is useful. Maybe it just needs to be switched from such a blanket statement to it is often undesired. Tempust ( talk) 18:30, 17 November 2009 (UTC)
In the leading section, where the article reads "Consider a capacitance C, holding a charge +q on one plate and −q on the other.": surely this should read "Consider a parallel plate capacitor C, holding a charge +q on one plate and −q on the other." ? JMatopos ( talk) 10:24, 23 March 2011 (UTC)
The following discussion has been moved to this page from a user talk page
Hi Materialscientist, I took a look at the reference you cited and looked at how it defined self-capacitance, and I can only say that I disagree with that definition. The electric charge required to raise the electric potential by one volt is still an electric charge, and therefore it is not a capacitance.
My formulation may be using bad English, but the current formulation is incorrect. If you do think my formulation is bad, you may instead help me to improve it. — Kri ( talk) 05:08, 4 December 2011 (UTC)
Should the first sentence say that capacitance is the ability to store charge? or should it say energy? I am under the impression that a capacitor stores energy and charges are not actually stored. Thanks, Vokesk ( talk) 00:44, 10 April 2012 (UTC)
The new text is:
The old text was something like:
Both are correct. The old text was a bit terse, but it wasn't backwards, and it did have the considerable merit of including the words is and per (or as I reinstated it for each). The new text on its own is ambiguous - it could equally well apply to reciprocal-farads. The notion that 1F & 1C => 1V rather suggests 2F & 1C => 2V. If you don't like my compromise wording, could you take another stab at this definition yourself? -- catslash ( talk) 15:51, 4 May 2012 (UTC)
In the section on frequency-dependent capacitors, there is an inconsistency in the use of the term C(ω). In Eq. (3) (the third equation in this section), where we see the term G + jωC(ω), this frequency-dependent capacitance value is real. It comes only from ε' (the real part of the complex ε). In Eq. (4), the term C(ω) is complex, and it comes from ε (which is complex in general). Therefore, the same notation is being used to describe two different things. Elee1l5 ( talk) 17:06, 24 September 2013 (UTC)
'Capacitors' section with formula was missing units; I put them in. Between people using cgs instead of mks, microns instead of meters, Farads per centimeter instead of Farads per meter, it's easy to get mixed up without rigorous definition. 71.139.169.27 ( talk) 04:26, 14 October 2013 (UTC)
It is not a good idea to say, for instance, that A is the area in square meters. A is an area and as such has a value and a unit, the unit may be square centimeters or anything else. radical_in_all_things ( talk) 19:24, 14 October 2013 (UTC)
Stated capacitance for this problem uses an approximation applied inconsistently between the argument of the and the . — Preceding unsigned comment added by 50.131.141.62 ( talk) 19:43, 11 March 2012 (UTC)
In the cited reference (Jackson, 2d Ed.), the capacitance is given as . This appears to disagree with the value given on the Wikipedia page, , unless some approximation is made to get rid of the -1. This approximation does not appear to have been made within the , however. — Preceding unsigned comment added by 50.131.141.62 ( talk) 06:58, 12 March 2012 (UTC)
It only appears so. Unfortunately Jackson doesn't use the simplest expression. The expressions are equivalent without approximation because of radical_in_all_things ( talk) 17:19, 12 March 2012 (UTC)
It'd be nice to add such hyperbolic trig identities to the wiki page on inverse hyperbolic functions. — Preceding unsigned comment added by 50.131.141.62 ( talk) 17:19, 14 March 2012 (UTC) I use of Image Theorem for sol this problem.(A straight conducting wire of radius a is parallel to and at height h from the surface of the earth). I have replacement alone D=2h in formula.thereupon do not to change coefficient of 1 to 2 in numerator. — Preceding unsigned comment added by Ghorbanib ( talk • contribs) 10:39, 15 November 2013 (UTC) The explanation for the factor 2 is the same as in Inductance#Method of images. radical_in_all_things ( talk) 16:54, 15 November 2013 (UTC)
Max energy in a capacitor moved here from article page Not really relevant to subject of capacitance
If the maximum voltage a capacitor can withstand is (equal to where is the dielectric strength), then the maximum energy it can store is:
— Preceding unsigned comment added by Light current ( talk • contribs) 01:43, 6 September 2005 (UTC)
The physicist James Clerk Maxwell invented the concept of displacement current in his 1861 paper in connection with the displacement of electrical particles: citation needed [1]
“ | Bodies which do not permit a current of electricity to flow through them are called insulators. But though electricity does not flow through them, electrical effects are propagated through them … a dielectric is like an elastic membrane which may be impervious to the fluid, but transmits the pressure of the fluid on one side to that on the other. | ” |
“ | Electromotive force acting on a dielectric produces a state of polarization of its parts...capable of being described as a state in which every particle has its poles in opposite conditions. | ” |
“ | ...we may conceive that the electricity in each molecule is so displaced that one side is rendered positively, and the other negatively electrical, but that the electricity remains entirety connected with the molecule, and does not pass from one molecule to another. | ” |
“ | This displacement does not amount to a current, because when it attains a certain value it remains constant, but it is the commencement of a current, and its variations constitute currents in the positive or negative direction, according as the displacement is increasing or diminishing. | ” |
“ | ...when the electromotive force varies, the electric displacement also varies. But a variation of displacement is equivalent to a current, and this current must be taken into account... | ” |
He then added displacement current to Ampère's law. citation needed [2] Maxwell's correction to Ampère's law remains valid today, and is expressed in the form:
with Jf the current density due to motion of free charges and the displacement current density given as ∂D/∂t with the electric displacement field D related to the electrical polarization density of the medium P as:
Here ε0 is the electric constant. The polarization is the contribution described by Maxwell in the quotations above, and is due to the separation and alignment of charge in the material that is not free to transport, but is free to align with an applied electric field, and to move over atomic dimensions, for example, by stretching of molecules. (This polarization in response to the field actually screens the dielectric from the electric field, resulting in a lower field the greater the polarization of the medium. citation needed See the figure.) In simple materials, the polarization is proportional to the electric field and an adequate approximation is:
with εr the relative static permittivity of the material. When there exists no material medium, εr = 1, so there still exists a displacement field when there is no medium present.
To connect the displacement to charge, Gauss's law is used, which in integral form relates the charge in a region to the surface integral over an enclosing surface Σ of the component of D normal to the surface:
where a vector dot product is indicated by the "·".
To relate this expression to a capacitor, the surface Σ is made to enclose the dielectric medium and one of the two electrodes of the capacitor. The electrode contains the net charge upon the capacitor, and the dielectric medium is charge neutral. Referring to the figure, suppose initially the dipoles in the dielectric are unpolarized, as on the left side of the figure. The electric field due to the charge on the capacitor plates is the same as though the dielectric were not present. Next, suppose the dipoles are able to respond to the applied field and become polarized, as on the right side of the figure. Then the field from the extended dipole opposes that of the electrodes and the electric field inside the dielectric decreases. Suppose the left panel corresponds to an initial time just after the field is applied and the dipole has not had time to respond, while on the right is a later time when the dipoles are in the process of becoming extended. During this extension of the dipoles, a displacement current flows across the Gaussian surface. The more polarizable the medium, the more current for a given voltage, and the greater the capacitance. The net displacement current I through the region Σ is related to the displacement current density through the equation:
(The partial time derivative is meant to emphasize that the spatial variables in D(r, t) are held fixed.) This equation includes current through the region Σ related to polarization of the medium, and is connected to capacitance and an applied voltage:
where C is capacitance, Q is charge, and V is the applied voltage responsible for the field causing the polarization of the medium inside the capacitor. For some materials represented by complicated behavior of D, the capacitance can be a function of voltage and may exhibit time dependence related to the ability of the medium to respond to the signal (see subsections below).
It should be mentioned that when there is no material medium in the capacitor, the displacement is not zero, but D = ε0E. Consequently, a capacitance still is present. For example, a system of metal electrodes in free space may possess a capacitance.
Maxwell never used the term electric charge, citation needed but he did refer to the "distribution of electricity in a body" and to the "quantity of electricity". Capacity C was stated in his equation (138) for two surfaces bearing equal and opposite quantities of electricity e and electric tensions or potentials ψ1 and ψ2 as the ratio C = e / (ψ1 - ψ2). Then the effect upon C of inserting a dielectric between the plates was determined. [3]
Today, capacitance is viewed primarily in terms of the capacity for storage of charge, whereas Maxwell's paper stressed the current that flowed through a capacitor. citation needed He calculated this current focusing upon the specific calculation of polarization for an "elastic sphere" distorting under an applied field and resisting deformation by virtue of its elastic properties, and the current that flowed when this state of polarization altered. citation needed The modern approach attempts to treat the polarization of materials by modeling the microscopic events contributing to the displacement field using quantum theory: for example, see below. citation needed
References
— Preceding unsigned comment added by Dicklyon ( talk • contribs) 18:05, 18 September 2009 (UTC)
What is the difference between capacitance and energy density?-- Wyn.junior ( talk) 03:01, 26 February 2014 (UTC)
I added the "cmplx" subscript to denote complex capacitance. Elee1l5 ( talk) 21:09, 9 March 2014 (UTC)
The main article currently says "If the charges on the plates are +q and −q", then C = q/V They should explain why a charge difference of '2q' doesn't result in (2q)/V. This means : why q/V and not (2q)/V? KorgBoy ( talk) 23:46, 6 July 2017 (UTC)
In Wikipedia article "Farad", the character "C" is used for the Electric charge. In the article "Capacitance", the same character "C" is used for Capacitance. This is confusing.
Regards, Boris Spasov (bspasov@yahoo.com). — Preceding unsigned comment added by 107.184.14.103 ( talk) 05:48, 24 June 2018 (UTC)
This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
"Just as two or more inductors can be magnetically coupled to make a transformer, two or more charged conductors can be electrostatically coupled to make a capacitor. The mutual capacitance of two conductors is defined as the current that flows in one when the voltage across the other changes by unit voltage in unit time."
I have reverted the edits by Machtzu for the following reasons:
(1) Reactance is the imaginary part of the impedance and as such, is real:
(2) Impedance is complex in general but capacitive impedance is pure imaginary:
Thank you. Alfred Centauri 18:04, 31 August 2005 (UTC)
All the 'electric cct' stuff in this article is really to do with practical capacitors and not with the concept of capacitance. I therefore propose moving all this stuff to the capacitor page. Any comments/objections etc? Light current 17:33, 3 September 2005 (UTC)
Thanks for your vote of confidence!! ;-) Light current 18:28, 3 September 2005 (UTC) Done it! Light current 18:42, 3 September 2005 (UTC)
Never heard of it?? No neither have I. Yet this is what we are to infer exists if we believe in back emf for inductors (since capacitors and inductors are duals of each other). If a capacitor has been charged and then the leads are short circuited, a large current will flow in the opposite direction to the original charging current. This is never called a back current yet is is the exact analogy of an open circuited inductor with a magnetic field surrounding it (due to previous current in the inductor). Note that the emf generated in an open cct inductor is caused by the collapsing magnetic field previously established (or in deed any external changing magnetic field). The fact that the mag. field may have been, in the first place, generated by the inductor is neither here nor there. The inductor is not aware of this.
Also, when a capacitor is being charged, there is no mention made of the electric field generated producing a back emf, yet this is exactly what it does do. The more voltage on the plates, the more back emf generated thus giving the expected capacitor charging response by opposing the applied voltage. Why have we not heard of this? Any comments?? Light current 04:59, 4 September 2005 (UTC)
I'm not neccesarily advocating the proposed point of view on back current. I was engaging in sarcasm trying to debunk the ideas of 'back' anything and using a capacitor as a 'dual' example of an inductor. The point is, current does flow out of the capacitor but we dont call it a back current!. Light current 21:24, 4 September 2005 (UTC)
Yes, sorry. Over here people call this 'kickback' a 'back emf'. I think it's an induced voltage due to collapsing magnetic field-- this is obviously in reverse direction to the initial applied voltage, but this is OK because it is created by an 'external' field (ie the field that the coil created before it was switched off). This obeys Amperes law of induction? I think that the direction of energy flow may help us out in terms of sign of voltage/current here-- Any thoughts? Light current 22:46, 4 September 2005 (UTC)
Yes I = Cdv/dt. I is rate of charge affected by back emf in a capacitor.Hence slowing its charge rate up. Yes?? Light current 21:24, 4 September 2005 (UTC)
Sorry, I thought I mentioned a cap charging thro' a resistor-- but I may have forgotten to mention it in the excitement! (Bear in mind I'm trying to debunk the notion of 'back emf', 'back current' by saying that it can all be explained by the simple familiar equations. So I'm not putting up bait for you, I'm simply playing Devils advocate. Light current 22:52, 4 September 2005 (UTC)
Yes, you are of course strictly correct, but I dont think we should be sidelined by considering the capacitor inductance-- its complex enough as it is! Light current 23:01, 4 September 2005 (UTC)
What I was intending to say here before my brain got addled was this:
If a capacitor is being charged from a voltage source via a resistor, the changing electric flux between the plates generates a magnetic field in opposite? direction but exactly equal in magnitude to to the magnetic field that would be caused by a real current passing between the plates of the capacitor. This real current passing between the plates we call 'displacement' current. Now the question is, is this displacement current real or is it just imagined to exist because the magnetic field between the capacitor plates indicates it does? If this current actually exists, one would assume that it was in the same direction as the conduction current and gives a complete circuit for the battery to drive charge around. If it does not really exist, then charge will stack up on the top plate with nowhere to go. Now in reality, we know that charge does indeed stack up on the top plate (assuming bottom plate is earthed/ common/ 0v etc). So what does this say about displacement current -- is it a lie? No I dont think so, but the only solution to this anomaly (that I can see) is that there must be a current generated inside the capacitor in the reverse direction to that flowing in the wires outside the capacitor. So there is current apparently flowing between the plates but its cancelled by an equal but opposite current generated by the aforementioned magnetic field. This seems to me to satisfy three apparently contradictary arguments:
a) there is currrent flowing between the plates,
b) there is no current passing between the plates and
c) charge is forced to stack up on the top plate becuase it cant pass thro the dielectric. Now my brain really hurts! Light current 00:18, 6 September 2005 (UTC)
"The induced magnetic current through a capacitor due to a changing electric flux between the capacitor plates produces an electric field that opposes the change in electric flux that induced the magnetic current".
Alfred Centauri 21:02, 4 September 2005 (UTC)
LC: Sorry, but I had to revert your statement that a physical capacitor is dual to an inductor because it is not true. This is the insight I came upon this afternoon. A physical capacitor is governed (mostly) by the divergence equations in Maxwell's equations while a physical inductor is governed (mostly) by the curl equations. Thus, they are not physical duals. They operate on different physical principles. The duality in circuit theory is a mathematical duality. The amazing (to me anyhow) duality I discovered this afternoon is that there are actually two measures of inductance - one has units of henries and the other has units of farads! Similarly, there are two measures of capacitance - one in farads and the other in, you guessed it, henries. I'm still working on the presentation of these ideas in my sandbox. Alfred Centauri 02:10, 6 September 2005 (UTC)
Here's the short version. The origin of the physical non-duality is in the nature of the fields but not in the sense you might be imagining. I'm sure you heard it said that "a capacitor stores energy in the electric field" and "and inductor stores energy in the magnetic field". So yes, the fields are different in this regard. But the difference that I'm referring to is whether the field is conservative or not. In the case of the capacitor, the electric field is conservative - that is, the field is generated by a charge density. Thus, the capacitance C = Q/V refers to charge per potential difference. Further, if you exchanged electric charge for magnetic charge, the capacitor would store energy in a magnetic field and a conservative magnetic field at that. In this case, the 'capacity' to store a given amount of magnetic charge would given by weber/amp otherwise known as the henry! Alas, magnetic charge has not been found so it might not exist.
Conversely, the inductor stores energy in a non-conservative field. A non-conservative field is not associated with charge but is instead 'induced' by a current. What we usually think of as an inductor stores energy in a non-conservative magnetic field produced by an electric current (which includes charge and displacement currents). Since the closed contour integral of this non-conservative magnetic field is not necessarily zero, we refer to this integral as the magneto-motive force (mmf) measured in amps. The inductance turns out to be the ratio of the magnetic flux integral to the magnetic field integral which gives units of weber/amp - the henry.
Now, replace electric current with magnetic current and you get energy stored in an electric field. Using the same logic as above, you get that the inductance is the ratio of the electric flux integral to the electric field integral which gives units of Coulomb per volt - the farad! But - and this is crucial - the Coulomb in the numerator is not a quantity of charge - it is the total electric flux along a closed path. Likewise, the volt in the numerator is not a potential difference - it is the total electric field along a closed path otherwise known as the emf!
This is why the capacitor and inductor are not physically dual. Despite the fact that the units work out, the meaning of the units are different, e.g., using volts to measure potential difference AND emf which are quite different ideas. Alfred Centauri 03:03, 6 September 2005 (UTC)
Isn't this guy asking for a permanent block for repeated vandalism and refusing to discuss on the talk pages? Could admins please take note?-- Light current 20:20, 24 September 2005 (UTC)
There's a contradiction in our article, and I wonder if anybody thinks it is significant.
In statement (2), where is the second conductor implied by statement (1)? I think I know the answer to this question, and it will require the article to be reworded slightly.
I've been reading articles like these two [2] and [3] by Fred Erickson, which explain the difference between the self-capacitance of a conductor and the mutual capacitance of two conductors. Perhaps we need to make this distinction in our article. The value printed on a parallel-plate capacitor is the mutual capacitance between its plates, and this is good enough for most circuit designs. However, to be precise, each plate also has its own self-capacitance, which could be thought of as the capacitance between the plate and the rest of the universe. Normally, these self-capacitances are much smaller than the mutual capacitance, so they can be ignored (although they sometimes need to be considered as parasitics). However, as you increase the plate separation, the mutual capacitance drops and the self-capacitances eventually become dominant. An example of the widely separated case is the capacitance between the Earth and the Moon, as discussed in the above-mentioned articles. Here, the mutual capacitance is small (about 3 μF) and the self-capacitances (about 680 μF for the Earth, as our article says, or 710 μF by my reckoning; and 193 μF for the Moon) dominate. The total capacitance is that of the mutual capacitance in parallel with the two self-capacitances:
(Imagine an equivalent circuit with C_mutual between the two bodies, and a C_self between each body and the universe, which acts as a ground plane.) Plugging the Earth/Moon values into this, I get a C_total of about 152 μF, which is close enough to Erickson's value of 159 μF.
I think our article blurs the difference between these two types of capacitance. Any thoughts? -- Heron 19:32, 12 November 2005 (UTC)
This article has been taken from article Capacitor to replace the former 'redirect to article Capacitor'. It has enabled the appropriate categorisation of the physical quantity capacitance, without introducing inappropriate categorisation for the physical objects, capacitors. I would hope that, in due course, it may be possible to remove the 'capacitance' aspects of the capacitor article to avoid duplication. Ian Cairns 15:03, 14 Nov 2004 (UTC)
The scope of this article is capacitance. There is a substantial amount of information on capacitors in this article that is, IMHO, outside the scope of capacitance. I propose that this information be deleted or merged with the Capacitor article. Alfred Centauri 22:49, 26 May 2005 (UTC)
I'm coming from a biological background. In neurones there is an important concept called the membrane potential. In studying the action potential a very critical determining factor is the capacitance of the membrane. Now I’m not particularly qualified to write much on the topic, but it would be good to include the biological perspective on membrane capacitance. -- Amelvin 14:53, 13 May 2006 (UTC)
c is acapacitance expressed in FARAD. 1/c is invrse of capacitance & its unit is 1/F = --------
'LC': I'm not so sure about your alternate definition of capacitance. For inductance, we find the magnetic flux by integrating (B dot dS) along a closed contour that defines a bounded surface. We find that this flux is determined by the total electric current through the surface. If we have a coil of wire, the current through the wire pierces the surface N times where N is the number of turns in the coil. Thus, for a given amount of flux, the required current through the coil divided by N. The inductance is defined as the ratio of the flux to the current through the coil:
where is the flux produced by the current i alone.
If you are trying to find an analogous equation for capacitance, you would start with finding the emf by integrating (E dot dS) along a closed contour that defines a bounded surface. Find that this emf is determined by the negative of a total current through the surface. What current? Let's call it the magnetic flux current in analogy to the electric flux current (displacement current). Now multiply this result by the permittivity of the medium and then find that the ratio of the electric flux to the magnetic flux current has units of capacitance. This is your analogous equation:
Regardless, I do feel that such and alternate and non-standard 'definition' needs to be at the end of the article as an interesting footnote. Alfred Centauri 19:49, 3 September 2005 (UTC)
Give me an example of how you would apply your formula to some physical system to calculate a capacitance. Alfred Centauri 20:31, 3 September 2005 (UTC)
I'll answer your last comment first. The numerator contains the electric flux in Coulombs. The denominator contains the time rate of change of magnetic flux which has units of weber/second. But a weber is Volt-seconds. Thus so 1 weber/second = 1 Volt. Thus, the ratio is Coulomb/Volt = farad.
Now, consider this. Imagine a parallel plate capacitor with +Q on the top plate and -Q on the bottom and separated by a distance r. The electric flux that exists between the plates depends on the value of Q but not on r. On the other hand, the voltage between the plates depends on the value of Q and r. Thus, dphi/dv = dphi/dr dr/dv = 0. So, this formula for capacitance doesn't give the correct answer. If you use C = phi/V, you get the right answer for a parallel plate capacitor if phi is the flux out of a surface containing one of the plates and V is the voltage across the plates. If you have an isolated conductor, phi is the flux through a surface enclosing the conductor and V is the potential with respect to infinity. But, it is the application of Gauss Law here that gives you the form C = Q/V, not the other way around. BTW, compare the definition of inductance I gave above to the wording in the new opening sentence for the Inductance article. Alfred Centauri 21:46, 3 September 2005 (UTC)
The alternate definition in terms of the flux is incorrect. Q is not identically equal to the flux, not in cgs units, and not in SI units. At best they differ by a factor of 4pi, and even then there would need to be an explanation of what gaussian surface was being referred to.-- 24.52.254.62 16:11, 3 November 2006 (UTC)
I think that the electrical equations should use E instead of W as well as the text should refer to Energy instead of Work. The concept electrical work is barely represented on Wikipedia, whereas electrical energy is much more detailed. But, being a Swedish engineer, I'm not confident enough about this linguistic issue to make the changes myself. Mumiemonstret ( talk) 13:27, 18 December 2007 (UTC)
Diffusion capacitance is a change in charge with voltage, but that is all that it has to do with capacitance in the normal sense. In semiconductor device with a current flowing through it (an ongoing transport of charge by diffusion) there is necessarily some charge in the process of transit. If the applied voltage changes and the current in transit chges, a different amount of charge will be in transit. This change in the transiting charge is the diffusion capacitance. I think this is a different enough phenomena that it is only confusing to merge the articles. Brews ohare 03:36, 5 November 2007 (UTC)
Also, Capacitance has nothing to do with nominal capacity and the latter should not redirect to the former. - Nathan24601 ( talk) 18:32, 25 February 2008 (UTC)
Brews, That's quite a good tidy up that you did on the capacitance and displacement current section. The only reason that I touched it last night was because it was in such a bad state. For your information, the equation in question in the 1861 paper is equation (105). That equation is also mentioned, unnumbered, in the preamble to part III. The nearest modern day equivalent is Q = CV, but as I'm sure you can see, the two equations are not exactly the same. At any rate, if we differentiate either of these two versions, we will obtain the displacement current equation, which is equation (111) in the 1861 paper. I notice that in your verison on the main article, you have used the variable capacitance version. While that is technically correct, you do need to ask yourself if it is not perhaps an unneccessary complication for the immediate purposes in hand. Anyway, as you rightly acknowledge, Maxwell did not explicitly talk about charge. To get a clearer picture on Maxwell's ideas about charge, we need to look at letters which he wrote to Lord Kelvin in the late 1860's. It would seem that he had it linked to the stress associated with linear polarization of a dielectric. Hence, for the purposes of analogy, we could probably safely link 'charge' in the modern equation, to electric displacement in the Maxwell version. Capacitance then of course links to the inverse of the dielectric constant, and voltage interestingly links to electromotive force, and indeed we nowadays consider voltage and electromative force to be equivalent, whereas Maxwell's use of electromotive force was closer to the concept of electric field E. If we have a constant capacitance, then that capacitance will bear all the hall marks of the reciprocal of dielectric constant. But when we consider that the capacitance can vary, then it's meaning switches to that of being the capacity to store charge. David Tombe ( talk) 14:47, 18 November 2008 (UTC)
Brews, I've looked at your latest edits. Here's a few points to bear in mind.
(1) Equation (105) is the beginnings of Maxwell's displacement current. But it seems that since Heaviside in 1884, the concept has got tied up with equation (138) instead.
(2) Equation (138) leads us straight down the road into Gauss's law. In fact Maxwell led us down that road straight after equation (112).
(3) When Maxwell used the displacement current in his 1864 paper to derive the EM wave equation, he only derived the H equation. If he'd tried to do the E equation too, Gauss's law would have tripped him up.
(4) The point is that Maxwell's displacement current term may only be useful in wireless telegraphy where the E term can match up with the E term in Faraday's law (the -(partial)dA/dt term). In that case div E will always equal zero. Your section contains good information. I wouldn't want to delete any of it. But ask yourself 'what is the focus?'. When you have answered that, you may wish to play around a bit with the sequencing. At least you've already debunked the myth that Maxwell invented displacement current in connection with capacitors. David Tombe ( talk) 18:59, 18 November 2008 (UTC)
Brews, does capacitance depend on voltage? Anyway, keep in mind these points. Maxwell's equation (105) is all about wireless telegraphy. However his equation (138) is all ultimately about cable telegraphy, but it was Heaviside who developed that aspect later on. For the former, you want to have div E = 0, with E = -(partial)dA/dt, because that is the term in Faraday's law (or the Lorentz force) which is needed to derive the EM wave equation. For the latter you get into the realms of Gauss's law where dive E does not equal zero in general. David Tombe ( talk) 17:36, 19 November 2008 (UTC)
Brews, You've explained Maxwell's views on the elasticity very well. As regards C being a function of V, it's OK. I personally wouldn't have bothered introducing that extra complication for that particular section, but it's OK. And yes, cable telegraphy would indeed be a bit of a digression. But do bear in mind the close connection between capacitance and cable telegraphy which doesn't appear to be so with wireless telegraphy. Maxwell's displacement current dealt with the latter, but the modern equations around Q = CV deal with the former. You're making good progress with Maxwell's 1861 paper. What do you think of the centrifugal term in equation (5)? Equation (77) is actually the Lorentz force term as per equation (D) in the 1864 paper. There is no centrifugal force term in it. But I'll be interested to hear what you make of equation (5). Between the two equations, do you not see the inverse square law attractive force, the Coriolis force, the centrifugal force, and the Euler force staring out at you? Kepler's second law gets rid of the curl bits of Faraday's law and leaves us with the radial orbital equation including centrifugal force. Maxwell uses the centrifugal force to account for magnetic repulsion between like poles. David Tombe ( talk) 18:25, 19 November 2008 (UTC)
It is actually quite incorrect to say that a capacitor blocks direct current. Consider the simple example of an ideal constant current source connected to an ideal capacitor. Clearly, the capacitor does not block this current. Instead, the voltage across the capacitor changes linearly with time at a rate given by I / C. That is, the voltage across the capacitor is unbounded. Of course, a real capacitor would eventually breakdown at some voltage. Or, a real current source would fall out of its compliance range. The phenomenon described in this article as justification for the claim that capacitors block direct current is in fact the observation that the DC steady state solution for capacitor current is identically zero.
Further, consider that a circuit that includes a capacitor or inductor is not, strictly speaking, a DC circuit! However, such a circuit may or may not possess a 'DC solution' otherwise known as the steady state solution.
All of this may seem pedantic but it is nevertheless true that capacitors do not block direct current. Alfred Centauri 15:27, 11 August 2005 (UTC)
Another problem: it is stated in the AC Circuits part of the article about capacitive reactance: "Since DC has a frequency of zero, the formula confirms that capacitors completely block direct current." This is a case of extrapolating a concept beyond the point that it is valid. The concept of reactance in AC circuits is intimately tied to the notion of AC steady state where the peak amplitudes of the sinusoidal voltages and currents are constant. Thus, setting the frequency to zero is not valid for the reactance formula. Consider letting the frequency be arbitrarily close to zero. It is evident that a small peak amplitude sinusoidal current through the capacitor produces an arbitrarily large peak sinusoidal voltage across the capacitor. In the limit as f goes to zero, the peak voltage does in fact go to infinity. What must be understood is that this peak voltage is, by definition, the voltage in AC steady state which, due to the fact that the frequency is zero, is never reached in finite time. The correct interpretation of this formula is that for an AC current of zero frequency, the voltage increases with time and is unbounded as t goes to infinity - precisely the result I described above for a constant (DC) current source. Alfred Centauri 01:44, 12 August 2005 (UTC)
So your argument is that it doesn't block dc current--it just requires infinite voltage to pass dc. Similarly an open switch or a blown fuse doesn't block current, it just requires infinite (in theory, for an ideal switch) or very large (in practice, for physical element) voltage. I don't think we need to re-write all of Wikipedia taking into account thought experiments involving non-physical infinite contingencies. Ccrrccrr ( talk) 14:26, 5 January 2008 (UTC)
The statement in the article is wrong. Capacitance is the reciprocal of inductance only in the case of parallel wires (with arbitrary cross section), see Jackson, "Classical Electrodynamics". —Preceding unsigned comment added by 88.64.74.16 ( talk) 09:06, 24 May 2009 (UTC)
A volt is one joule of energy per coulomb of charge. The energy that results from volts is volts times the number of charges () The work required to charge a capacitor equals one-half of VQ:
VQ is twice a capacitor's charging energy. Within a capacitor, Q does not seem to represent electrons and V does not seem to be energy per Q. Otherwise, the energy due to a capacitor's electrons would be V joules per coulomb of electrons, regardless of any particular value of Q or V.
Volt was originally defined as 1/1.434 of the emf of a Clark cell. This definition assumed that one electron per volt producing event occurred in a Clark cell.
In a point charge simulation of voltage, capacitors contain an equal number of plus and minus charges. Capacitor discharge converts pairs of opposite charges into other energy. Therefore, in the definition of capacitance, each Q represents a pair of charged particles. -- Vze2wgsm1 ( talk) 13:41, 24 May 2009 (UTC)
The section Capacitance#Capacitance and 'displacement current' that intervenes between the lead and the more intelligible content sections seems to be the work product of Brews ohare under the influence of David Tombe, per the discussion above. It is sourced only to Maxwell's primary writings, and is all about interpretations thereof. Can't we have a simple section, later instead of here, on a modern statement of the relevant EM theory and displacement current, with links to the main articles? Does anyone understand a reason why it would be appropriate to have the Maxwell quotes there, or why we might want a lengthy diversion about displacement current before talking about the topic of the article? Dicklyon ( talk) 05:10, 10 September 2009 (UTC)
The section is about Maxwell's work on capacitance and displacement. He's a pretty good source. How about rolling up your sleeves and looking further if you are interested? Brews ohare ( talk) 13:05, 10 September 2009 (UTC)
For now, I've taken it out. If the selection of quotes and the interpretive comments can be sourced and tied directly to capacitance, something like this could go back in. I'll put it below as a talk section for now, and tagged a few places where citations to secondary sources would be appropriate:
I firmly think that stating stray capacitance is unwanted is misleading and a biased view. There are several instances when it is useful. Maybe it just needs to be switched from such a blanket statement to it is often undesired. Tempust ( talk) 18:30, 17 November 2009 (UTC)
In the leading section, where the article reads "Consider a capacitance C, holding a charge +q on one plate and −q on the other.": surely this should read "Consider a parallel plate capacitor C, holding a charge +q on one plate and −q on the other." ? JMatopos ( talk) 10:24, 23 March 2011 (UTC)
The following discussion has been moved to this page from a user talk page
Hi Materialscientist, I took a look at the reference you cited and looked at how it defined self-capacitance, and I can only say that I disagree with that definition. The electric charge required to raise the electric potential by one volt is still an electric charge, and therefore it is not a capacitance.
My formulation may be using bad English, but the current formulation is incorrect. If you do think my formulation is bad, you may instead help me to improve it. — Kri ( talk) 05:08, 4 December 2011 (UTC)
Should the first sentence say that capacitance is the ability to store charge? or should it say energy? I am under the impression that a capacitor stores energy and charges are not actually stored. Thanks, Vokesk ( talk) 00:44, 10 April 2012 (UTC)
The new text is:
The old text was something like:
Both are correct. The old text was a bit terse, but it wasn't backwards, and it did have the considerable merit of including the words is and per (or as I reinstated it for each). The new text on its own is ambiguous - it could equally well apply to reciprocal-farads. The notion that 1F & 1C => 1V rather suggests 2F & 1C => 2V. If you don't like my compromise wording, could you take another stab at this definition yourself? -- catslash ( talk) 15:51, 4 May 2012 (UTC)
In the section on frequency-dependent capacitors, there is an inconsistency in the use of the term C(ω). In Eq. (3) (the third equation in this section), where we see the term G + jωC(ω), this frequency-dependent capacitance value is real. It comes only from ε' (the real part of the complex ε). In Eq. (4), the term C(ω) is complex, and it comes from ε (which is complex in general). Therefore, the same notation is being used to describe two different things. Elee1l5 ( talk) 17:06, 24 September 2013 (UTC)
'Capacitors' section with formula was missing units; I put them in. Between people using cgs instead of mks, microns instead of meters, Farads per centimeter instead of Farads per meter, it's easy to get mixed up without rigorous definition. 71.139.169.27 ( talk) 04:26, 14 October 2013 (UTC)
It is not a good idea to say, for instance, that A is the area in square meters. A is an area and as such has a value and a unit, the unit may be square centimeters or anything else. radical_in_all_things ( talk) 19:24, 14 October 2013 (UTC)
Stated capacitance for this problem uses an approximation applied inconsistently between the argument of the and the . — Preceding unsigned comment added by 50.131.141.62 ( talk) 19:43, 11 March 2012 (UTC)
In the cited reference (Jackson, 2d Ed.), the capacitance is given as . This appears to disagree with the value given on the Wikipedia page, , unless some approximation is made to get rid of the -1. This approximation does not appear to have been made within the , however. — Preceding unsigned comment added by 50.131.141.62 ( talk) 06:58, 12 March 2012 (UTC)
It only appears so. Unfortunately Jackson doesn't use the simplest expression. The expressions are equivalent without approximation because of radical_in_all_things ( talk) 17:19, 12 March 2012 (UTC)
It'd be nice to add such hyperbolic trig identities to the wiki page on inverse hyperbolic functions. — Preceding unsigned comment added by 50.131.141.62 ( talk) 17:19, 14 March 2012 (UTC) I use of Image Theorem for sol this problem.(A straight conducting wire of radius a is parallel to and at height h from the surface of the earth). I have replacement alone D=2h in formula.thereupon do not to change coefficient of 1 to 2 in numerator. — Preceding unsigned comment added by Ghorbanib ( talk • contribs) 10:39, 15 November 2013 (UTC) The explanation for the factor 2 is the same as in Inductance#Method of images. radical_in_all_things ( talk) 16:54, 15 November 2013 (UTC)
Max energy in a capacitor moved here from article page Not really relevant to subject of capacitance
If the maximum voltage a capacitor can withstand is (equal to where is the dielectric strength), then the maximum energy it can store is:
— Preceding unsigned comment added by Light current ( talk • contribs) 01:43, 6 September 2005 (UTC)
The physicist James Clerk Maxwell invented the concept of displacement current in his 1861 paper in connection with the displacement of electrical particles: citation needed [1]
“ | Bodies which do not permit a current of electricity to flow through them are called insulators. But though electricity does not flow through them, electrical effects are propagated through them … a dielectric is like an elastic membrane which may be impervious to the fluid, but transmits the pressure of the fluid on one side to that on the other. | ” |
“ | Electromotive force acting on a dielectric produces a state of polarization of its parts...capable of being described as a state in which every particle has its poles in opposite conditions. | ” |
“ | ...we may conceive that the electricity in each molecule is so displaced that one side is rendered positively, and the other negatively electrical, but that the electricity remains entirety connected with the molecule, and does not pass from one molecule to another. | ” |
“ | This displacement does not amount to a current, because when it attains a certain value it remains constant, but it is the commencement of a current, and its variations constitute currents in the positive or negative direction, according as the displacement is increasing or diminishing. | ” |
“ | ...when the electromotive force varies, the electric displacement also varies. But a variation of displacement is equivalent to a current, and this current must be taken into account... | ” |
He then added displacement current to Ampère's law. citation needed [2] Maxwell's correction to Ampère's law remains valid today, and is expressed in the form:
with Jf the current density due to motion of free charges and the displacement current density given as ∂D/∂t with the electric displacement field D related to the electrical polarization density of the medium P as:
Here ε0 is the electric constant. The polarization is the contribution described by Maxwell in the quotations above, and is due to the separation and alignment of charge in the material that is not free to transport, but is free to align with an applied electric field, and to move over atomic dimensions, for example, by stretching of molecules. (This polarization in response to the field actually screens the dielectric from the electric field, resulting in a lower field the greater the polarization of the medium. citation needed See the figure.) In simple materials, the polarization is proportional to the electric field and an adequate approximation is:
with εr the relative static permittivity of the material. When there exists no material medium, εr = 1, so there still exists a displacement field when there is no medium present.
To connect the displacement to charge, Gauss's law is used, which in integral form relates the charge in a region to the surface integral over an enclosing surface Σ of the component of D normal to the surface:
where a vector dot product is indicated by the "·".
To relate this expression to a capacitor, the surface Σ is made to enclose the dielectric medium and one of the two electrodes of the capacitor. The electrode contains the net charge upon the capacitor, and the dielectric medium is charge neutral. Referring to the figure, suppose initially the dipoles in the dielectric are unpolarized, as on the left side of the figure. The electric field due to the charge on the capacitor plates is the same as though the dielectric were not present. Next, suppose the dipoles are able to respond to the applied field and become polarized, as on the right side of the figure. Then the field from the extended dipole opposes that of the electrodes and the electric field inside the dielectric decreases. Suppose the left panel corresponds to an initial time just after the field is applied and the dipole has not had time to respond, while on the right is a later time when the dipoles are in the process of becoming extended. During this extension of the dipoles, a displacement current flows across the Gaussian surface. The more polarizable the medium, the more current for a given voltage, and the greater the capacitance. The net displacement current I through the region Σ is related to the displacement current density through the equation:
(The partial time derivative is meant to emphasize that the spatial variables in D(r, t) are held fixed.) This equation includes current through the region Σ related to polarization of the medium, and is connected to capacitance and an applied voltage:
where C is capacitance, Q is charge, and V is the applied voltage responsible for the field causing the polarization of the medium inside the capacitor. For some materials represented by complicated behavior of D, the capacitance can be a function of voltage and may exhibit time dependence related to the ability of the medium to respond to the signal (see subsections below).
It should be mentioned that when there is no material medium in the capacitor, the displacement is not zero, but D = ε0E. Consequently, a capacitance still is present. For example, a system of metal electrodes in free space may possess a capacitance.
Maxwell never used the term electric charge, citation needed but he did refer to the "distribution of electricity in a body" and to the "quantity of electricity". Capacity C was stated in his equation (138) for two surfaces bearing equal and opposite quantities of electricity e and electric tensions or potentials ψ1 and ψ2 as the ratio C = e / (ψ1 - ψ2). Then the effect upon C of inserting a dielectric between the plates was determined. [3]
Today, capacitance is viewed primarily in terms of the capacity for storage of charge, whereas Maxwell's paper stressed the current that flowed through a capacitor. citation needed He calculated this current focusing upon the specific calculation of polarization for an "elastic sphere" distorting under an applied field and resisting deformation by virtue of its elastic properties, and the current that flowed when this state of polarization altered. citation needed The modern approach attempts to treat the polarization of materials by modeling the microscopic events contributing to the displacement field using quantum theory: for example, see below. citation needed
References
— Preceding unsigned comment added by Dicklyon ( talk • contribs) 18:05, 18 September 2009 (UTC)
What is the difference between capacitance and energy density?-- Wyn.junior ( talk) 03:01, 26 February 2014 (UTC)
I added the "cmplx" subscript to denote complex capacitance. Elee1l5 ( talk) 21:09, 9 March 2014 (UTC)
The main article currently says "If the charges on the plates are +q and −q", then C = q/V They should explain why a charge difference of '2q' doesn't result in (2q)/V. This means : why q/V and not (2q)/V? KorgBoy ( talk) 23:46, 6 July 2017 (UTC)
In Wikipedia article "Farad", the character "C" is used for the Electric charge. In the article "Capacitance", the same character "C" is used for Capacitance. This is confusing.
Regards, Boris Spasov (bspasov@yahoo.com). — Preceding unsigned comment added by 107.184.14.103 ( talk) 05:48, 24 June 2018 (UTC)