Can this capacitor cycle generate electricity?

Question

Imagine a capacitor where the distance between charged plates can be changed. It is connected to a circuit such that the following cycle is possible:

1. Capacitor is connected.
2. Plates are charged.
3. Capacitor is disconnected.
4. Plates are pulled apart.
5. Capacitor is connected again.
6. Plates are discharged at a higher voltage.
7. Capacitor is disconnected.
8. Discharged plates are brought back together. Repeat.

During step 4, work is done on the system to pull the plates apart. Because the plates are charged and disconnected, their charge does not change but the capacitance, ruled by C = εA/d becomes smaller because d is increasing. If the charge remains the same because the capacitor is disconnected, the voltage between the plates is inversely proportional to the capacitance. It should increase during step 4.

During step 6, we inject more Joules back into the circuit than what was used to charge the plates. A transformer can bring this current back to the nominal voltage, recharge the plates, and use the remainder.

Now, we obviously don't use capacitors to generate electricity, so there must be some flaw in the process above. What is it?

Answer 1

This is, in essence, how a Van de Graaff generator works. The only difference is that your "plates" are instead locations on an insulating belt.

This is a good way to make high voltages at low currents. It's hard to make a high current version of this because the belt can't carry much charge,

Answer 2

The electrophorus is a device which only needs to be charged at the start and then can be used to produce electric potential energy from the work done in separating charges.
It consists of a grounded insulator which has been charged negatively by friction and a metal sheet with a handle made of an insulator as shown in diagram 1.

The metal plate is put on top of the charged insulator and charges are induced on the metal plate as in diagram 2.
The charged insulator and the metal plate are not perfectly flat so there is limited contact between them and so the charged insulator loses very little charge.
The metal plate is earthed and the metal plate is left with a net positive charge as shown in diagram 3.
The last stage as shown in diagram 4 has work being done separating the charges and the potential of the metal plate increasing a great deal.
Early experimenters would then store the charge from the metal plate in a Leyden jar (an early form of capacitor) and then repeat the process 1 to 4 without having to charge the sheet of insulator again.

A video of one in action - Big sparks from a handheld electrophorus

Answer 3

Yes, this would be a way of converting mechanical energy to electrical energy. It would be a pretty cumbersome way of doing so though, it's way easier to get electrical energy from faraday induction.

Another practical consideration is that V only increases with d when d is much smaller than $\sqrt(A)$, so you'd see diminishing returns as you kept pulling the plates further apart.

Answer 4

The process you have described would generate electricity, or you could use the process attach the capacitor to a wheel via a pushrod) in reverse to make a sort of motor. The problem will be in the practicality of engineering an efficient version of your concept.

At a rough guess, there will be:

• energy lost in resistance of the circuit
• energy lost in displacing air from between the two plates as they move
• the capacitors will need to have a large surface area so will be bulky
• the capacitors will need to be rigid so likely rather heavy
• the mechanics of moving two parallel plates together and apart will require some clever and probably expensive engineering.
• etc...

In conclusion, just because something can be done in principle, it doesn't follow that it can be done with any degree of efficiency or practicality.