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# Is my understanding of capacitors correct? Answered

I am currently working on a "Tutorial Tuesdays" video for my YT channel about capacitors covering some of the basic theory, real-world ratings and considerations, and maybe some cool demonstrations with how to use them and stuff. I just want to make sure that I do understand them correctly,so hopefully you smarter people out there can tell me if I am wrong in any way.

1) A capacitor stores energy in a electric field between two electrically insulated conductive plates, the strength of which will depend on the proximity and surface area of the plates, the dielectric constant.

2) Can I compare "electric charge" to mass; "voltage" to density; and "capacitance" to volume as an analogy? (yes, I know I am ignoring dielectric constants and strengths.)

3) If I look at the peak to peak AC current through a capacitor, and the peak to peak AC voltage, can compare the ratio of the two figures to figure out capacitive reactance? (example: If I have one volt peak to peak AC applied across a capacitor, and I see 10mA of current peak to peak, does that mean the inductive reactance is 100 ohms?)

4) Are the most important things to keep in mind with capacitors in general are "working voltage" (the maximum voltage a cap can withstand), "capacitance" (how much charge a capacitor can store for some given voltage)  "ESR" Equivalent Series Resistance, which is how 'good' the capacitor is, and "temperature" (which can potentially adversely affect the performance and ratings of a capacitor)?

5)Uses for capacitors include Energy storage, analog filters, DC removal, voltage transient suppression, voltage smoothing, timing/counting AC coupling, data storage, phase shifting, motor starting, etc.

6) The ---| |---- symbol represents a generic non-polarized capacitor
The ---| (---- or --[] []-- (with one box colored in) symbol represents polarized capacitors
The ---|/|---- symbol (with a slash in the middle being a slanted arrow) represents variably capacitors

7) Should I try to learn how to work with complex impedance (capacitors, resistors, and inductors in all sorts of weird configurations) Also, can I treat reactance in general as a resistance when looking at capacitors in series or parallel with resistive loads and stuff?

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## Discussions

1)
For the beginner, I don't think it is really important to know how a capacitor stores energy, except that it does. It is enough to know the charge Q, stored on each plate of a capacitor, is proportional to the voltage measured across its terminals. Q =C*V where the C is capacitance. Thus a bigger C allows you store more charge Q for a given voltage V.

The formula for energy stored in a capacitor,
U = 0.5*C*V^2 = 0.5*Q*V = (1/C)*Q^2,
is the result of an integral over dU=V(Q)*dQ = (1/C)*Q*dQ, essentially calculating how much work it takes to move all those little pieces of charge dQ, in the face of a changing voltage, V = (1/C)*Q.

For a capacitor with vacuum, or air, between its plates, you could say the energy is stored in the electric field between the plates. Although this is NOT true for capacitors with a dielectric material between the plates.

For capacitors with dielectric, the energy is being stored in some kind reversible deformation, like stretching, or twisting, of microscopic electric dipoles in the dielectric material.

So the mechanism by which energy is being stored in dielectric material is something complicated. Although, curiously, this complicated interaction gets reduced to a single constant (called dielectric constant, or relative permitivity) in the formula for the capacitance of a capacitor consisting of two plates with area A, separated by distance d.

C = k*epsilon0*(A/d)

For capacitor with vacuum between the plates, k = 1.

For capacitor with dielectric material between the plates, k is some number greater than 1.

And of course, k is a constant, but kind of, sort of, not really, because it depends on other things, like frequency, and temperature.
https://en.wikipedia.org/wiki/Relative_permittivit...

2)
Charge is like mass? Voltage is like mass density? Capacitance is like volume? I don't understand this analogy at all.

3)
I suppose voltage magnitude and current magnitude are enough to measure reactance, if you also know (or expect) the device is a capacitor. I mean, in general, impedance is complex voltage divided by complex current, so I am expecting the answer to have a -j in it, if it is a capacitor; i.e. Z = (1 V)/(j * 10 mA) = -j*100 ohms. I am also expecting impedance for a capacitor to depend on frequency, as
Z=1/(j*omega*C) where omega is angular frequency (radians/second)

4)
I suppose voltage rating is the number I worry about most, for non-polarized capacitors. For polarized capacitors, I have to worry about the upper voltage rating, and also making sure the capacitor never gets reverse biased; i.e. it always has some positive voltage on it.

5)
Yeah. Capacitors. They are very useful! For all of those things.

6)Yeah. Symbols. OK.

Wow, that's a LOT of great info to keep in mind! :D Thanks! Following the logic in your first sentence, why would Q be of any importance for that matter to a electronics tinkerer? My plan is to gloss over some of the theory, just wanted to make sure that there is nothing majorly wrong with what I know!

The analogy is because charge is the sheer quantity of electrons (sort of like mass After all, x moles of gas will always have some weight according to atomic mass), voltage is kind of like how much charge in a given volume, and capacitance is like volume, a large pressure tank (like a outdoor propane tank) where having more of it means that you need to add or take away a lot more charge in order to make a significant difference in pressure (voltage).

Complex impedance and power factor (real vs apperant vs reactive) is not something I fully understand. Should I study up on that to demonstrate the capacitive reactance formula? My understanding is that capacitive reactance can be treated like resistance.

I see what you're saying now, about charge being like mass. The kind of mass you meant was like a compressible gas. More specifically, charging a capacitor is like filling a steel tank with compressed air. The more air you put in the tank, the higher the pressure in the tank, and the more work you have to do per small quantity (microgram, micromole?) of gas to put in the tank.

I dunno. There are other, maybe more simple, physical systems that sort of do the same thing. Like a steel spring, that pushes back with force proportional to displacement, F =k*x. It gets harder to push against the more it is compressed, and the energy stored in it has the formula U=0.5*k*x^2 = 0.5*F*x = 0.5*(1/k)*F^2, similar to energy stored in a capacitor, U = 0.5*C*V^2 = 0.5*Q*V = 0.5*(1/C)*Q^2

Also, regarding analogies, I just noticed there is a Wikipedia page all about the electricity-is-like water analogy; aka the hydraulic analogy, here:
https://en.wikipedia.org/wiki/Hydraulic_analogy

This page says a capacitor is like a flexible elastic diaphram sealed inside a pipe. Someone even made a cute little animated gif for this.

Actually I kind of like this analogy. One of things it illustrates clearly, is the ability of capacitors to block DC, since a constant flow of water cannot just move through a rubber sheet.

Regarding real loads and inductive loads, a reactor (capacitor or inductor) is like a resistor, in that both can limit current flow. However a reactor, unlike a resistor, does not dissipate power as heat. The reactor just sort of stores a quantity of energy for half a cycle, and then gives (exactly the same quantity of) energy back during the other half of the cycle.

That's kind of a hand-waving explanation of how reactance works, but I think it is the best I can do without writing a bunch of equations.

Anyway, I think you've pretty good grasp of this topic. I wish you luck in explaining it to others.

I like the hydraulic analogy a lot, I may make a separate video just about it. Too bad it does not work too well with power and energy. I certainly have considered the spring analogy, though I always thought of springs more like inductors, and flywheels like capacitors. I think it works both ways, depending on what terms you declare analogous.

"The reactor just sort of stores a quantity of energy for half a cycle, and then gives (exactly the same quantity of) energy back during the other half of the cycle." Ahh, now I understand why they don't dissipate much power! Never thought of it that way before!

1.) Yes

2.) I find the analogy with water volume and height better

3.) Yes, of course.

4.) The type of dielectric is central to capacitor selection, after value. In some circuits low ESR can be a PITA.

5.) Resonant circuits.

6.) Yes. Word is "variable"

Great! Good point about ESR, I found that a high value ideal capacitors make my simulated linear power supply oscilate! However could you elaborate on the dielectric, what kinds (of capacitors) to use for certain applications, and I know capacitance of ceramics can change with the voltage applied and temperature, but I don't know the details. Any good trustworthy sources? Thanks!

A lot of the stuff about dielectrics I know has been absorbed over the years, I'm not sure where best to look for a better source. There are effects like dielectric leakage, storage and recovery, as well as piezo electric effects

A capacitor is 2 conductors separated by an insulator.

It stores electrons on the fairly large area of one conductor conductor. The other has any surplus electrons stripped off it.

This creates a potential between the 2 conductors.

Capacitance is, (simply), expressed as KA/D where K is the dielectric constant (1 for dry air), A is the area of the conductors and D is the distance between them. There are other factors but this gives the essence.

2. Your an analogy may hold together but like the water vs electricity analogy it only goes so far.

3. Yes (he says slowly) instantaneous voltage changes pass directly through a Capacitor. It can not develop a charge fast enough. Steve can better give you the maths.

4. Working voltage - important - although 90% of electronics these days is at such a low voltage that it almost becomes irrelevant. Not like in the good old days of valves!

The actual capacitance is critical because this is most probably why the Cap is there in the first place, obviously frequency dependent as well. having said that the tolerance on CAPs is usually huge. they are not very precise components.

Many uses, phase changing, interesting application, Tuned ccts including filters, DC blocking, smoothing, These days CAPs are used where a small battery may have been used before, Super CAPS may even replace batteries in fairly heavy current applications where a fast charge is beneficial. maintenance voltage on memory chips (old application), Power storage to allow tidy shut down in case of power loss. In the case of my son as a night light , a super CAP with an LED across it will keep the LED alight most of the night, his children appreciate it, and it charges really fast.