For Woopy: Explanation for why you lose 1/2 energy in a capacitor

[Magluvin]

Magluvin:

Ever since I told you that your one-magnet no-bearing spinner was never going to work and your friend's clip was a fake you have gone ape-shit on me.  You have looked for opportunities to give me a hard time and you get argumentative to the point where most of what you say makes no sense and it's intentionally said just to add fuel to the fire.

The question that you posed to me that Poynt answered was a rigged question you intentionally made up to be as difficult as possible to start the same ridiculousness all over again.  You had no interest in getting the answer to that question, it was just an attempt to engage me in a fight.

So before I even discuss this, the question for you is this:

Is this over and are you going to stop this behaviour from now on or are you going to continue looking for opportunities to have "big fights" and throw insults at me and wig out?

So what's it going to be from this point onwards?

MileHigh

Cmon M.  My first post was intended for you. Your thread. But Poynt nailed it. Not so complicated. He even went beyond.  The only things I would maybe disagree on is the 7.07 v results, because as he said, these would be ideal situations and they dont exist, sooo, are we sure. And its the ferromagnetic, end of the universe stuff, as we had no inductance and no resistance in the example. So currents should flow fast and smooth and no magnetic pulses or fields as inductance doesnt exist, and the closing of a switch should produce no sparks as there is no resistance.     But that wasnt a trick. I was just eliminating any criteria other than capacitance. Just to isolate the idea of capacitance. 

As for my last experiment, I just came up with that after TK posted the series parallel cap post.  It doesnt even really match what he said, bit something clicked when he said it. So I tried it in sim, with a variation, and I was a little freaked out by it. I tried it again, different values and such, but look what I got. Is it not interesting?

Are we not creating a level of efficiency in what I have shown, on the whim, as compared to what this thread was intended to show in the first place? Think jim. 

Now look. You blow up over what? Im ok. TK is ok. Poynt is ok.

I wanted you to answer because you are the one that is making a point here by starting the thread. My lil circuit is definitely on topic. No?  Im not here Shootin off at anyone. ;] Im showin real deal stuff also. No games.

U civil, me civil. Simple.  But if I smell a hint of insult, I will not remain in an imaginary corner. Does that make sense?

I think I know why the circuit gives the results, but I want to know if your explanation in the first post here can be applied to my lil version as well. Im just not sure how really.

Because, in my circuit, we didnt lose 50% total as in your first example, and we didnt use inductors, just caps.

So maybe it is a seed of something better than just a cap to cap exchange. Maybe it could be expanded upon to do better. Maybe TK's Post was a good hint. Can you explain why he posted that?

But maybe this doesnt sound good at all to you. We are always seemingly on the opposite sides of the table.

Anyways, take it for what you will.

Mags

[MileHigh]

Magluvin:

I told you the first "no bearing" setup was not going to work because I was speaking the truth and it was sound advice so you would not waste your time.  That was a crazy fight and subsequent to that the discussion about the setup with the two spinning magnets and the LEDs was borderline psycho.

So I am asking you for a straight answer to my question:  So what's it going to be from this point onwards?

MileHigh

[woopy]

Hi MileHigh

Thank's to come back to this topic, because as you know i made a lot of experiments some time ago with those cap transfer,
And of course each time we apply the famous stored energy formula  (1/2CV2), we always loose half the energy after the transfer of one charged cap in an other same but discharged one.

I am  not completely sastified with that situation, but i have to accept it because it seems to be a fact.

But today i am puzzled by the reply  number 8 by NerzhDishual on this thread, where he discharge the caps accross a motor and he counts the number of revolution per discharge , and it seems that he get no  loss in revolutions after the transfer.

And also Magluvin get some special result in the Falstad sim ??

Any explanations ?

Youp !! the thread will hopefully be of  great interest

good luck at all

Laurent

[TinselKoala]

@Mags: Your problem is an interesting one. But I don't agree with the numbers you get. Are your numbers measurements?

Here's how I am reasoning, and I haven't done this problem in a while so please check my work and tell me if I'm screwing up somewhere.

Energy is conserved. Charge is conserved. Not voltage. In a capacitor, the energy boils down to a product (technical term: means the result of multiplication) of the voltage on the cap and its capacitance. But the energy is directly proportional to the capacitance and to the _square_ of the voltage.

To find the capacitance of parallel capacitors you simply add the capacitances. And of course if caps are in parallel they are all at the same voltage. To find the capacitance of series capacitors, it's the same formula as _parallel_ resistors: 1/C_total = 1/C₁ + 1/C₂ + ... + 1/C_n.  And if two identical caps are in series and charged and then separated, they will each be at half the voltage of the series pair, just like matched batteries in series.

So.... now we can calculate. The CofE tells us that, barring losses, we have to have the same energy after as before. How much is that?
The Energy E on a cap is given by E = (CVV)/2, with the capacitance in Farads, the voltage in Volts and the answer is in Joules.
So after you charge the one 10uF cap to 5 volts I get 0.000125 J in the system. This energy will be conserved, I already know that much. Right?

Now I close the switch and charge the second lone 10uf cap. That original energy is now distributed in two identical caps, so half of it is in one, and half in the other. Since these caps are in parallel now, they are at the same voltage. (Yes, they are in series too, but we are going to "measure" their total voltage in parallel, aren't we?) But caps in parallel have total capacity equal to the sum of their capacitances. So we now have 0.000125 Joules in 20 uf. This means the voltage on the parallel pair, therefore on each cap, will be 3.53 V, from the cap energy equation.

Now we do it again, but instead of a single 10 uf cap in the second position we have two in series. Putting these in a black bag, we see a 5 uf cap (two 10s in series inside the black bag). So now we close the charging switch as before.

Now, the original 0.000125 J is distributed among the 10uF of the original cap and the 5 uF of the black bag. But since the 10 uf and the black bag are in parallel for the measurement, they are at the same voltage. So... calculating, we find that 0.000125 J in 15 uF will be at a voltage of 4.08 V , and since the 10 uf and the black bag are in parallel they both are at 4.08 V. And when we open the black bag we find two identical caps in series carrying the same charge, so they must be at 2.04 volts each.

So we have one 10uF cap at 4.08 V, and two 10uF caps at 2.04 V each. Computing backwards to the energy, it adds up to what we started with.

So now we take one of the 10 uF caps from the black bag  at 2.04 V and the original 10 uF cap at 4.08 V and close the switch. The charge equalizes across the caps again. Since the capacitances are equal the charge will be equal in each cap. The total energy will be E = 0.000125 J - 0.000021 J = 0.000104 J held in 20 uF of capacitance. This will give us a voltage of  V=sqrt((2xE)/C) = 3.25 Volts on each cap.

So now we have two caps at 3.25 volts and one at 2.04 volts. The two at 3.25 volts have 2 x (CVV)/2 = 0.000106 J
and the other one at 2.04 V has CVV/2 or 0.0000208 J and again we have the same total of 0.000125 J energy we started with.

In the real world there will be resistive and radiative losses at every stage so the resultant Voltages will be lower and so the energy totals will be lower at every stage.

But....if we hook our now charged ideal caps in series, we can measure almost 8.6 volts across the resulting 3.3 uF stack. What is its energy?
E= CVV/2 = 0.0000033 x 8.6 x 8.6 / 2 =  the same 0.000125 Joules we started with by charging the initial 10 uF cap to 5 volts.
Minus losses of course. (And we have just invented the "Mags Bank" voltage  multiplier.)



Sorry, what was the question again?

Here's a way to think about charge, voltage and capacitance. Charge is the fundamental conserved quantity. Who cares what it is.... we just need to know about one property, and that is that like charges repel, and the force of repulsion is as the inverse square of the separation. So the closer you get like charges together the stronger they repel each other.
This repulsion of like charges IS voltage. ( Actually voltage is the result of the gradient of the E field, but it's simpler just to think of it as the "tension" of opposite charges attracting or the "pressure" of like charges repelling.)
And capacitance is like.... the space in a room. There is only so much space in any given room and the walls are only so strong. So now you start stuffing charge carriers (electrostatically charged ping pong balls, electrons, holes, cats,  whatever) into your room. The first one goes in easy. The second one not so easy, it is repelled by the one already in there, so to get the second one in you have to push it in harder (raise the voltage). The third one ditto. Eventually you reach the point where the _capacity_ of the room just can't hold any more of these mutually repelling charges and one of them punches through the wall and they all leak out fast through the hole in the dielectric wall.
So the bigger the room, the more charge it will hold at a given "pressure". And if you make the walls stronger the same sized room will hold more charge at higher pressure. There is more energy in the "pressure" than there is in the plain number of charges (the size of the room) so the higher the voltage, the "more more" higher the energy stored in the pressure.

I really like Jean's motor-counter idea. I'll have to build one myself, I have a counter like that in one of my boxes somewhere I think.

[MileHigh]

Magluvin:

Okay, in the spirit of cooperation I am going to assume that the crazy times are over and done with and it's water under the bridge.  Plus we need a simple explanation for this phenomenon.

I am going to assume that you have worked through the problem and you have confirmed that the simulation's numbers are correct.  If you haven't then I strongly advise that you do work through the problem.  If you crunch the numbers then you should see that it all checks out.  If you crunch the numbers the answer is basically staring right back at you.  Not trying to work through the problem is a mistake.  In other words saying, "If I short two capacitors together I get result A, so if I short some capacitors together together in a different sequence I am expecting result A but my simulation is giving me result B, what happened?"

The way to do the number crunching is that you always know that you have conservation of charge.  You know ahead of time that you don't have conservation of energy because of the presence of the resistor, but for sure you know that you have the conservation of charge.

I will leave it to anybody that is interested to crunch the numbers and I will give the answer in the next posting.

MileHigh