Farads and Coulombs

Thread Starter

cmartinez

Joined Jan 17, 2007
8,286
They are measures of different things. A farad is a measure of how much charge a capacitance can hold for each volt of potential difference across it. It describes the structure and applies whether or not there is any charge stored there at all. A coulomb is a measure of how much charge is actually stored on that capacitance at a particular time (or under a particular set of conditions).

Neither is a measure of energy, though both can be a proxy in a given context. If I tell you that one capacitor has 1 mC of charge on it and another has 2 mC of charge on it, can you tell me which one has more energy stored in it? Of course not, since the energy stored on a capacitor is CV²/2. Since Q = CV, this can be written as Q²/(2C). So if the 1 mC charge is on a capacitor that has ten times the capacitance, the energy stored in it will be many times smaller than the capacitor charged to 1 mC due to the much higher voltage required to place the smaller amount of charge on the smaller capacitor.

As for transistor ratings, I've only seen capacitance values given since they are descriptive of the structure. But in cases where you have a relatively fixed voltage, such as the base-emitter junction of a BJT transistor, I can see it being convenient to describe the capacitance in terms of the amount of charge that is stored there at that operating voltage. In designing imagers we commonly did the same thing -- the pixel capacitance was often discussed in terms of the number of electrons (not coulombs, but the number of electrons) it could hold at it's saturation level (usually defined as the point at which it either became too nonlinear or the point at which charge would start to be lost through some mechanism).
Please correct me if I'm wrong, but this is how I understand things so far:
  • The Coulomb is a unit of charge, and therefore it can also be interpreted as a certain quantity of electrons. 6.241509×10^18 to be precise, according to the Wikipedia.
  • A Farad is a unit of capacity of charge, and it helps to more easily calculate the amount of energy stored in a device when the potential (Voltage) is known.
This begs my next question:
If temperature is the average velocity of the molecules in a substance, and if heat is the total kinetic energy of the molecules present in that substance, what does one Volt in a single electron represent?

That is, I find temperature (and heat) easy to visualize in physical terms. But what's the difference between one electron with a potential of 1V and another with a potential of 100V? They are both electrons with exactly the same charge, of course, but somehow I don't think that their voltage difference relates to a kinetic characteristic, such as their relative speed.
 

#12

Joined Nov 30, 2010
18,224
somehow I don't think that their voltage difference relates to a kinetic characteristic, such as their relative speed.
Boy, you've wandered off into Disneyland now! I can't see how random motion relates to differing concentrations of charge. Take milk, for example. It is not a solution, it is a colloid. The particles remain suspended by random (Brownian) motion. How much voltage does a milk molecule have? Does the voltage change if you throw the glass of milk? Look up posts by Gerry Rzeppa to learn about the relationship between velocity and several aspects of electrical circuits.:D
 
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WBahn

Joined Mar 31, 2012
30,303
One volt is, by definition, a potential energy of one joule per coulomb of charge.

Voltage is inherently differential (or referential).

Consider a gravitational analogy. Altitude in a gravitational field is a measure of gravitational potential energy per unit mass. Let's define the unit cmart to be a potential energy of one joule per kilogram. Near the Earth's surface, you have to lift a 1 kg mass roughly 10 cm (let's pretend the gravitational constant is 10 m/s² which is also 10 N/kg) to increase its gravitational potential energy by one joule. Thus we arbitrarily define some reference level to be 0 cmarts and we have 1 cmart for every 10 cm above that reference level.

So if we have 1 kg at the 1 cmart it has 1 kg-cmart of potential energy and if we have 1 kg at 100 cmarts it has 100 kg-cmart of potential energy. How much energy is a kg-cmart? Well, we defined the cmart as being 1 joule per kilogram, so 1 kg-cmart is 1 J.

What this means is that it took 100 J of energy to raise that 1 kg mass from the zero reference level to the 100 cmart level and, similarly, it will release 100 J of energy if it is lowered to the zero reference level.

Saying that an electron is at a voltage of 100 V is the same thing -- it tells you how much energy was required to position that electron at that voltage relative to if it had started at the zero voltage reference level and also how much potential energy it will give up if it is returned to that level.

Just as knowing a mass' gravitational potential will let you calculate it's speed if it is dropped through some distance, so to does knowing an electron's electrical potential allow you to know it's speed if it is dropped through some voltage difference.
 

Thread Starter

cmartinez

Joined Jan 17, 2007
8,286
One volt is, by definition, a potential energy of one joule per coulomb of charge.

Voltage is inherently differential (or referential).
No problem for me accepting those two points.

What I'm trying to visualize here is, what's the physical difference between two single electrons with a potential of one volt between them. Their speed? (I doubt that), their charge? (most certainly not, of course), their energy? (certainly yes, but how?). Or maybe, is my question the wrong question here? Like asking how many liters there are in a furlong, or something like that?

As suggested by @#12, I'm in the middle of reading your answers in this thread. It's fascinating reading, to say the least.
 

#12

Joined Nov 30, 2010
18,224
Let me try again. Heat is the random motion of molecules. You can infer that the molecules are knocking electrons around. That doesn't change the amount of charge on the electron and it doesn't change the voltage of the mass. I would be curious about the calculation of the apparent current flow of one electron during one bounce in a kilogram at different temperatures, but it's pointless because all the motion averages out to zero.

Voltage is about a difference in concentration of electrons. All the electrons have the same charge and the same mass. To get 100 volts, you have to stuff the right number of electrical charges into a certain amount of capacitance. The electrons which carry the charge will have a velocity as they move into the capacitor, and that can be calculated, too. A hundred volts worth of electrons aren't going to wander into the capacitor by random.
 

WBahn

Joined Mar 31, 2012
30,303
What I'm trying to visualize here is, what's the physical difference between two single electrons with a potential of one volt between them.
Let's work two analogous situations.

We have Mass A at 100 m and Mass B at 101 m. We have point C at 99 m.

We have Electron X is at 100 V and Electron Y is at 101 V. We have point Z at 99 V.

Since the mass is positive, it will give up energy as it goes to a lower potential height. Moving Mass B to point C will give up twice as much energy as moving Mass A to point C.

Since the charge on the electron is negative, it will require energy to move the electron to a lower electrical potential. Moving Electron Y to point Z will require twice as much energy as moving Electron Y to point Z.

In both situations, the assumption is that all other forms of energy, such as kinetic, are kept the same at both ends. So each item starts at rest, is moved, and then returned to rest at the end of its journey.
 

BR-549

Joined Sep 22, 2013
4,928
A volt is a unit of potential. But potential can also move. The velocity of potential adds to the original potential.

If the potential is static, the voltage is related to charge location.

If the potential is moving, the voltage is related to charge velocity.
 

Thread Starter

cmartinez

Joined Jan 17, 2007
8,286
Voltage is about a difference in concentration of electrons
You mean like electron density? More electrons in less volume? If that is so, then I think that my mind has just gone click.

So, say, I have a capacitor or 1µF, and I charge it to a potential of 1V. If I were to charge it to 2V, then by necessity it's total charge would change as well, because the two properties are dependent.

Energy-Capacitor.jpg

It's like ohm's law, in which voltage, current and resistance (and hence also power) are related, and one can't change one without affecting the others.

And yes, @WBahn, I perfectly understand the potential energy analogy between objects at different height, and objects at different voltage. Thanks for the explanation.
 

WBahn

Joined Mar 31, 2012
30,303
A volt is a unit of potential. But potential can also move. The velocity of potential adds to the original potential.

If the potential is static, the voltage is related to charge location.

If the potential is moving, the voltage is related to charge velocity.
You need to brush up on the notions of "potential" versus "kinetic".
 

WBahn

Joined Mar 31, 2012
30,303
You mean like electron density? More electrons in less volume? If that is so, then I think that my mind has just gone click.
To some degree you can think of it this way, but you can have two capacitors with the same volume and the same configuration and the same number of electrons stored yet have different voltages and different amounts of energy stored. All that is needed is to use a different dielectric between the plates.
 

Thread Starter

cmartinez

Joined Jan 17, 2007
8,286
To some degree you can think of it this way, but you can have two capacitors with the same volume and the same configuration and the same number of electrons stored yet have different voltages and different amounts of energy stored. All that is needed is to use a different dielectric between the plates.
Yes, that different materials have different dielectric properties, I get, thank you.

One of the reasons for my initial confusion is that in a particle accelerator, for instance, energy is expressed in electron-volts. And since an electron has a fundamental charge, and one farad=1*coulomb*volt, I got kind of mixed up. But then it occurred to me that an electron also has mass, and that's why an electron-volt is not the same as a fraction of a farad, but rather a unit of energy.
 

WBahn

Joined Mar 31, 2012
30,303
Yes, that different materials have different dielectric properties, I get, thank you.

One of the reasons for my initial confusion is that in a particle accelerator, for instance, energy is expressed in electron-volts. And since an electron has a fundamental charge, and one farad=1*coulomb*volt, I got kind of mixed up. But then it occurred to me that an electron also has mass, and that's why an electron-volt is not the same as a fraction of a farad, but rather a unit of energy.
An electron-volt is the product of an amount of charge (one electron charge, which is 1.602E-19 coulomb) with an amount of potential energy per charge (one volt, which is one joule per coulomb). Thus the result has to be energy since it is expressed in joules (1 eV = 1.602E-19 J).

It has absolutely nothing to do with whether the electron has mass and whether the electron has mass has absolutely nothing to do with the electron-volt not being the same as a fraction of a farad. A farad is simply not a measure of energy and is simply not the same as ANY measure that is.

In common usage, saying that an electron has, say, 40 keV of energy is saying that it has the kinetic energy that results from letting one electron's worth of charge accelerate through a 40 kV potential difference. In going through that potential difference, the electron converts electrical potential energy to kinetic energy. How much energy was converted? 40 keV. How much did the kinetic energy increase by? 40 keV. Notice that mass has not entered into the discussion at all yet. Now, if you want to know how fast the electron is moving, then you need to use the mass of the electron.
 

Thread Starter

cmartinez

Joined Jan 17, 2007
8,286
:mad: I hate it when this happens... my bad:
No, one farad of capacitance will store one coulomb of charge PER volt. C = Q/V, not C = Q*V.
Yes, I got that from the start, got a little mixed up there while typing.

But what's really bad:
A farad is simply not a measure of energy and is simply not the same as ANY measure that is.
It shows that I didn't do my research very well before my last post... how embarrassing. Anyway, rest assured. After all of your patient explanation, I think I got it now. So thank you all.

On the other hand, if:
An electron-volt is the product of an amount of charge (one electron charge, which is 1.602E-19 coulomb) with an amount of potential energy per charge (one volt, which is one joule per coulomb). Thus the result has to be energy since it is expressed in joules (1 eV = 1.602E-19 J).
Then, if we consider that energy is equivalent to mass, then I might have the base for an argument. But I don't want to go there... 'cause I don't want to start looking like a Troll here :oops:

Anyway, I have another question, this time regarding the nature of fields. But I think I'll open a new thread for that, and also go dig a little deeper before posting it... lest I lose another tooth in the face of my already badly beaten self-esteem... :confused:
 

#12

Joined Nov 30, 2010
18,224
you can have two capacitors with the same volume and the same configuration and the same number of electrons stored yet have different voltages and different amounts of energy stored. All that is needed is to use a different dielectric between the plates.
ACK! Do not confuse the volume of a cylinder with the amount of capacitance. It just muddies the waters. In this conversation, it is sufficient for capacitors of equal size have equal capacitance.

You could type for a week explaining all the different dielectrics, the advances in thin film technology in the last thirty years, and the different properties of each mechanical configuration, but it will not help Mr. Martinez with this question.
 
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crutschow

Joined Mar 14, 2008
34,843
You mean like electron density? More electrons in less volume? If that is so, then I think that my mind has just gone click.
............
Electrons repel each other so if you apply a voltage to the electrons in a conductor then they will move slightly closer to each other until their mutual repulsion matches the added voltage.
I suspect the change is small for typical electronic voltages.
 
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