Understanding Capacitors Better

[magu1re]

Hey.

My textbook states of a capacitor that: "If one plate stores a charge +Q, then the other stores an equal and opposite charge -Q".

I understand the electrons flow onto one plate and this excess of electrons causes the plate to have an overall negative charge which then repels electrons on the opposite plate causing them to flow out of that plate, thus leaving it with a positive charge. However, why is it that an equal amount of electrons must flow out of the positive plate as flow into the negative plate?

Also, why is it that a capacitor discharges when it's leads are connected together having be charged up. Is this because electrons in the wire are repelled by the negative plate and attracted to the positive plate and so flow in one direction around the wire? This makes sense to me. What does not make sense to me is that electrons on the positive plate are still being repelled by the negative charge on the positive plate and so should flow out of the plate rather than into the plate from the wire. Perhaps I should ignore this second thought and just be satisfied that the first explains this but if anyone could give me a greater insight into what is going on it would be much appreciated.

P.S. If this simplistic view is, in fact, wrong. Please enlighten me :P

 

[Vanadium]

Well, I don't want to confuse you, but the electrons don't actually "flow". That's just a convenient mental model. In actuality, each electron nudges nearby electrons with its electric field, and the *effect* is similar to one electron entering one end of a wire nudging one electron out the far end. Imagine a a car in a 44 million car traffic jam on Interstate 95. As on car leaves Maine, another car enters Florida, but each individual car moves very slowly

To illustrate: Let's say for the sake of the math that 1m of 10 AWG copper wire used in household wiring contains 100g of copper (sorry I don't have suitable wire charts handy to give the correct figures, all further numbers will be more accurate), and the wire run from your light switch, up the wall across the ceiling and into your light fixture is 10m. That means 1kg of copper separates the switch from the light. Since copper has an atomic weight of 63.5, 1 kg of Cu is 15.75 moles; since copper is atomic number 29, and there are 6.02x10^23 atoms in a mole, 15.75 moles of copper contains 2.75x10^26 electrons. Let's say the fixture hold two 60W light bulbs @ 120V. That's one amp of current or one coulomb/second of electrons flowing in the wire. 1 Coulomb is 6.2x10^18 electrons. so it would take (2.75x10^26) / (6.2x10^18)= 4.4 x 10^7 sec (1.4 years) on average for an electron that leaves the switch to enter the light fixture. even if we only count the 11 electrons in copper's outer shell, instead of all 29 of copper's electrons, it'd still be over 6 months -- but I bet your light turns a lot faster than that!

In fact, household wiring is AC (alternating current), with the direction changing 60 times a second (in the US; 50 times a second in many other countries). In other words, the electrons barely have a chance to move at all, before they have to turn around and move in the other direction. In a 120V DC (direct current) lighting circuit, the electrons would be moving 10m/1.4 years (0.22 microns/second), but with the AC power most of us have at home, the electrons don't have any net motion at all.

This is a greatly simplified illustration, but with it in mind, here's how a capacitor works:

If we place a single free electron on one plate of a capacitor, it will be an unbalanced negative charge in a very small spot -- an intense electric field. This field will tend to repel other nearby electrons: a force that is absolutely palpable -- in fact, the repulsion of the electrons in the atoms of your skin against the atoms of all other atoms in all other objects are responsible for the "solidity" of every hard object you've ever felt. Next time you stand up and bang your head on an open cabinet, try to disregard it as "mere electron repulsion". I haven't had much luck with that, personally.

Those nearby electrons, which are directly repelled, will in turn repel electrons that are further away, and so on. Of course, all those electrons will also repel back. In addition to repelling other electrons, it will tend to attract positive charges. In actual wires, these "positive charges" tend not to be actual positive charges (like protons, which are nicely shielded by their atom's shell of electrons) but "virtual charges" called holes. A hole ia a place where a negative electron Would be, in a perfectly neutral mass of atoms, but *isn't* (perhaps due to the diffuse repulsion of distant surplus electrons)

I don't want to dwell on that, but it'll be useful when you get further in your study of electronics, such as understanding semiconductors like transistors: the free electron we added creates an "induced charge" on the opposite plate. Beginner texts often call these positive charges, but they are actually just "virtual charges" or holes cause by the electron's repulsion. Holes *act* like positive charges but aren't physical particles.

Okay, so we have this capacitor, charged with a single free electron. The effect of the one negative charge almost instantly spreads across the entire capacitor. This is a less repulsive (lower energy) state than having all the effect in one tiny spot. In fact, the energy is so low that it's easy (requires little energy) to add a single electron.

You may also be interested to know that the charge effect diffuses (equilibrates) over the entire system at "the speed of light" but that's not the speed of light (c or the ideal speed of light in a vacuum) that we often talk about. It's the speed of light in copper -- which can be described as the time it takes all those electric field interactions to interact and spread. On a subatomic level, the pure EM field of an electron moves at c, but on a large scale, electricity in a wire travels somewhat slower [ but not nearly as slowly as the actual electric flow

If there is a [conductive] defect in the capacitor's insulation. our one free electron will nudge (indirectly) some electron from the negative plate into the hole [virtual charge] on the other side. This same indirect nudging will equalize the charges between sides if we use a wire to connect the two sides, instead of a defect in the insulation. Because the charge is now more spread out, the electric field has less stored energy.

Now, as I mentioned up top, real electric currents are *entirely* nudging. Any actual movements of physical electrons is tiny. The nudging starts at the power plant's generators, and is performed by magnetic fields which are moved by engines, like steam or water turbine, driven by things like fossil fuels or water pressure.

So in a real capacitor, there aren't really physical electrons entering the capacitor, or physical positive charges on the opposite plate. It's all electromagnetic nudging. On a subatomic scale, you can think of the repulsion as tiny springs between the electrons, on a slightly larger scale, you can think of changes in water pressure in a pipe. The "induced charge" on the other plate is the same thing -repulsion- just harder to imagine. There are no actual physical point-like positive charge involved, just some places that are less negative than others, and therefore *relatively* positive compared to the overall circuit. [You could trace the circuit back to the power plant, and reference it to various local grounds, as required by the Building Code -- but trust me, that won't help you understand capacitors any better, and I know some electricians who don't "get it"]

On the scale that we humans live on, we can pretend the electrons are actually flowing in pipe-like wires. It's really not such a bad model, but don't take it literally.

 

[Naty1]

I like the prior description...

In fact, the energy is so low that it's easy (requires little energy) to add a single electron.

yes...and as each susbequent electron is pushed along it is a bit more difficult to add ..because there is a bit more repulsion...more potential...when you get to the last electron, as the capacitor reaches whatever potential is applied, its really tough to add it...that's why a dc potential (like a battery) when first applied across a capacitor allows current to briefly flow as charge builds...then current stops as potentials equalize.

 

[tiny-tim]

welcome to pf!

hey magu1re! welcome to pf!

… why is it that an equal amount of electrons must flow out of the positive plate as flow into the negative plate?

because of conservation of charge!

suppose you have two equally negatively charged plates …

connect them with a wire, the plates will still be negatively charged …

now introduce a battery into the wire, it will move some of the charge from one plate to the other, and the charges wil no longer be equal!

the difference between the charges depends on the voltage

the sum of the charges is unaffected by the voltage: it's the same as it was before you started, and of course is usually zero! ​

 

[magu1re]

hey magu1re! welcome to pf!


because of conservation of charge!

suppose you have two equally negatively charged plates …

connect them with a wire, the plates will still be negatively charged …

now introduce a battery into the wire, it will move some of the charge from one plate to the other, and the charges wil no longer be equal!

the difference between the charges depends on the voltage

the sum of the charges is unaffected by the voltage: it's the same as it was before you started, and of course is usually zero! ​

Thank-you for taking the time out to help me.

When the electrons initially flow onto the (soon to become negative) plate I can see that electrons will be repelled from the other plate, leaving it with an overall positive charge. I had also thought that "the current is the same at all points in a series circuit" was likely to have something to do with this. What I cannot understand is how this is still the case here.

I know it is a series circuit but it is not truly a fully connected circuit. So instead of all electrons nudging one another and thus inducing the same current at all points in the circuit, it would appear, in this case, that electrons leaving the positive plate are almost pulling electrons away with them to maintain this uniform flow of electrons. I know this is not really the case but I hope you can see where I am coming from.

Would your perhaps elaborate more on this point?

 

[Naty1]

I know it is a series circuit but it is not truly a fully connected circuit.

See my post above...while charging it does briefly act as a "connected circuit"...

I had also thought that "the current is the same at all points in a series circuit" was likely to have something to do with this.

That's the idea! a valid perspective///// Where could the charge go if it were different?

Yu can also think of this in terms of the battery supplying the potential...ions (charged particles) flow in the electrolyte...one leaves one terminal and migrates to the other...this flow enables the chemical reactions to continue and the potential developed pushes electrons externally to the battery...Check out recent discussions on how batteries work...