Capacitors and Inductors

[steve66]

Re: Capacitors and Inductors

If this plate is considered an overgrown node and apply Kirchhoffs current law it appears not to hold, ie current is approaching the plate from external circuit, but it is not flowing out of the plate into the 'internal circuit'.
Why is this ?

Maxwells laws describe this with what is called a "displacement flux". Kirchoffs current law is really a special case of Maxwells law where the displacement flux is assumed to be zero.
Kirchoffs law works for an entire capacitor, but not a single plate. It also won't work for an antenna if you don't include the ground plane.

An alternate way to look at it would be to consider the displacement flux a current, but one that is radiated through a dielectric instead of a current passed through a conductor.

Steve

[ January 07, 2005, 01:40 PM: Message edited by: steve66 ]

 

[coulter]

Re: Capacitors and Inductors

First - I like Steve's answer. But, "Maxwell who?" (just kidding)

Second - The case of dividing by ever smaller time slices:

I commented that I was going to divide by ever smaller time slices until the function was no longer jumpy. Some might interpret this as eventually dividing by zero. If one wants to look at the rate of change at a point, then dt could be seen as having to be zero.

My engineering response would be, "Well, exceedingly small, not zero, but close enough."

Let me illustrate:

A psychologist puts an engineer and a physicist in a three cornered (triangular) room. In the third corner there is a piece of pie known to be the favorite of both the engineer and the physicist.

The psychologist tells the two, "I'm going to leave the room and a bell will sound. At that time both of you may head toward the pie. But, you must stop at halfway before continuing on. Each time you start moving, you must again stop each time you have covered half of the remaining distance. There will be a substantial reward for exactly following the directions. The room will be video taped to insure compliance."

Psychologist leaves, bell sounds, and one hour later the psychologist enters the room. The physicist is still standing in his corner, looking perplexed and frustrated. The engineer is sitting at the pie, just finishing the remaining crumbs.

Psychologist asks the physicist, "What happened?"

Physicist: "After analyzing the problem I realized that being able to only move half of the remaining distance each time, I would never get there. I could not see any way to get around that while maintaining your directives."

The psychologist looks at the engineer with a raised eyebrow (sort of like your mother used to do when you got caught with your hand in the cookie jar).

Engineer (with satisfied smile): "The physicist is correct, following your direction exactly, one would never get exactly there. However, I did in fact follow your direction exactly. It took me a while, but eventually I got close enough."

So, no we are not dividing by zero.

carl

[ January 07, 2005, 02:54 PM: Message edited by: coulter ]

 

[physis]

Re: Capacitors and Inductors

I think Kirchoff's law for current holds.

This is the best I've got in my one remaining physics book.

"The algebraic sum of all currents entering a node equals the algebraic sum of all currents leaving it."

First is the idea of the node.

I don't have a definition. But if the capacitor or it's dielectric satisfy the definition of the node then we have one.

Second, is the, in a literal sense, equal motion of electrons on either side of the dielectric. Remember that the conductors connected to the capacitor are a source of electrons. As electrons are forced onto one plate the electric field on that plate, through the dielectric, pushes electrons off of the opposite plate.

Currents on either side are equal.

Kirchoff goes home happy.

Edit: The capacitor isn't a bucket you put electrons in, the electric field at the dielectric can't be ignored.

[ January 07, 2005, 04:43 PM: Message edited by: physis ]

 

[rattus]

Re: Capacitors and Inductors

Kirchoff rules! A capacitor is not a node. Furthermore, for every electron that arrives on one plate, another electron leaves the other plate. The bucket analogy is rather crude, but it is a place to start.

 

[physis]

Re: Capacitors and Inductors

I don't have one Rattus so you are elected to hand down the definition of the node.

And I disagree that a capacitor wont satisfy the requirements. I don't think it will become more complicated than a component in a circuit. But I may be wrong.

Edit: I figure if you want to invoke Kirchoff you're no longer allowed the water model.

[ January 07, 2005, 07:28 PM: Message edited by: physis ]

 

[physis]

Re: Capacitors and Inductors

By Steve:

An alternate way to look at it would be to consider the displacement flux a current, but one that is radiated through a dielectric instead of a current passed through a conductor.

I just saw that Steve. That's right, it's very much the same as in a wire. The electric field of one electron pushes the next away. In the same way elctrons are pushed off an opposing plate of a capacitor.

 

[steve66]

Re: Capacitors and Inductors

Kirchoffs law works with more than just nodes (if you consider a node to be a point or a slice through a wire.) It will also work with entire circuits and black boxes. Picture a black box with 10 wires going into it. The algebraic sum of the currents on 9 of the wires will add up to the current on the 10 wire. For any circuit, you can draw an enclosed box or sphere, and currents in equal currents out. But again the above assumes there is no displacement current.

Someone pointed out that if you draw your box around half of a capacitor (include one plate, but not the other), Kirchoffs current law doesn't seem to apply. Currrent flows in on to one plate, but the current flowing out the other plate isn't in our "box". That is when you have to consider displacement current.

Of course, if you just be a little more careful how you draw the box, and if you aren't dealing with antennas or radiating signals, you don't have to worry about displacement currents.

Steve

 

[Ed MacLaren]

Re: Capacitors and Inductors

you don't have to worry about displacement currents.

Do you mean by "displacement current" the distortion, or "stretching" of the orbits of the dielectric atoms?

Ed

 

[peter d]

Re: Capacitors and Inductors

Wow!! This is an excellent discussion. Thanks to all that have responded. My understanding of this subject is much better now.

What a great forum!!

[ January 10, 2005, 06:13 PM: Message edited by: peter d ]

 

[physis]

Re: Capacitors and Inductors

Oh yeah, well there's a test Peter. But it's only one quetion.

How does a capacitor oppose voltage change?

 

[physis]

Re: Capacitors and Inductors

Ed, I think Steve has invoked some of Maxwells equations. I'm not equiped to engage the topic on that (unnecessary) level because I don't have enough Maxwell material.

Nothing personal Steve, I actually wish I could go Maxwell with it.

 

[bphgravity]

Re: Capacitors and Inductors

I feel the problem with explaining capacitors is the use of the word "charge". Capacitors don't store a charge, they store energy. The act of "charging" a capacitor has more to do with the transfer of energy than it does with the creating of charges. At least that's how Isee it.

 

[peter d]

Re: Capacitors and Inductors

Originally posted by physis:

How does a capacitor oppose voltage change?

This is just a guess on my part, but is it because of the nature of the capacitor itself, that is, one plate acts against the other?

 

[rattus]

Re: Capacitors and Inductors

The capacitor does not exactly oppose a change in voltage, but voltage is an indication of the energy stored:

W = (CV^2)/2 Joules or Watt-sec

It takes time to transfer this energy to the cap.

With an inductor the energy stored is:

W = (LI^2)/2 Joules

Same argument except now current is an indication of the energy stored.

 

[physis]

Re: Capacitors and Inductors

I have to disagree with both of you, Rattus and Bryan.


Bryan: if you remove the source and the conductors from a capacitor, you have a stored "charge". You are correct that it takes "energy" to cause the charge to be stored.

Rattus: I'm surprised at you. Capacitor doesn't oppose change in voltage? What gives?

Edit: Bryan, I looked at what you said again and you said mostly what I did except the part where it stores energy. You can say that there is potential energy stored but that is less specific than calling it a charge.

[ January 11, 2005, 01:43 AM: Message edited by: physis ]

 

[steve66]

Re: Capacitors and Inductors

Posted by Ed:

Do you mean by "displacement current" the distortion, or "stretching" of the orbits of the dielectric atoms?

Sorry Ed, but I don't remember exactly what the displacement current is, and I don't really want to dig out my old electromagnetics textbook, but I am willing to wing it

I think the displacement current is the electric field (ie. the Electro-magnetic field that can induce a current in another wire or plate). I don't think it is the displacement of the electron orbits, but I think it causes the displacement of the electron orbits.

P.S. We were always told the energy in a capactior is stored in the dielectric and in the displacement of the electron orbits, but I never understood that. It seems like the energy would be on the plates where the + and - charges are.

Steve

 

[Ed MacLaren]

Re: Capacitors and Inductors

Just a few observations to add to an interesting discussion.

I think the word "charge" is the accepted term for the surplus of electrons on one plate, and the deficiency of electrons on the other plate.

Another term for the above condition is a "difference of potential" also known as "voltage".

In that sense, it can be said that a capacitor stores a voltage, when connected to a DC source. Remove that source, connect a load across the capacitor, and that voltage causes a current to flow from the negative plate to the positive plate, through the load.

However, the energy is stored in the "stretched orbits" of the dielectric atoms. Think of how energy can be stored in stretched rubber bands.

When a capacitor is connected to a AC source, current flows, but virtually no power is used, because the current is almost 90 degrees out-of-phase, with the current leading the line voltage.

To explain, without using complex math, why the current leads the voltage in a capacitive circuit, I used this mechanical analogy with my apprentice students.

Think of a person compressing, and then stretching, a spring fastened to a wall. The force exerted by the person represents the AC voltage. The reciprocating motion represents the current.

Ed

 

[rattus]

Re: Capacitors and Inductors

Let's be precise. "Charge" is the property of electrons and protons which causes these atomic particles to either attract each other if they are opposite or repel each other if they are alike. Although not quite correct, we can speak of charge if it were a particle itself.

We can say that the capacitor stores energy, and it does so by maintaining an imbalance of electrons between its two plates. We do not create electrons, we merely push them around. We live in a sea of electrons, gazillions of them, and we only use a tiny fraction for electric power.

What is voltage anyway? Simply put, voltage is an indication of the potential energy of the electrons at one point relative to the potential energy at another--always two points.

Current of course the the rate of charge flow in Coulombs/sec or Amperes. It takes about .6 x 10^19 electrons to make up a Coulomb! But, who is counting?

As for opposing a change in voltage, I would rather say that the capacitor controls the rate of change in voltage as an inductor controls the rate of change in current.

But whatever the words we use, we all understand each other--well, most of the time anyway.

 

[physis]

Re: Capacitors and Inductors

Ed,

You get the best graphics award.

It gets a little harder to seperate things when considering the plate charge and the stretched orbits. The electron orbits are responding to the presence of like charges.

Will elctrons be ejected from the plate because of like charges in the dielectric or will they come off the plate in an attempt to equalize there distribution?

Bryan, I think this morning I'm not as reluctant to think of the charge as stored energy. Maybe it's Ed's fault.

 

[Ed MacLaren]

Re: Capacitors and Inductors

I would rather say that the capacitor controls the rate of change in voltage

I'm not sure what that statement means.

Wouldn't you agree that the only "rate of change in voltage" that could be controlled by a capacitor would be the rate of the build-up of voltage across the capacitor plates (charge rate) as it charges from a DC source, which is actually determined by the time constant of the circuit.

A capacitor has no effect on the supply voltage in either a DC or an AC circuit.

The "rate of change in voltage" in an AC system is a function of the generator frequency.

Ed