Two capacitor paradox

Re:Two capacitor paradox by tijsvd on Monday May 25, 2020 @03:10PM (#23303905)

To say that the energy of the water is mgh is a simplification. It's really 1/2 * h^2 * A * mass density. The water at the top has more energy than the water on the bottom. The energy in the water is square to the water level, but the amount of water is linear. It's the same with a capacitor, the energy is square to the voltage, but the number of electrons is linear.

It works out to the same 50% because the analogy is just very good. Dividing over two barrels/capacitors means halving the potential level (amount of water/load doesn't change), which means 1/4 of the energy in each barrel.

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Re:Two capacitor paradox by agapon on Monday May 25, 2020 @03:37PM (#23304149)

This is wrong. The energy is proportional to the height, not its square. You would get wrong units otherwise.

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Re:Two capacitor paradox by tijsvd on Monday May 25, 2020 @06:35PM (#23305637)

The energy is proportional to both the height and the mass. The mass is proportional to the height itself. Hence the energy is proportional to the square of the height.

If the fill level is h, so the weighted average of the mass is at h/2,then

E = m * g * h / 2

m = V * r

V = A * h

E = A * r * g * h^2 / 2

m2 * kg/m3 * m/s2 * m2 = kg m2 / s2 = J

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Re:Two capacitor paradox by agapon on Wednesday May 27, 2020 @05:51AM (#23321221)

Yeah, I totally forgot that there is a height component in the mass as well.

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