# Is capacitor capacity linear with voltage?

• stargazer193857
In summary: The energy is the integral of voltage*charge for a capacitor. This is a quadratic function, so the energy stored in 40V is 1600X the energy stored in 1V.In summary, the conversation discusses the relationship between voltage, charge, and energy in capacitors. It is noted that while the charge on a capacitor is linear with voltage, the energy stored is a quadratic function. The use of different dielectric materials can also affect the behavior of capacitors.

#### stargazer193857

They are rated at 1V. Suppose they are in a 40V circuit, and rated to handle 40V. Would they then hold 40x the charge? I tried to calculate it base on electron repulsion, but I remember reading that electrons are not like gasses: they all go to the surface of the material in counter intuitive densities.

interesting puzzle.

Electrons are added to one plate and removed from the other so net charge in the capacitor doesn't change ,,,,
What does change is the energy stored in the field between the plates.

I'll guess that the answer to your question depends on the nature of whatever's in that volume between the plates.
C =εA/D
Dielectrics have polar molecules that align as the electric field tugs on them...
Is permittivity linear with applied voltage ? Surely for free space it is, but how about liquid electrolytes or polypropylene?

I'm on wife's IPad and haven't figured out yet how to paste links... Searching on permittivity dielectric function of voltage turned up some scholarly articles..

• Demforiq
stargazer193857 said:
They are rated at 1V. Suppose they are in a 40V circuit, and rated to handle 40V. Would they then hold 40x the charge? I tried to calculate it base on electron repulsion, but I remember reading that electrons are not like gasses: they all go to the surface of the material in counter intuitive densities.
Q = C.V so it's the charge that varies with voltage. C remains fixed. If C varied with voltage this would produce horrible distortion of signals in audio circuits, audio signals being AC.
http://thumbnails112.imagebam.com/37333/0363e9373324851.jpg [Broken]

Last edited by a moderator:
stargazer193857 said:
They are rated at 1V. Suppose they are in a 40V circuit, and rated to handle 40V. Would they then hold 40x the charge? I tried to calculate it base on electron repulsion, but I remember reading that electrons are not like gasses: they all go to the surface of the material in counter intuitive densities.
Caps with dielectric materials are made to operate with εrx=const. at given frequency fx. If relative permitivity εrx starts to vary with voltage at fixed frequency fx=const, expect bad things to happen.

Seems I can't quote.

Thank you to the second replier for that equation, q = c*v. That means capacity is linear with voltage. And you are right that capacitance is not, but that is different from capacity.

stargazer193857 said:
Seems I can't quote.

Thank you to the second replier for that equation, q = c*v. That means capacity is linear with voltage. And you are right that capacitance is not, but that is different from capacity.
'Constant' is the word you're after, I think. Charge is 'linear' with voltage. There will, almost certainly be substances with a dielectric 'constant' that isn't constant with the voltage across them but they are the last things that Capacitors would be made of.
Having said that, there are Varactor (Varicap) Diodes, which behave like regular diodes - only more so. When a diode junction is reverse biased, the capacity reduces as the bias voltage is increased. so their Capacitance can be controlled by varying the bias volts. But they have low Capacitance values and their use is pretty specialised and involves relatively high-ish frequency and low signal levels.

Last edited:
stargazer193857 said:
They are rated at 1V. Suppose they are in a 40V circuit, and rated to handle 40V.
A capacitor cannot be rated both for 1 V (only) and for 40 V, those would be two different objects.

A capacitor rated for 40 V, operated at 40 V, will store 40 times the charge it will store when operated at 1 V.
Therefore, charge is linear with voltage, and capacitance (which is the ratio between those values) is constant.

sophiecentaur said:
There will, almost certainly be substances with a dielectric 'constant' that isn't constant with the voltage across them but they are the last things that Capacitors would be made of.

Actually ceramic capacitors are made with a dielectric just as you describe. They are best avoided in audio applications as this results in distortion.

http://www.johansondielectrics.com/technical-notes/product-training/basics-of-ceramic-chip-capacitors.html#.VJdifP8-cg
http://www.maximintegrated.com/en/app-notes/index.mvp/id/5527

1. Capacitors are not constant capacitance with voltage, Some dielectrics have many effects with changing voltage. Some are rapid, some are slow. This becomes an interesting problem when trying to build precision sample and hold circuits, and, as stated above, can cause non-linearity in audio circuits.

2. Assuming a constant capacitance, the amount of charge on a capacitor is linear with voltage. It takes 40X the charge to charge to 40V than to charge to 1V. But the energy stored is a different matter. See http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capeng2.html