Hayseed Capacitance

Thread Starter

BR-549

Joined Sep 22, 2013
4,938
I would like to introduce a physical concept, and a physical model or structure for the property of capacitance. I have a screwball intellect that thinks in pictures and structures, sorta like when people sketch on bar napkins.

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?
 

joeyd999

Joined Jun 6, 2011
4,434
Or, one could just resort to calculus for a more rigorous (and accurate) understanding.

Why complicate the uncomplicated? And why suggest a paradox where none is evident?
 

joeyd999

Joined Jun 6, 2011
4,434
Further: regarding "paradox" (and that there is none):

Gravitational mass potential energy (elevation/height) is NOT the same as capacitance electrical potential. This is one of the reasons for the apparent paradox.
You seem to assume the presumed "equivalent" of charging a cap is raising a mass to a certain height. This is not the case.

The equivalent would be pumping water into a column. The diameter of the column would be analogous to capacitance, and the height of the water would be analogous to voltage.

As the water height increases, the pressure (and therefore work) required to incrementally add more water also increases. Thus, each successive drop adds more energy than the previous drop. This can be integrated into a form equivalent of the energy/volt equation for capacitance.

See comment #5.
 
Last edited:

Teljkon

Joined Jan 24, 2019
174
As a novice this kinda helped me understand that voltage is kinda logarithmic something I did not know previously. so really when were talking about voltage were talking about it in volume and pressure. The pressure can down while the overall volume is the same. As the exerted force on the outlet is less depending on the volume of the vessel. So assuming voltage is measure of both volume in conjunction with pressure. What is the parallel in electronics speak of pressure and volume. My limited understanding would lean into, current and amps. With no real qualifiers other than that's what left.
 

crutschow

Joined Mar 14, 2008
25,695
As the water height increases, the pressure (and therefore work) required to incrementally add more water also increases. Thus, each successive drop adds more energy than the previous drop. This can be integrated into a form equivalent of the energy/volt equation for capacitance.
That's a good analogy.
So I believe the analogy also shows a loss in energy if two columns of water of different water heights and with either the same or different diameters, are suddenly connected together.
 

joeyd999

Joined Jun 6, 2011
4,434
That's a good analogy.
So I believe the analogy also shows a loss in energy if two columns of water of different water heights and with either the same or different diameters, are suddenly connected together.
Yup. I didn't do the math, but the equivalence should be exact.
 

joeyd999

Joined Jun 6, 2011
4,434
Great.
So, if you don't mind, I may use that analogy the next time a capacitance charge question arises (if you don't beat me to it). :)
I know some on this site don't like water analogies, but I think it can help newbies understand the basics.
I was thinking of patenting the idea. Care to pay royalties? :D
 

cmartinez

Joined Jan 17, 2007
7,177
I was thinking of patenting the idea. Care to pay royalties? :D
How about you get recognition as one of the greats instead?... imagine your picture printed on a t-shirt ... in a pose such as that of Che Guevara, staring at infinity ... a heroic champion to be perpetually remembered in posterity as the watershed intellect that changed the course of the history of electronics... everything would now be referred to as BJ and AJ ... :D:p
 

joeyd999

Joined Jun 6, 2011
4,434
How about you get recognition as one of the greats instead?... imagine your picture printed on a t-shirt ... in a pose such as that of Che Guevara, staring at infinity ... a heroic champion to be perpetually remembered in posterity as the watershed intellect that changed the course of the history of electronics... everything would now be referred to as BJ and AJ ... :D:p
I like BJs. Good idea.
 

Teljkon

Joined Jan 24, 2019
174
That fell apart quickly.

So in BR549's example and joes example both show that excess capacitance will drop voltage potential. Is that a fair conclusion of what is accurate? What I don't understand is logic dictates that pressure will have a different arc coming out of a cone than a cylinder with the same volume. I'm not an expert in laminar flow but water is my playground surfing diving etc. I would bet money a conical vessel will dissipate energy on a smoother arch than a than a cylinder think about how a toilet sucks down water it would be less effective in a cylinder toilet and a whole lot more gross. Although I might try to get a bj on one for bragging rights.
 

Teljkon

Joined Jan 24, 2019
174
Im still thinking about this even if i just plug into BR549's motives a little better he is really just looking for a better mathematical analogy than your standard water analogy.

What i should glean from this is

Pressure is voltage,
volume is capacitance
laminar flow is resistance
current is speed
whats amps?
 

cmartinez

Joined Jan 17, 2007
7,177
Im still thinking about this even if i just plug into BR549's motives a little better he is really just looking for a better mathematical analogy than your standard water analogy.

What i should glean from this is

Pressure is voltage,
volume is capacitance
laminar flow is resistance
current is speed
whats amps?
Teljkon ... see Joey's post #4 ... I think he hit the nail in the head with his analogy
 
Top