The two capacitor paradox debate

[v8karlo]

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]

v8karlo

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]

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]

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]

Are you looking for another analogy for capacitors. If so you could replace the liquid  with a compressed gas.