# How can you achieve different voltages in an electric circuit?

• Opus_723
In summary: say two charges next to each other, but one is a lot closer to the other than the average person's fingertip - then the voltage would be higher than if they were a lot further apart.
Opus_723
I'm in Circuit Analysis I this quarter, and I'm having a bit of trouble understanding voltage conceptually.

I understand the water pump analogy. Voltage is analogous to water pressure, etc. I just need to clear up a few things.

My book describes voltage as potential energy. I understand that if you separate protons from electrons, they have potential energy, since there is an attractive force between them. In a battery, the electrons are separated from the protons, and this attractive force makes them pass through the wire in order to come together.

But now I'm wondering how you achieve different voltages. If I separate twice as many charges, I must have used twice as much energy to do so, in which case the energy per coulomb would be the same. At first I thought that changing the distance between the separated charges made sense, but in that case, charges that were barely separated would have a stronger attractive force between them, and thus more voltage. It seems then, that connecting the ends of a battery with a longer wire would result in less voltage. Intuitively, I don't think that happens. Also, the equation V=W/Q doesn't include distance as a factor. I'm just failing to see how you can change the amount of potential energy of a charge, without involving distance. But maybe I'm just stuck thinking of potential energy in terms of balls and gravity from high school.

I don't know if this makes any sense. I'm probably misinterpreting something very fundamental, but I can't seem to get at it by myself. Everything I look up uses terms I don't understand, and I don't know where to begin decoding.

I'd really appreciate some help.

(If this belongs in the EE forum, I apologize, but since this is a such a fundamental concept, I thought Physics would be more appropriate.)

It's potential energy because the electrons want to get over to the protons and will be able to produce work from their movement. Like if you pick up a ball and hold it in the air. The ball has potential energy due to gravity, but until you drop it the ball can't do anything or produce any work.

Also, consider a battery. The electrons can't get to the positive side through the battery itself so they need a circuit to go through. The electrons all repel each other so when you complete the circuit you have a neutral conductor with one end connected to a positve charge and the other to a negative. What this does is pull electrons from one end into the positive terminal and push electrons out of the negative terminal and into the wire. The negative and positve charges don't need to be close to each other to produce a voltage difference. You simply need an imbalance in charges. Imagine a collection of electrons on a plate or something. This could be analagous to picking up balls and putting them in a basket in the air. A positive plate is analagous to the ground. Except that instead of just having gravity exert a force on the balls, the electrons push each other along with the positive side pulling.

Also, for I=V/R, a longer wire results in more resistance, which results in less current but not less voltage.

Thanks, Drakkith, but unfortunately that's the stuff I already understand. I understand how voltage is like potential energy, and I understand how a battery works. I was trying to give an idea of what I already know so that it might be easier to get at what I don't know.

What I'm trying to understand is how one produces different amounts of voltage. I know you create voltage by separating charges, but how do you vary the voltage? Like you said, the length of the wire, or distance between charges, doesn't affect voltage. So what does?

Voltage is not "potential Energy" it's Potential Energy per Unit Charge.
Think in terms of a Volt being one Joule per Coulomb and forget about the 'Force' bit. The Force (i.e. Field) comes from the Gradient of Potential and not just the Potential.Do try to forget about Water as soon as you can - there madness lies.

Opus_723 said:
Thanks, Drakkith, but unfortunately that's the stuff I already understand. I understand how voltage is like potential energy, and I understand how a battery works. I was trying to give an idea of what I already know so that it might be easier to get at what I don't know.

What I'm trying to understand is how one produces different amounts of voltage. I know you create voltage by separating charges, but how do you vary the voltage? Like you said, the length of the wire, or distance between charges, doesn't affect voltage. So what does?

Hrmm. It's kind of hard to explain. Just talking about charges, if you put many like charges together, you get an increase in voltage from there to somewhere else since more charges in a given area exert more pressure on each other.

Unfortunently, with batteries, it's not so clear cut. The batteries have a chemical reaction that takes place at each electrode which usually only takes place at a certain rate. Overall the voltage doesn't vary by much until the battery starts to get very low. Exactly how you get more voltage out of something like a battery I am not sure. I know that you can connect them in series to get more, but beyond that I don't know.

@Opus
You can create a Potential Difference by physically transporting charges onto a capacitor plate (like the Van der Graaff generator), you can build up charge by what is called Electrostatic Induction (as in a Whimshurst Machine), you can cause photo-electrons to leave a metal surface with enough KE to hit an electrode, causing a charge to build up and, of course, you can make an electromagnetic generator, which will produce an emf by moving a conductor through a magnetic field. Etc. etc. And the voltage across a battery is fixed by the electrochemical potentials of the chemicals used - limited by the rate at which the chemical reaction can replenish the charges on each electrode.
All of those methods will cause charges to separate. The energy each unit of charge has is called the Voltage. A battery is not a good example to choose for this sort of discussion because of the added layer of the dreaded Chemistry. It is mucy easier, in fact, to think in terms of a generator. The emf can be varied by altering the speed of rotation (dΦ/dt) and the available current is limited by the thickness of wire and the mechanical power supplied to the generator. Each charge that emerges from the terminals has so much energy and that energy is transferred to heat / light / mechanical energy in the load, according to the effective resistance. In general, the energy for each charge which flows is transformed to the same amount of energy in the load. By the time it gets round the circuit, no energy is left. (I'm not talking about the electrons here because they may never get right round the circuit, before the switch opens again) That's Kirchoff's Second Law / Conservation of Energy.
I'm not sure what it is that you don't get about this stuff. There is something that doesn't quite come together in your mind. I can only suggest
2. That you pay attention to the strict definitions of the quantities that are used in EE. The answer, for you, is in the detail somewhere, I think.

And, I've said it once and I'll say it again. Try to forget about the water thing. It really won't help in making a final step towards understanding because it is by no means a complete analogy. A drive belt or a chain could possibly help as a picture but I would, personally, go straight to the electrical definitions and the Maths.

Imagine a large single positively charged plate, and a postively charged particle. If you increase the charge on the plate, the voltage increases. If you increase the distance between the point source and the charge plate the voltage decreases. Both the strength of the field and the position in the field are part of voltage.

As an example, define a reference plane to be 100 meters away from the positively charged plate. A positively charged particle is released (it's initial velocity is zero) at some initial distance from the charged plate, and when it crosses through the reference plane, that charged particle will have some amount of kinetic energy equal to 1/2 mass times it's velocity2. If the particle's initial position is closer to the plate, or if the plate has a higher amount of charge, the particle ends up with more kinetic energy when it travels through the reference plane. If you know the voltage at the initial position and at the reference plane, the difference in voltage times the amount of charge on the charged particle will equal the kinetic energy of that particle as it crosses through the plane.

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I understand that Voltage is energy per charge. What I've been trying to ask (and I'm sorry if I haven't been finding the right words) is how you can change the amount of energy without changing the amount of charge. In other words, how do you get more energy per charge.

Drakkith and rcgldr, thank you both. Your explanations really clicked. Now I see how energy can be manipulated while holding the charge constant. That really helped.

Thanks everybody.

Opus_723 said:
I'm in Circuit Analysis I this quarter, and I'm having a bit of trouble understanding voltage conceptually.

I understand the water pump analogy. Voltage is analogous to water pressure, etc.
Then you are NOT understanding. Voltage is not analogous to water pressure. It is potential energy so, in the water analogy, the energy contained in a mass of water at a given height over the pump.

I just need to clear up a few things.

My book describes voltage as potential energy. I understand that if you separate protons from electrons, they have potential energy, since there is an attractive force between them. In a battery, the electrons are separated from the protons, and this attractive force makes them pass through the wire in order to come together.

But now I'm wondering how you achieve different voltages. If I separate twice as many charges, I must have used twice as much energy to do so, in which case the energy per coulomb would be the same. At first I thought that changing the distance between the separated charges made sense, but in that case, charges that were barely separated would have a stronger attractive force between them, and thus more voltage. It seems then, that connecting the ends of a battery with a longer wire would result in less voltage.
No. Potential energy is not force. Potential energy is the amount of work you need to do to separate the protons and electrons. The farther you separate them the more work you have to do.

Intuitively, I don't think that happens. Also, the equation V=W/Q doesn't include distance as a factor. I'm just failing to see how you can change the amount of potential energy of a charge, without involving distance. But maybe I'm just stuck thinking of potential energy in terms of balls and gravity from high school.

I don't know if this makes any sense. I'm probably misinterpreting something very fundamental, but I can't seem to get at it by myself. Everything I look up uses terms I don't understand, and I don't know where to begin decoding.

I'd really appreciate some help.

(If this belongs in the EE forum, I apologize, but since this is a such a fundamental concept, I thought Physics would be more appropriate.)

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" At first I thought that changing the distance between the separated charges made sense, but in that case, charges that were barely separated would have a stronger attractive force between them, and thus more voltage."

It does make sense, except "and thus more voltage" but you need to remember that it takes MORE work to separate the charges even further. As distance increases between two attractive point charges it still takes more work to separate them even further. Just like rolling a ball up an incline gets a bit easier as gravity decreases with height, but it still takes effort (work) and potential energy continues to INCREASE with separation.

Am unsure just where the poster stands after all the posts...but trying to understand the chemical activity in a battery is a complicated way to start understanding voltage for circuit analysis.

Here is a look at charge,voltage,work, force:

voltage difference, electric potential is delta V

delta V = W/q where W is work and q a test charge.

[as noted, 1 volt is 1 joule/coulomb...for units,]

In a uniform electric field E, for example,

F = qE where F is the force.

Work = Fd where d is DISTANCE... so W = Fd = qEd.

Here we see work (W) is related to charge, electric field strength, and distance the test charge is moved.

And delta V = W/q =qEd/q = Ed

So potential difference (delta V) equals the electric field strength (E) times the distance.

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You really want to get an understanding of this?
That means that you must just stick to the definitions of all the quantities involved and not try to jump to your own conclusions about the relationships between them. Maths is everything in this basic electrical theory. The analogies just lead you astray.

Have a care talking about the work of separating charges.

Electric potential at a point is defined as work required to bring a charge from infinity to that point, not the work to separate that charge from somewhere.

Secondly the attraction may be negative (repulsive)

Studiot said:
Electric potential at a point is defined as work required to bring a charge from infinity to that point, not the work to separate that charge from somewhere.
Using infinity as a reference is the standard for a field generated by a point source, because the potential from a point source is finite. For an infinite wire or plane, the potential is also infinite, so some finite point needs to be used for a reference point. In the case of a plane the surface of the plane (or the positively charged plate in a capacitor) is normally used as the reference point.

Studiot said:
Have a care talking about the work of separating charges.
I couldn't agree more, in principle. However, the first time many people have to deal with Charge is with Capacitors and the 'charge on a capacitor' involves separated charges. When you have two plates, it is (I would think) relatively easy to talk in terms of capacity, charge and PD. The concept of capacity of a single object is much more abstract as it is referenced to 'infinity' and the 'absolute potential' of the object.
I guess what I am really saying is that the OP seems to be referring to a relatively practical situation as in a circuit and in that situation, separating charges (creating an imbalance) and Potential Difference is a good way into the concept. Let's face it - 'absolute' potential is only used because infinity is an arbitrary reference which everyone has in common. The Russians and the US are both happy to use it, where they might not be too happy to settle on a choice between Red Square or Time Square for an origin.

Isn't the voltage the energy required to ionize an atom? So a hydrogen battery would be 13.6 volts. Of course you can always put the battery in series to increase your voltage in case the ionization energy of the material is small (does anyone know where one can find a table of ionization energies?). If you want to decrease the voltage of your material, then you can put several in parallel.

I think you really have to consider quantum mechanics, because technically if a positive charge falls on a negative charge, that would release an infinite amount of energy. So you need a limit, and the ionization energy provides that limit. Ultimately it can be traced to the uncertainty principle which prevents the electron from falling into the nucleus and just staying there, so that there is a minimum energy (that's not equal to negative infinity).

Isn't the voltage the energy required to ionize an atom?

not really...

If you want to decrease the voltage of your material, then you can put several in parallel.

not so

I think you really have to consider quantum mechanics, because technically if a positive charge falls on a negative charge, that would release an infinite amount of energy.

not so E = mc2

So you need a limit, and the ionization energy provides that limit.

no

Ultimately it can be traced to the uncertainty principle which prevents the electron from falling into the nucleus and just staying there,

no

See here for some info on ionization energies...and a short table:

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

But voltage in circuit theory is a different idea than any in your post...E = IR...

Just where is this thread going?
What have the last few posts got to do with the OP?
I'm lost in a vague soup of buzzwords.

Ooookay. So I guess my class is just settling for a handwavey explanation of voltage, then. Maybe I should just get a new book and come back later?

Oh, and sorry about the water analogy. I worded that terribly for some reason. I understand that it's pretty inadequate, but everyone else I ask about this just starts with that water analogy, so I meant to get that out of the way and move on to better explanations. Like I said, I worded that pretty poorly though.

Anyway, let's see if I understand this better.

So, let's say you have an electron and a proton, and you manage to hold the proton in place, while moving the electron away from it. At any particular distance, there is an attractive force between them. I think I was stuck thinking of this force as being the voltage, but now I see that's wrong. The force decreases as the electron moves farther away, but the total work done increases with distance. Like, if you had force as a function of distance, the work done would be the integral of that function over an interval of distance, right?

Which makes voltage the difference in potential energy of that electron between its current position and its initial position. But you could also measure its voltage between its current position and ANY position between it and the proton. Maybe even any position at all. Correct?

If that's the case, this makes a lot more sense. I think I still have a lot of questions, but hopefully this is a start.

Why not actually use the PROPER definition of Voltage? Don't go for a handwavey one. (This is supposed to be a Physics forum.) It's written down in every book you can read about the topic and also in several places in this thread. It's just the energy per coulomb when a charge moves from place to place. Distance needn't come into it at all. 1V can supply the energy to get a few amps through miles of cable - or- it can supply the energy to get 1mA through a 1kohm resistor that is 10mm long.

How much energy do you think it takes to move an electron from one place to another inside a lump of Copper? What has that got to do with separating an electron from a proton in a Hydrogen atom?

I think you have a problem in actually knowing what question you really want to ask. Yes yes yes - get another book. It's the only way (and sit on your hands when you want to explain volts.

sophiecentaur said:
Why not actually use the PROPER definition of Voltage? Don't go for a handwavey one. (This is supposed to be a Physics forum.) It's written down in every book you can read about the topic and also in several places in this thread. It's just the energy per coulomb when a charge moves from place to place. Distance needn't come into it at all. 1V can supply the energy to get a few amps through miles of cable - or- it can supply the energy to get 1mA through a 1kohm resistor that is 10mm long.

How much energy do you think it takes to move an electron from one place to another inside a lump of Copper? What has that got to do with separating an electron from a proton in a Hydrogen atom?

I think you have a problem in actually knowing what question you really want to ask. Yes yes yes - get another book. It's the only way (and sit on your hands when you want to explain volts.

I'm trying NOT to use a handwavey definition. That's why I'm here and not reading my book. I understand that voltage is energy per coulomb. But that's not helping me by itself. What I'm trying to understand is how voltage is physically produced, how and why it varies, and how it interacts with other electrical properties.

If voltage is the energy per coulomb when a charge moves "from place to place," doesn't distance come into that somewhere? I don't understand how you can describe something that describes the movement of a charge without including distance. Also,

Naty1 said:
And delta V = W/q =qEd/q = Ed

So potential difference (delta V) equals the electric field strength (E) times the distance.

Examples help me. Earlier, you said that "separating charges (creating an imbalance) and Potential Difference is a good way into the concept." Isn't that what I was getting at with the example of a proton and electron?

Am I completely wrong in my earlier post? If so, please tell me.

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The meanderings of this thread seem to have opened it out somewhat.

So try this.

Charge, like mass, is a property of matter.
It is more complicated than mass because simple experiments show that there are two types or polarities.
All matter possesses mass, but not all matter possesses charge.

Experiments show that uncharged (neutral) matter exerts a force of attraction between two masses and that this force is governed by the inverse square law. We call this gravitational attraction.

Work is therefore done on the mass of any matter moved against this force.

Further experiments show that an additional force exists between charged matter, over and above that exerted by gravity. It is further observed that the direction of this force depends upon the relative polarities of the participating charges. We call this electrostatic attraction or repulsion.

Work is therefore done on the mass of any matter that we move against this force.

It is often stated, rather loosely, that work is done on the charge. This is not so. Work is done on the mass of the matter. So you will find the mass of the charged particle appear in many equations.

It just so happens that the units chosen hide this so the standard definition of the volt, referred to by Sophie Centaur is defined in terms of a force exerted by a fixed number of electrons and a distance. In other words our units of charge incorporate a mass term.

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A chemical reaction in the battery separates an electron from the anode, and this electron goes through the circuit and is deposited on the cathode. When this happens another chemical reaction takes the electron from the cathode and puts it back on the anode, this time through the battery.

The voltage would be the energy of all chemical reactions divided by the number of electrons produced per reaction.

What's going on in the battery is what determines the voltage. Even if you have two parallel plates with a wire connecting them outside of the plates, it is the voltage on the inside that is calculable as V=E*d. On the outside is a fringe field between parallel plates.

So it is awkward trying to calculate voltage by speaking about the circuit outside the battery. The voltage ought to be gotten just by considering the inside of the battery.

@Opus
I think you are looking for something that doesn't actually exist. You might as well ask what Speed is 'really'. Speed is a ratio of two quantities and so is Voltage.
Studiot has put an alternative take on it, which is useful, and he also is saying that, when you get down to it, we're talking about the relationship between two quantities.

People make a similar mistake when they try to say what Resistance is. Descriptions like "it's a kind of force against an electric current". That's another dead end description (and even more wrong). I am pleased that you don;t want Volts to be a kind of force or pressure. You are not far from redemption, Grasshopper. (Is that reference too obscure?)

It doesn't help that so many people, who don't get it, actually try to 'explain it' to other people. The blind leading the blind, with half baked models and inconsistent Maths. I can see you are trying to get past this morass of ignorance - which is excellent. But I thinnk you may have to be prepared just to 'go along with' the definition and see where it applies. Familiarity will lead to acceptance and it will make sense!

Opus

Studiot has put an alternative take on it, which is useful,

I can develop this further if you are interested.

The night is young...

I really appreciate all of the help. I think what I'll do for now is just run with the definition, and see where that goes.

As I understand it, the most basic thing everyone has been trying to tell me is this: Voltage is the difference in potential energy per charge between two points. Is that correct? If so, then I will stick with that for now.

I think what I was trying to ask earlier was: How does the charge acquire this potential energy, and what determines how much it has? Maybe I'm just getting ahead of myself there, but for now I'll be happy with the above definition (providing that I haven't butchered it).

As I wrote earlier_
"You can create a Potential Difference by physically transporting charges onto a capacitor plate (like the Van der Graaff generator), you can build up charge by what is called Electrostatic Induction (as in a Whimshurst Machine), you can cause photo-electrons to leave a metal surface with enough KE to hit an electrode, causing a charge to build up and, of course, you can make an electromagnetic generator, which will produce an emf by moving a conductor through a magnetic field. Etc. etc. And the voltage across a battery is fixed by the electrochemical potentials of the chemicals used - limited by the rate at which the chemical reaction can replenish the charges on each electrode."

The amount of Voltage that you achieve by moving these charges relates to the work you do to separate them. Each case is specific but, in the case of an electrical generator, it will relate to the speed of rotation, the magnetic field and the number of turns of wire. It relates to the rate of change of magnetic flux that is 'cut' by the wire.

Isn't that basically what I was saying before? If you separate a positive and a negative charge, then the work done (and therefore potential difference) increases with the distance you separate them by?

I'm afraid I don't know enough about your examples to understand them, so I was trying to think of the simplest example I could.

Can you do the integral of 1/r2?

A simple yes or no will let me explain the next bit.

Isn't that basically what I was saying before? If you separate a positive and a negative charge, then the work done (and therefore potential difference) increases with the distance you separate them by?

I'm afraid I don't know enough about your examples to understand them, so I was trying to think of the simplest example I could.

That is mostly correct I believe. Do you have a specific example or question in mind that you would like to ask about? This is a very big subject and there is no way we can explain every situation.

Studiot said:
Can you do the integral of 1/r2?

A simple yes or no will let me explain the next bit.

Yes. -1/r + C.

Drakkith said:
That is mostly correct I believe. Do you have a specific example or question in mind that you would like to ask about? This is a very big subject and there is no way we can explain every situation.

Sadly, I don't think so. I don't know enough about practical electronics to think of anything specific. But if what I said earlier IS correct, then that helps me a lot, I think.

Well I'll try anyway since I want to go to bed.

Isn't that basically what I was saying before? If you separate a positive and a negative charge, then the work done (and therefore potential difference) increases with the distance you separate them by?

The problem with this is the following.

Work = force x distance.

The work done in moving (separating) these charges a small distance dr is

Force x dr

Now the force is given by the inverse square law as inversely proportional to the square of the distance

$$F = \frac{K}{{{r^2}}}$$

So if we try to substitute into the expression for work and integrate from r = 0 to r = some distance say a we get.

Edit: Sign correction, work is against force ie negative.

$$\int\limits_0^a {-Fdr} = \int\limits_0^a {\frac{K}{{{r^2}}}} dr = \left[ {\frac{K}{r}} \right]_0^a = -\infty +\frac{K}{a}$$

Now can you see why we do not define potential energy this way?

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There is a point of diminishing returns: you can't just separate two charges forever and increase your voltage to any high value you want.

What's more important than how far you can separate two charges, is how close the positive and negative charges are together to begin with. Then you can define a so-called ionization energy.

But batteries don't really work like this. But ultimately that's where you are going if you insist on thinking of everything in terms of point charges.

Studiot said:
The problem with this is the following.

Work = force x distance.

The work done in moving (separating) these charges a small distance dr is

Force x dr

Now the force is given by the inverse square law as inversely proportional to the square of the distance
So if we try to substitute into the expression for work and integrate from r = 0 to r = some distance say a we get
Now can you see why we do not define potential energy this way?
Alright. I understand that that doesn't work. But I thought potential energy was defined in terms of work, and W = F*d?

What am I missing? Apparently potential energy is not defined in terms of work? Or does work have a broader definition that I'm not aware of?

Opus_723 said:
Alright. I understand that that doesn't work. But I thought potential energy was defined in terms of work, and W = F*d?

What am I missing? Apparently potential energy is not defined in terms of work? Or does work have a broader definition that I'm not aware of?

(I hope I'm using the right terms here)

Potential Energy and Potential Difference are NOT the same thing. If an electron and a proton are 100 miles apart with nothing in between them, they effectively have Zero voltage, or potential difference. But they both have potential energy, because if I did move them together they would attract. The potential energy is equal to the amount of work required to separate the charges. The voltage is not however.

The closer two charges are, the MORE voltage they have between them because their attractive force increases the closer they are brought together. This is why a capacitor acquires more capacitance the closer you bring the plates together. The charges between the plates attract each other, and the closer you bring them together the more charges you can move between the plates for the same applied voltage.

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