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#### onepower

• Hero Member
• Posts: 1008
##### The two capacitor paradox debate
« on: September 02, 2020, 07:19:20 PM »
The two capacitor paradox and moving zero planes.

I have one charged capacitor with +/- potentials and a difference of 10v. Now I connect an uncharged capacitor, they balance and both capacitors then have 5v on each but somehow I have lost 1/2 the energy... where did it go?.

Most say it was dissipated as heat or radiation but that's a weak explanation at best because it does not define the exact cause of how the energy was dissipated. When I did the experiment I found something quite amazing. We started with two +/- potentials at a difference of 10v with one zero plane dividing them however we ended with four +/- potentials and two zero planes over twice the surface area. So when we divided the energy into two distinct elements having twice the surface area the energy density must be 1/2 because the energy is dependent on the amount of electrical pressure per unit of area is it not?.

It's a chicken and egg dilemma, did the energy dissipate because it was flowing into the second capacitor or did the energy dissipate because it was flowing into the second capacitor which doubled the surface area decreasing the energy density by 1/2?. If the surface area did not increase the energy could not flow into the second capacitor but when it did it lowered the energy density so which mechanism caused the dissipation of energy?... exactly.

Contrary to popular belief the two higher potentials in the first capacitor sensing a path to a lower potential or greater surface area is the first cause not a current flow. As well the doubling of the surface area lowering the energy density by 1/2 is how the supposedly missing energy dissipated not the current flow. The current flow is an effect of the cause not the impetus which drives it.

Now the kicker, I have justified how a doubling of the surface area must reduce the energy density by 1/2 in the the two capacitor paradox which constitutes the cause of the dissipation of energy so if the conductor connecting the two capacitors dissipated energy as well ... then where did it come from exactly?.

You see we have to look at the bigger picture with respect to these problems because it is seldom cut and dry. The solution is actually quite easy so I thought I would throw this out as a brain teaser.

Regards

#### v8karlo

• Sr. Member
• Posts: 385
##### Re: The two capacitor paradox debate
« Reply #1 on: September 02, 2020, 07:56:56 PM »
If that is true, just raise voltage in cap from 10V to 20V and you will gain extra energy just like that.
If it works in one way, it should work in opposite.

Or maybe something is wrong?

#### onepower

• Hero Member
• Posts: 1008
##### Re: The two capacitor paradox debate
« Reply #2 on: September 02, 2020, 08:25:01 PM »
In the Wikipedia link, https://en.wikipedia.org/wiki/Two_capacitor_paradox, all there solutions relate specifically to losses in the conductor and they have completely ignored the source/sink. In which case I suspect they don't actually understand the concept of Energy. What energy is, When it is, Where it is, Why it is and How it is.

There lies the real problem and a majority of people do not understand Energy.

Regards

#### v8karlo

• Sr. Member
• Posts: 385
##### Re: The two capacitor paradox debate
« Reply #3 on: September 02, 2020, 08:40:35 PM »
Doubling or halfing voltage is done in linear fashion.

Power is calculated in exponential manner.

When our mind tries to connect dots from linear to exponential,
paradox occur, because it is unlogical for us.

Does that means that energy is 4 times smaller with halfing voltage ?
(not power but energy in cap)

So, you see,
everything is correct and
nothing is correct.

Glich in system.

#### forest

• Hero Member
• Posts: 4045
##### Re: The two capacitor paradox debate
« Reply #4 on: September 02, 2020, 10:14:13 PM »
is that related somehow to charge density ?

#### v8karlo

• Sr. Member
• Posts: 385
##### Re: The two capacitor paradox debate
« Reply #5 on: September 02, 2020, 11:01:01 PM »
I can only speculate about root of problem.

Charge density depends on charge field which repel each other.

Charge field strength relates to the inverse square law, which is exponential.
When this rule is translated via equations to the power,
it ends that power follow same rule and is exponential.

Just a guess. Never dived into math of power equations to try to find cause.

But I believe that cause is in equations.

#### onepower

• Hero Member
• Posts: 1008
##### Re: The two capacitor paradox debate
« Reply #6 on: September 03, 2020, 03:19:12 AM »
v8karlo
Quote
Doubling or halfing voltage is done in linear fashion.
Power is calculated in exponential manner.
When our mind tries to connect dots from linear to exponential,
paradox occur, because it is unlogical for us.
Does that means that energy is 4 times smaller with halfing voltage ?
(not power but energy in cap)

Exactly, while the voltage may be 1/2 the energy changes at a different rate which is exponential based on the charge density not the voltage following the inverse square law. More charges in a given area require more force to move them against the force of repulsion/attraction based on the number of charges already present. So energy is never 1+1=2 but 1+1=3, 2+2=9 and so on while the voltage is linear.

Which ultimately begs the question of how we could use this to our advantage given energy is everywhere in everything.

Regards

#### v8karlo

• Sr. Member
• Posts: 385
##### Re: The two capacitor paradox debate
« Reply #7 on: September 03, 2020, 04:51:41 PM »
P = U * I

Power is product.

Where do you see inverse square law in this simple equation.

Power should not follow inverse square law.
Inverse square law is reserved for strength of field of charges and should not be integrated into power calculations.

Somebody mixed apples and oranges and as result expect only apples.
Which can not be.

Otherwise, just keep adding voltage in cap and soon you will have so much power that you can power the city from capacitor.

Is it like that in reality?

#### Lunkster

• Full Member
• Posts: 176
##### Re: The two capacitor paradox debate
« Reply #8 on: September 03, 2020, 06:37:26 PM »
Doubling or halfing voltage is done in linear fashion.

Power is calculated in exponential manner.

When our mind tries to connect dots from linear to exponential,
paradox occur, because it is unlogical for us.

Does that means that energy is 4 times smaller with halfing voltage ?
(not power but energy in cap)

So, you see,
everything is correct and
nothing is correct.

Glich in system.

Can this problem be simulated by another method like the one in the attached drawing?

#### kajunbee

• Full Member
• Posts: 165
##### Re: The two capacitor paradox debate
« Reply #9 on: September 04, 2020, 12:51:15 AM »
Are you looking for another analogy for capacitors. If so you could replace the liquid  with a compressed gas.

#### WhatIsIt

• Hero Member
• Posts: 651
##### Re: The two capacitor paradox debate
« Reply #10 on: September 04, 2020, 01:43:35 AM »
Compressed gas is far more accurate representation
of charges and forces between them, which are calculated
with inverse square law.

#### onepower

• Hero Member
• Posts: 1008
##### Re: The two capacitor paradox debate
« Reply #11 on: September 04, 2020, 06:27:16 AM »
V8karlo
Quote
P = U * I
Power is product.
Where do you see inverse square law in this simple equation.
Power should not follow inverse square law.
Inverse square law is reserved for strength of field of charges and should not be integrated into power calculations.

Power is simply the rate at which electrical energy is transferred not energy in itself... so what caused the energy to transfer?.

Quote
Somebody mixed apples and oranges and as result expect only apples.
Which can not be.
Otherwise, just keep adding voltage in cap and soon you will have so much power that you can power the city from capacitor.

I think your confusing power and energy as many do. Energy is the thing which causes something to move and power is only a measure of the rate at which it moved. Energy encompasses everything not only the rate of transfer like power. Can you calculate why your car accelerates or brakes and the energy required based solely on it's velocity in Km/hr?. Well no power is at best a simplistic measure.

Quote
Is it like that in reality?

Yes, no professional uses simple power calculations they always use Energy calculations which why so many seem confused by the two capacitor paradox.

Regards

#### lancaIV

• elite_member
• Hero Member
• Posts: 5010
##### Re: The two capacitor paradox debate
« Reply #12 on: September 04, 2020, 11:56:19 AM »
Harold " Aspden Notes On Berlin Lecture "

Not full/empty caps but full/full caps dispute !

#### v8karlo

• Sr. Member
• Posts: 385
##### Re: The two capacitor paradox debate
« Reply #13 on: September 04, 2020, 01:25:24 PM »
V8karlo
Power is simply the rate at which electrical energy is transferred not energy in itself... so what caused the energy to transfer?.

I think your confusing power and energy as many do. Energy is the thing which causes something to move and power is only a measure of the rate at which it moved. Energy encompasses everything not only the rate of transfer like power. Can you calculate why your car accelerates or brakes and the energy required based solely on it's velocity in Km/hr?. Well no power is at best a simplistic measure.

Yes, no professional uses simple power calculations they always use Energy calculations which why so many seem confused by the two capacitor paradox.

Regards

I said that I can only speculate and try to find reason other than losses.

and I am confused why you opened thread if all of that is known to you?

Did you want to hear others opinions, or to find some victim so you can preach to that person how wrong he is?

Neither you or I are right.
Why?
Because it is still cap conundrum and is not solved.
Once when it will be solved you will know that you were right or wrong.
Until then, all your knowing is just as mine, rant on the moon.

But, been pleasure talking with you.

#### v8karlo

• Sr. Member
• Posts: 385
##### Re: The two capacitor paradox debate
« Reply #14 on: September 04, 2020, 03:52:21 PM »
Analogy of water, analogy of compressed gas.
Both share one thing.
The molecules will travel from first container to second until are equal.

Lets put 10m of wire between caps.

Electrons are charge carriers and they travel few meters per second through conductor.

So electrons will travel few seconds through 10m of wire.
But caps will equalize in nanoseconds even if wire is 100m long.

Charges can not travel between caps that fast.

That means that same amount of charges are same in both caps all the time.
Only pressure travels between caps, or voltage.

But in equation we calculate that half of charges will remain in first cap,
and half will travel to second.
While actually all charges stay in first cap and same amout of charges will be and was in second cap, just at different pressure, voltage.
So, no changes in charge amount.

But still we calculate half of charges and half of voltage, which means twice half.

Does this make any sense?
Or is just another rant?