# calculus in electronics

Discussion in 'General Electronics Chat' started by Parth86, Aug 29, 2016.

1. ### ericgibbsWell-Known MemberMost Helpful Member

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Hi Al,
What is the smallest 'volume' a 'hole' could be and still be a hole.???

Eric

2. ### MrAlWell-Known MemberMost Helpful Member

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Hi there Eric,

You mean still be called a hole?

3. ### MrAlWell-Known MemberMost Helpful Member

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Hi,

Do you? Then i guess you know more than all the philosophers that came before you that pondered this very deeply.

The main issue seems to be that a 'hole' as we call it, has different properties than 'matter', so it is hard to say if it exists or not. The hole is a prototype of various other 'entities' that we call something that are not really made of anything.

For just a couple examples...
When we make something, we add stuff to it. But when we make a hole, we take something away.
When we talk about a hammer, we can talk just about just the hammer without referring to anything else, but when we talk about a hole we have to reference what that hole is 'in'. The hammer has a hole in the handle for hanging, the ground has a hole in it filled with water.
We can have a rock on top of another rock. Can we have a hole on top of another hole, or a hole inside another hole? If we have a hole inside another hole, isnt it just a single hole?
We cant even call a dive bar a "hole in the wall" place without referring to something else, "the wall".

But the pro's and con's of whether or not a hole can be said to really exist has been argued for many years now, so i seriously doubt that anyone can clear this up in a week or two of forum chatting...but feel free to try, i think this is always an interesting topic. The way i see it now is that for every point that can be made to prove that the hole is real another point can be made to show that the hole is not real. The two sides of the argument are very informative though about the metaphysical world.

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5. ### tcmtechWell-Known MemberMost Helpful Member

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One Helium atom in volume or ~62 Picometers in diameter and depth.. That's as small a hole that can be statically located, measured and observed in normal material in normal conditions.

Anything smaller than that either gets into that damn Quantum level quirkiness of not holding all three defining criteria at once or requires non standard environmental conditions to achieve which if they are used then theoretically ~1 Planck length in diameter and depth would be it.

My definition of a hole is any space that can be filled with a definable matter of some kind.

6. ### RatchitWell-Known Member

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Will someone tell me how many joules of electrical energy a ten volt constant DC voltage source will use to energize to ten volts, a one farad capacitor whick is connected directly to the voltage source. I know that an infinite current surge will ensue for an infinitesimal amount of time, but how much energy will the voltage source expend?

Ratch

7. ### nsaspookWell-Known Member

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No need for the metaphysical, a hole is hole no matter its name.

Holes (at least the ones in space) are hungry.
https://www.ligo.caltech.edu/system/media_files/binaries/301/original/detection-science-summary.pdf

8. ### ericgibbsWell-Known MemberMost Helpful Member

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hi tcm,
But isn't Helium, 'Matter' and not a 'hole'?
We explain the state of P type semiconductors as having 'holes' in their electron shell's that can be filled by Electrons, which are very much smaller than He or H atoms.

I would agree that if we considered Quantum theory that 'holes' could be even smaller.
Some scientists postulate that Time and Space is 'granular' , so perhaps there is no such entity as a 'hole'.

I would say what we consider as a hole, is a volume which has a lower density than the surrounding mass.

Eric

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9. ### tcmtechWell-Known MemberMost Helpful Member

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If there was a grid of Helium atoms (solid crystalline Helium matrix?) and one was missing that would be where the Helium atom sized hole is.

Electrons being mobile sub atomic particles are dynamic so I don't consider them to be capable of supporting any form of equivalent matrix formation like a atom or a substance that is at or above the atomic scale limit can.

That's my thoughts on where I would draw the line on how small a hole can be.

10. ### MrAlWell-Known MemberMost Helpful Member

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Hi,

I always thought that it was infinite, but it may not exist at all. We'd have to find a limit that exists to say that it exists even in theory.
If we look at then impulse response for voltage it looks like we have Vc=10, so the voltage jumps up at t=0 and stays at 10v, but as you said the current is infinite for an infinitesimally short time which leads to a problem because that means the resistance goes to zero, and since the time goes to zero we have to choose what goes to zero first, or if they both go to zero at the same time,but if they both go to zero at the same time the limit is zero, so they cant both go to zero at the same time, yet there appears to be no reason for them not to.
We can look at this more if you like.

11. ### MrAlWell-Known MemberMost Helpful Member

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Hi again,

That's very interesting, but i dont know if you realize it or not, but you are arguing half of my point. The other half is that a hole is not a real entity, and am certainly not alone in this dual property point of view. The best thinkers out there believe this too.
So dont you think you should at least read up on the pro-real and con-real sides of the argument?
It's ok if you want to be dogmatic about it as i know it is hard to see this because we use the word 'hole' so much in language ever since we were born just about so it's hard to think of it as something that is not real.
I should also mention that quoting applications does not prove that a hole is really real.

So it is expected that you and some others would deny this view at first, then later get angry about it because you know it might be true, then later try to bargain about why it shouldnt be true, then later still get depressed about it, then finally accept it

Seriously though you might want to read up on it, especially at a site like U of Stanford.

Metaphysics:
The branch of philosophy that deals with the first principles of things, including abstract concepts such as being, knowing, substance, cause, identity, time, and space.

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12. ### RatchitWell-Known Member

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I already know the answer. I was just asking if anyone else did. You know that the capacitor is going to energize up to 10 volts sooner or later. Therefore, it does store a finite amount of energy, and the voltage source has to supply that energy. How much energy does the voltage source lose energizing the capacitor up to 10 volts? I will wait a little longer before revealing the answer and explanation.

Ratch

13. ### specWell-Known MemberMost Helpful Member

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Some interesting stuff on this thread: I can hardly wait for the next post.

spec

14. ### MrAlWell-Known MemberMost Helpful Member

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Hi Ratch,

Ok great, sounds interesting. I did this a long time ago but forgot what i did now.

Before i go any farther, i could guess the cap has (1/2)*C*V^2 and because there is no energy dissipation the source would have to supply that. But i didnt want to take any short cuts, i wanted to have a rigorous analysis that spits out the answer in the limit.
In an RC circuit the energy is always twice the energy stored in the cap, but with no R there can be no energy dissipation.
Since with R we have I^2R loss then with no R we have:
limit I^2*R as I goes to infinity and R goes to zero. That makes it look infinite, but then we have t going to zero also so I gets shorter and shorter as it gets taller and taller and as R gets smaller and smaller. So we end up with zero dissipation.

I'll wait though for your reply, take your time and see what anyone else comes up with.

Last edited: Sep 2, 2016
15. ### nsaspookWell-Known Member

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You and a few others are the only ones arguing I'm only seeing half the point. In solid-state physics semiconductor holes are quasiparticles (not a real entity but a group property). The aggregate motion of electrons in the valence band (the lack of an electron in a state) is the same as positively charged 'hole'. This 'hole' greatly simplify's the mathematical description of charge carriers in a P-N junction but its not 'real' as the effective mass of a hole is larger than a electron resulting in a lower mobility for holes in a electric field.

Last edited: Sep 2, 2016
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16. ### nsaspookWell-Known Member

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A constant voltage source has zero source resistance. The capacitor will charge 'instantly' (the exponential function turns into a step response) in circuit theory. The problem with 'instantly' is that the universe doesn't work that way (division by zero issues).

The electric field inside the capacitor will not change 'instantly' (instead change as a Heaviside function) causing a delta-like displacement current, magnetic field and induced emf to counter the rise of current. (Lenz's law) So we will have finite charge time.

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17. ### The ElectricianActive Member

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http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capeng2.html#c4

18. ### cowboybobWell-Known MemberMost Helpful Member

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Agreed.

In a not dissimilar fashion, when a photon strikes an electron in an orbit around a nucleus, its energy is transferred to that electron, forcing it to "jump" to a higher band, where it does not belong. It then "immediately" returns to its appropriate band and in doing so, ejects (emits, lets loose, whatever) a photon, thereby restoring valence equilibrium.

I used this visual to flesh out my understanding of solid state "hole" theory, with the primary difference being that the electrons actually "move" atom to atom (due to the absence of an electron as the result of either a positive or negative electrical charge) thus allowing for a current to flow.

I know there's a great deal more to it, but this is enough for me.

I might add that electron movement in tube type theory was a lot easier to understand...

Last edited: Sep 2, 2016
19. ### RatchitWell-Known Member

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Yes, that reference shows it all, but I will work it out for my example. Assume V = 10 volts, C = 1 farad, and R = 1 microhm. The equation for the current supplied by the voltage source is

Substituting the parameters from above gives

and plotting the curve gives

Energy = charge times volts, so

In other words, the area under current curve with respect to time equals the charge. The total charge times the voltage is the work or energy the voltage source had to do to energize the capacitor to ten volts. If I specified the resistance to be one nanohm, the result would be the same. The shape of the curve would show a higher initial value at t = 0, but it would decline faster. The area under the current curve will be the same no matter what the resistance is. Ultimately, if the resistance is zero, the current would be a spike of infinite height and infinitesimal time with an area of 10. The energy stored in the capacitor is 50 joules instead of the 100 joules the voltage source expended. Therefore, for every two joules the voltage source outputs, only one joule is stored in the capacitor.

Now, can anyone do the problem I proposed in post #31?

Ratch

20. ### MrAlWell-Known MemberMost Helpful Member

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Hi,

I partially agree, but you're doing the same thing Ratch is doing now, which is picking and choosing what factors you want to include and which you dont. If you want to use the standard electric lumped circuit element, then we have something to talk about. If you want to include various things like fields then you might as well include lead resistance, because why include theory about the field and leave out something so simple as lead resistance and plate resistance. If you want to be realistic then be realistic, dont cut it short for no good reason.
The better equation would turn into a coupled PDE.

21. ### MrAlWell-Known MemberMost Helpful Member

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Hello again,

Well that's nice but you're allowing at least some resistance which is the only energy dissipator. If you show 99.9J and the cap only has 50J then you've got to show where that other 49.9 went, and it you want to say it is radiated then we have to see it being radiated in some form.

Not only that, but why do we say that there is only resistance and (possibly) only radiated power? There's also dielectric losses and inductance leading to a set of coupled PDE's such as:
Vx=-I*R-It*L
Ix=-V*G-Vt*C

where
I is the current,
V is the voltage,
Vx is the partial of V with x, x being a spatial variable,
Ix is the partial of I with x,
Vt is the partial of V with t, t being time,
It is the partial of I with t,
C is the capacitance per unit length assuming uniform cross section,
R is resistance per unit length,
G is equivalent dielectric conductance per unit length,
L is total series inductance per unit length.

And even that's an approximation because we'd have to handle the plate area and the leads differently.
We might also have to include another equation such as Vy=-Iy*R-Iyt*L for the plate in the other direction if we dont consider it uniform.
The main point is if we are to pick and choose what we want to allow, then we get off too easy and it turns out to be just a short cut.

But i guess i would settle for seeing the equation with the radiated energy being shown in one of the equations without assuming "it's just there somewhere".