See the attached drawing. Trying to prove:

1/C total = 1/C1 + 1/C2 + ..... for series connected capacitors. My math is based on the entropy idea that matter and energy seek equal distribution. An example would be the Nernst equation from biology, whereby osmotic pressure, transmembrane potential, pH, and individual solute concentrations co-regulate each other.

Assuming 2 identical series connected capacitors. The system voltage would first charge the outer plates. This would be, for example, +3 and -3. The two electrical fields would develope based on a charge difference in plates c1a and c1b or c2a and c2b, charging the inner plates to +3 and -3. (Equal distribution of field and charge, thus including Equal distribution of associated voltages. If total voltage = v1+ v2...... then you soon arrive at the correct formula for series capacitors. The example assumes identical caps, and equal charge distribution. But, based on the Nernst equation idea, any series of caps with different plate areas, gaps and permitivities, would seek the most optimal distribution of charge, field and voltage. Thus, acting like a series of average-value identical caps. ????

 

Using the Nernst equation (or derivations) to calculate capacitor charge is an interesting idea but I don't think it's practical for two main reasons:

1) It's usually applied to redox reactions in solution with highly mobile charge carriers. Since a capacitor is a solid or semi-solid, the exact dimensions of the device come into play because the redox potential depends on the concentration. Determining the concentration for a solid is harder than a liquid or gas because the volume takes up a rigid shape.

2) The plates of a capacitor normally do not participate in redox reactions.

Despite these points, we can still use the Nernst equation to compute how much charge needs to accumulate before the activation energy threshold for a given reaction is reached. However, the Nernst equation predicts the equilibrium condition but a capacitor technically never reaches equilibrium (asymptotic, tends towards infinity but never reaches it).

I can't say much more on the topic as I only have a year of college chemistry. But to quote my favourite physicist: "The energy of a system tends towards less". Even in a closed system where the total energy remains constant, the charge differential will try to equalize itself as best it can, and that's what the Nernst equation is getting at.

 

Using the Nernst equation (or derivations) to calculate capacitor charge is an interesting idea but I don't think it's practical for two main reasons:

1) It's usually applied to redox reactions in solution with highly mobile charge carriers. Since a capacitor is a solid or semi-solid, the exact dimensions of the device come into play because the redox potential depends on the concentration. Determining the concentration for a solid is harder than a liquid or gas because the volume takes up a rigid shape.

2) The plates of a capacitor normally do not participate in redox reactions.

Despite these points, we can still use the Nernst equation to compute how much charge needs to accumulate before the activation energy threshold for a given reaction is reached. However, the Nernst equation predicts the equilibrium condition but a capacitor technically never reaches equilibrium (asymptotic, tends towards infinity but never reaches it).

I can't say much more on the topic as I only have a year of college chemistry. But to quote my favourite physicist: "The energy of a system tends towards less". Even in a closed system where the total energy remains constant, the charge differential will try to equalize itself as best it can, and that's what the Nernst equation is getting at.

You are correct in dismissing the application of the chemistry involved. My mention of Nernst was more as an example of math, displaying the tendency of a system to seek the most "peaceful" distribution of both material and all forms of energy. My relatively modest background as a nurse and now an electrician, leave me with my inherent abstract mind, but limited advanced math. My life can be lived by blindly looking up formulas and applying them. They are very old, true and tested.

But I always feel better if I've proven them once. The math analogy is to see if a multifactoral self-adjustment like the Nernst equation would allow projecting the properties of equal caps to include unequal ones.

Side note: what are you aiming for in your studies?

 

You are correct in dismissing the application of the chemistry involved. My mention of Nernst was more as an example of math, displaying the tendency of a system to seek the most "peaceful" distribution of both material and all forms of energy. My relatively modest background as a nurse and now an electrician, leave me with my inherent abstract mind, but limited advanced math. My life can be lived by blindly looking up formulas and applying them. They are very old, true and tested.

But I always feel better if I've proven them once. The math analogy is to see if a multifactoral self-adjustment like the Nernst equation would allow projecting the properties of equal caps to include unequal ones.

Side note: what are you aiming for in your studies?

Generating a proof for a solid capacitor using Nernst equation seems like a tall order but you could model a capacitor using two jars filled with liquid. A primary difference between a capacitor and electro-chemical cell is the presence of a salt bridge. Remove the bridge and you're essentially left with two conductors separated by a dialectic (ie. a capacitor). Consider this experiment:

1) Fill two identical glass jars with 1L of de-ionized water.
2) Place jars 1cm apart but never touching.
3) Place a platinum or other inert electrode in each jar and apply a voltage.
4) Time how long it takes for the terminal voltage to reach 63.2% of the supply voltage (1 time constant).

Then run the experiment again but this time only put 500mL water in one jar and 1L in the other. If I'm not mistaken, the decrease in water should correlate to a proportional decrease in capacitance. Once you get the result, see if you can generate a (partial) proof using the Nernst equation. I imagine you'll have a real hard time because it's effectively comparing apples to oranges (electrodynamics vs electrostatics).

What made you switch from nursing to electrician? That's quite the shift. For one thing, I found biology to be the hardest natural science by far. I switched majors from biology to computer science because I couldn't stand the process of science with the bazillion abstract and loosely defined concepts. Super interesting stuff but maddening from an academic perspective.

 

See the attached drawing. Trying to prove:

1/C total = 1/C1 + 1/C2 + ..... for series connected capacitors. My math is based on the entropy idea that matter and energy seek equal distribution. An example would be the Nernst equation from biology, whereby osmotic pressure, transmembrane potential, pH, and individual solute concentrations co-regulate each other.

Assuming 2 identical series connected capacitors. The system voltage would first charge the outer plates. This would be, for example, +3 and -3. The two electrical fields would develope based on a charge difference in plates c1a and c1b or c2a and c2b, charging the inner plates to +3 and -3. (Equal distribution of field and charge, thus including Equal distribution of associated voltages. If total voltage = v1+ v2...... then you soon arrive at the correct formula for series capacitors. The example assumes identical caps, and equal charge distribution. But, based on the Nernst equation idea, any series of caps with different plate areas, gaps and permitivities, would seek the most optimal distribution of charge, field and voltage. Thus, acting like a series of average-value identical caps. ????

The capacitance in series will be related to the inverse of them in parallel, its easy to see that in parallel one is basically creating a new capacitor who's plate areas are the sum of the individual plate areas.

Two identical capacitors in series is basically doubling the gap between the outermost plates, i.e. halving the capacitance.