This post is a follow up of the "Finding how much energy disappears in two connected capacitors" thread in the Homework Forum.

Gravitational mass potential energy (elevation/height) is NOT the same as capacitance electrical potential. This is one of the reasons for the apparent paradox.

When we raise 1lb of mass 5 ft..........the mass does not change. And the potential is only proportional to the height.

But the electrical potential of capacitance, does not work like that. With capacitance, as we lift the 1lb mass, the mass would grow. Not only does it grow, but it grows in a set proportion with the height. So, electrical potential depends on the voltage.......BUT ALSO the set amount of charge at that voltage.

See the difference?

Let me make a clear picture for you. Please imagine an upside down cone, with the apex touching the ground. The height of the cone represents voltage. You will please notice, that as we raise the base of the cone(to make the cone higher), the area of the base increases. At ground the base area is zero. As we increase the height, the area grows. This area grows in proportion to the height, because of the constant angle of the apex. The apex angle, represents the value of capacitance. It can be varied at manufacture. The base area represents the amount of charge. You will notice that the base area(charge in Coulombs) is in proportion with the voltage(height). So, with capacitance.....the value of charge(mass) is totally dependent on the voltage(height) proportion. You can not change that setting.

With gravity, we can move 1lb from 10 ft to 5 ft. BUT, we can not do that with capacitance. Because the amount of mass(charge) depends on height(voltage).

It's not a fair comparison. Because mass does not change with height, but charge does change with voltage.

If we drop the voltage by 1/2.......look at how much the area decreased. That area is charge capacity.

Take two inverted cones. One has a high base at 20 volts with an base area of 1. The other is empty.

When we bottom connect the two......the high base falls and the low base raises to 10 volts, both at ten volts. The two resulting areas(charge), are equal to the starting area,,,,,,,BUT it is only at 10 volts. One half starting voltage.

Which is exactly equal to 1/4 of the original potential energy.

It's this mis-understanding of capacitance, the led to this paradox.

One can vary the starting voltages and different cap values...........but the same "cone mechanics" should apply.

Does that help anybody, or just make it more confusing?

Gobbly Goop?