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# [Phys-L] Fw: non-polarized capacitor

________________________________________
From: Jeffrey Schnick <JSchnick@Anselm.Edu>
Sent: Friday, February 26, 2021 12:51 PM
To: John Denker
Subject: Re: [Phys-L] non-polarized capacitor

________________________________________
From: John Denker <jsd@av8n.com>
Sent: Thursday, February 25, 2021 10:30 PM
To: Jeffrey Schnick
Subject: Re: [Phys-L] non-polarized capacitor

On 2/25/21 7:56 PM, you wrote:

[...]

Do you accept the idea that the circuit with the diodes is a
faithful model of the circuit with the non-ideal electrolytics?
It is a good model for our purposes. I used it to prove that the central conductor acquires a negative charge.

If the central node had an appreciable number of field lines spewing
out in all directions and terminating at infinity (or on the chassis),
like the pole of a van de Graaf generator, then it would be a clear
violation of the Kirchhoff "laws" ... but it doesn't. 99.999% of the
charge associated with the central node is inside the capacitors.
Agreed.

The field lines go from plate to plate. This keeps Kirchhoff happy.
I agree with the first sentence, not the second. Let's establish a gaussian surface that encloses the central conductor and nothing else. It encloses one plate from each capacitor and the wire connecting those two plates. Prior to application of the source voltage, both capacitors have 0 gorge and 0 charge. The net outward flux through the gaussian surface is zero. The charge enclosed by the gaussian surface is zero. Now we connect the oscillatory voltage source to the system and let it run until there is no more leakage current. From then on, one or both of the capacitors has non-zero gorge. Whenever the upper capacitor has gorge, there is an electric field in the region between its plates and that electric field is directed from the top plate toward the bottom plate, thus inward through the gaussian surface. Whenever the lower capacitor has gorge, there is an electric field in the region between its plates and that electric field is directed from the bottom plate toward the top plate, thus inward through the gaussian surface. The flux through the gaussian surface at points outside the two regions just discussed (I am aware of the fringing nitpick that could be made here but the argument still holds with fringing taken into account) is negligible. The net flux through the gaussian surface is thus inward. Thus, there is a net negative charge inside the gaussian surface. The only thing inside the gaussian surface is the central conductor, so, the central conductor has a net negative charge. There is no field-line concentration exception to Gauss's law. There is charge on the central conductor even though the electric field is non-zero only in the regions between the two plates of each capacitor.

My main point is that the central conductor starts out uncharged, and, after a transient phase of operation, the central conductor is charged. The fact that Kirchhoff's current law, the one that can be stated as, "the net current into a node is always zero," is violated, is secondary. Given that the net charge on the central conductor starts out zero and becomes −Q, conservation of charge tells us that there must have been a non-zero net current out of the junction that I have been referring to as the central conductor. That current represents a violation of Kirchhoff's current law. The amount of charge is not negligible. If V_max is 10 volts and the capacitors are 100mF capacitors, then Q is 1 coulomb. In your model, that much charge flows from the central conductor, out through a diode, in less than half a cycle of the source voltage.

Again I say: This is just like any other circuit you could build.
They all obey the same actual laws of physics.

Floating nodes are weird, and have to be analyzed carefully, but they're
not so weird that we can't analyze them with standard concepts, carefully
applied.
I think I have analyzed this one with standard physics concepts, carefully applied.

Would it help to clip out one of the capacitors?
I don't think so.

Would it help to remove the diodes and instead use a battery and a
high-value resistor to charge up the central node to −⌈V⌉/2 at some
ancient time, before the capacitor-pair gets used? Then you don't
have a floating node at all.
Presetting the voltage of the central conductor to −V_max/2 is neither necessary nor, in general, sufficient to make it so that when you apply the sinusoidal source voltage to the combo capacitor there is no transient phase. What you would have to do in advance is to put charge q <= −Q on the central conductor. You could do this by connecting the low side of a V_max battery to the central conductor and momentarily connecting the high side of that battery: to the top plate of the upper capacitor (thus leaving the preset voltage of the central node at 0), or, to the bottom plate of the lower capacitor (making the preset voltage of the central node −V_max). Or, you could connect the low side of a V_max/2 battery to the central conductor and momentarily touch the high side to both the top of the upper capacitor and the bottom of the lower capacitor, either simultaneously or in turn (this would make the preset voltage of the central node −V_max/2 which, I think, is the value you had in mind). In both cases, you can use a higher voltage battery than specified just above, thus putting some extra negative charge on that central conductor; the extra negative charge will just sit there as a uniform charge distribution on the central conductor once you apply the sinusoidal source voltage that oscillates between −V_max and V_max; only −Q of the charge will surge up and down from one end of the central conductor to the other. Note that if, starting with everything neutral (and the diodes in the circuit, or, with the capacitors being electrolytics), you preset the voltage of the central conductor simply by momentarily connecting the low side of a V_max/2 battery to the central conductor and the high side to the bottom of the lower capacitor, you would only put a charge of −Q/2 on the central conductor and once you removed the battery and applied the sinusoidal source voltage there would be transient current until the charge on the central conductor got to be −Q.

If your goal is to avoid leakage current, presetting the charge of the central conductor to q <= −Q would do the trick.