Having trouble visualizing Voltage = Joules / Coulombs

[NuLED]

Voltage = Joules / Coulombs

I am having difficulty getting this definition.

The other common equations make sense; Ohm's Law, and even Power = Volts X Amps.

But for a higher potential difference (higher voltage), it seems there is more energy per unit charge, but it is the "per unit charge" that I am tripping over.

For example, a coulomb is a bunch of electrons (6.25 x 10^18). So, at the very extreme, if I have only ONE ELECTRON, and a lot of energy in Joules, I have very high voltage. I totally do not understand how that is. One electron should have one unit of charge and the energy from that should be constant (?)

 

[(*steve*)]

imagine a lake of electrons (charge). Now imagine raising that lake up to the top of a mountain.

The same lake of electrons now has more energy when it pours out.

The change is height is really a change in voltage.

Does that work for you?

 

[NuLED]

Hi Steve - thanks, that helps a lot. So the VOLUME of charge is measured by coulombs. Nothing new but your image helped me visualize it better.

BUT here is still the problem: I thought voltage is the magnitude of potential difference across two points. So, the way I thought about it was, the MORE ELECTRONS at one side, and the MORE HOLES on the other side (or more deficit of electrons) then the MORE VOLTAGE.

Thus, in my understanding, the volume of electrons (coulombs) is still related to the potential difference.

I think I need to be able to understand how the height of the lake becomes analogous to the potential difference. (It would not be the physical distance between two points in voltage, and it would be inversely proportional anyway).

 

[NuLED]

Another part of this is, the way I thought about it is that the VOLUME should be on top, the numerator, and not the denominator. And that is why I don't get it. The larger the volume the larger the voltage, but in the equation it is the opposite way around.

 

[BobK]

V = Joules / Coulomb, is not an equation is a defintion of the unit of voltage.

The equivalant equations would be:

V = E / Q

Where E is energy in Joules and Q is change in Coulombs.

Now, rewrite this as:

E = V * Q

The energy is the product of the charge and the voltage. Which makese sends, the more charge or the the higher the voltage, the more energy we have.

If we took the original equation and put Q in the numerator, we would have:

V = E * Q

Or, solving for energy:

E = V / Q

The less charge you have, the more energy you have at a given voltage. Surely that does not make sense.

Bob

 

[davenn]

So the VOLUME of charge is measured by coulombs. Nothing new but your image helped me visualize it better.

No, read below

Thus, in my understanding, the volume of electrons (coulombs) is still related to the potential difference.

thats not the definition of Coulombs.... its not about how many there are available

The coulomb (unit symbol: C) is the SI derived unit of electric charge (symbol: Q or q). It is defined as the charge transported by a steady current of one ampere in one second: 1C = 1A x 1s

the second definition of a Coulomb is....
One coulomb is also the amount of excess charge on the positive side of a capacitance of one farad charged to a potential difference of one volt:

BUT here is still the problem: I thought voltage is the magnitude of potential difference across two points.

Yes

So, the way I thought about it was, the MORE ELECTRONS at one side, and the MORE HOLES on the other side (or more deficit of electrons) then the MORE VOLTAGE.

No .... from Wiki ....

Voltage, electrical potential difference, or an electric tension (denoted ∆V and measured in units of electric potential: volts, or joules per coulomb) is the electric potential difference between two points, or the difference in electric potential energy of a unit test charge transported between two points.[1] Voltage is equal to the work done per unit charge against a static electric field to move the charge between two points. A voltage may represent either a source of energy (electromotive force), or lost, used, or stored energy (potential drop).


Dave

 

[NuLED]

Hey thanks for jolting me with that; it was a fundamental misunderstanding. I have since researched it a bit more:

http://en.wikipedia.org/wiki/Elementary_charge

But still not really sure I have 100% gotten what you guys are saying. I will mull over it a bit more first.

 

[(*steve*)]

I will mull over it a bit more first.

Think of that lake of electrons again. As you pump them up the hill you are doing work on them.

That work increases the voltage.

Bob made he observation almost exactly correctly.

The equivalant equations would be:

V = E / Q

Where E is energy in Joules and Q is change in Coulombs.

(However he made a small algebraic error after that)

That tells you for a given amount of work (E), you will get a higher voltage (distance up the hill/Voltage) if there is a lower charge (smaller lake of electrons) to move.

And that fits in well with how we observe the world.

 

[(*steve*)]

V = E / Q

yes

E = V * Q

yes

V = E * Q

No, divide both sides by Q ==> V = E / Q (you're taking a step back to the original equation)

E = V / Q

And thus E = V * Q (take the same step forward)

Surely that does not make sense.

I bet it was late when you typed that. I've been down that path before

I must admit, it took me a few minutes looking at this before I figured out where the error was.

 

[NuLED]

Guys, thanks for bearing with me on this.

Actually Bob made no mistake. He transposed the charge Q to the numerator because I had said it didn't make sense for me that it is the denominator, since the more charge the higher the voltage (in my understanding). So that is why he illustrated it and showed me it didn't make sense algebraically.

Anyway, I think that is where the crux of my hiccup is. I don't get the CHARGE part.

So, let's see, Energy I get. Joules, whatever. That is not a problem.

Voltage I get. Voltage is the "potential force" or tension or strength. So it makes sense to be called the Electromotive Force. When "The Force" is strong enough, you get arcing across the air gap.

NOW, the CHARGE thing is the troubling aspect for me. What the heck is CHARGE?!

I had thought the Q Coulombs measured the quantity of electrons. Now I realize that was wrong and in fact an electron has a certain level of elementary charge. (Or the opposite of the positive proton charge e). Unfortunately, the elementary charge itself is also defined in terms of coulombs...

So if you can explain what the heck we are looking at when we talk about dividing Energy by Charges, then maybe I will get the missing link.

What is this Charge thing and why is less of them a higher voltage (when you spread more energy across less charges)? It almost seems like charges are buckets. And if you put more energy (water) into fewer buckets (charges) then the water height (voltage) is higher for each of these containers.

To explain my dilemma another way, if you had defined Voltage in terms of charge and distance, that would make sense to me. For example if you said Voltage = Charge divided by Distance, then the less distance, the higher voltage, or the more charge across the same distance, the higher voltage. (Something like that).

 

[wannabegeek]

Hey thanks for jolting me with that; it was a fundamental misunderstanding. I have since researched it a bit more:

http://en.wikipedia.org/wiki/Elementary_charge

But still not really sure I have 100% gotten what you guys are saying. I will mull over it a bit more first.

You might not "get it" fully, until you learn the calculus behind it...I was very confused too when I started to learn these principals...I confused the equations with the unit identities.

Electric potential is the potential to have electric energy....it's like holding a stone in the air 1 meter off the ground...the kinetic energy is mgh. Now, remove the stone, just consider the height which COULD occupy a stone...that's V. There's a gravitational field with out without a stone...

If there's an electric field, it's possible to have a charge and know it's electric energy. But even if there's no charge, we have a way to describe
how likely a charge would be to fall down the potential hill created by the field.

The way that electric potential can be shown to be a voltage in a wire in not easy...it' has to do with path integrals and the like....

let it go for now and memorize a bunch of stuff...it will make sense later...
wbg

Super mods can correct me if I'm wrong and I'll be staying up late reviewing this too...

 

[Number]

Well there are some great explanations here! Can I jump in on this and see how my own definition of voltage compares? I would like to see if how it was explained to me stands to be correct; more or less.

Voltage: The difference of an electrical field between two points in reference to another electrical field.

The way I interpret that is that the electrical field measured between two points (anode and cathode) compared to another reference electrical field (ground/earth) gives the difference in the potential or ability of electrical charge to move between the two points.

One example was given to me of saying, "12 volts." 12 volts compared to what ? The difference between two very large electrical fields might be 12 volts, but that same field when referenced to another electrical field could be significantly higher or lower. Example, 120V AC from wall to step-down transformer in reference to earth ground, that same step-down transformer when referenced to earth ground and say a resistor, might be much less, say 30V AC. The electrical fields are significantly different but can have the same current across all nodes.

I just think of volts as electrical fields in reference to some other electrical field. After all, it is electromagnetism that volts come from. Magnetic field from the magnetism section of the word, and electrical field from the electro part of the words. This is how it was explained to me and for the most part has held true.

My imagination tells me that there is probably some flaws in there, but I think as long as the structure of electromagnetism and the associated electrical fields is clear, then it should be fairly firm and sound in reasoning yes?

Please feel free to criticise. Can't learn the proper definition unless our own is tested against others.

 

[(*steve*)]

One example was given to me of saying, "12 volts." 12 volts compared to what ?

That's a key understanding. Voltage is relative.

 

[NuLED]

Number - yes your understanding is pretty much the same as mine. I think we are good with it. Voltage is the difference between two points, relatively. It makes sense because it is a motive force, and the stronger that difference, the more "motivation" - the best example is that when voltage is insufficient, there is insufficient difference, and therefore motivation, for charge carriers to get from A to B. With insufficient voltage, components don't work. With strong enough voltage, they even arc from clouds in the sky across the air.

(The trouble for me is not voltage itself but the definition that uses Q in the denominator.)

 

[(*steve*)]

(The trouble for me is not voltage itself but the definition that uses Q in the denominator.)

But you're not worried by that any more, right?

 

[NuLED]

Actually I still have not GROK it. I know I don't *absolutely* need to understand it to make circuits work but I just like to make sure I fully understand. It's like the holes and electron flow. Most people told me I don't really need to worry about it on the atomic level but I wanted to know.

Anyway, I don't know how else to explain why I am confused by it still.

 

[(*steve*)]

It's like speed is miles per hour. Hours is on the denominator.

Speed increases for a given distance if you have less time.

Voltage increases for a given amount of energy if you have less charge.

 

[NuLED]

OK let's try this: Can someone please define "charge" for me?

Thanks.

 

[davenn]

OK let's try this: Can someone please define "charge" for me?

Thanks.

http://en.wikipedia.org/wiki/Electric_charge

Dave

 

[Number]

This may or may not be off topic but I feel it relates to voltage and Q.

If you were to connect a voltmeter (I plan on doing this myself at some point) to an electromagnet, or permanent magnet, since the electrons are lined up in such a way to create a more negative and more positive side (poles), could you potentially get a reading for high voltage?

My reasoning is that since they are lined up (they being the electrons) then a charge flowing from one side to the other would have much more "motivation" to get from one side to the other, or vice versa, not being motivated to go from one side to the other. Electromagnetism defines the electric & magnetic fields, to me it would make sense that matter which is "organised" would allow charge to flow much easier due to a much greater potential difference between the poles.

Also my thinking is that since magnetic fields induce electric fields, which is the voltage, it makes sense to me that a magnet would allow charge to flow more or less easily.

Is there a formal definition or relatable term that relates this concept? Obviously Electromagnetism is the root behind all of this, but I'm interested to see if there's a deeper explanation for this. Google seems like a good place to start. Except that for a search query I really have no idea how to phrase it. :sad: