What is voltage exactly? [duplicate]

This question already has an answer here:

First, let me start off by saying that I have read the answers to this question (which is the same as mine), but the answers basically explain the different ways voltage is created or compare it to water in a pipe or altitude above the Earth's surface, so I was still a bit curious after reading those answers.

So, when I learned about voltage, it was often compared to height of a waterfall, pressure in a water pump, etc. The cartoon below helped me remember Ohm's law easily. But, I want to to know exactly what voltage IS, not really what it's LIKE. As the top answerer of this question said, "If someone really wants to understand electricity, they need to dispense with the fluid analogies and just learn how electrical fields and charges work." So, I guess my question is: in terms of electric fields and charges, what exactly is voltage, what is happening in the circuit to make one point at a higher potential than at another, and why does increasing that difference increase how much charge passes between those two points, assuming constant resistance?

marked as duplicate by Bimpelrekkie, PlasmaHH, Harry Svensson, Olin Lathrop voltage StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 20 '18 at 12:06

• As I mentioned in your previous question I recommend a physics site for an answer. – Andy aka Feb 20 '18 at 10:16
• How do I migrate a question to another site? Can I even do that with 30 reputation? – Lew Rod Feb 20 '18 at 16:17
• If you have trouble understanding voltage then use the analogy between electrical and mechanical systems. Voltage plays the same rule that force plays in mechanical systems. – CroCo Feb 20 '18 at 17:50

I want to to know exactly what voltage IS, not really what it's LIKE.

It is a mathematical construct, created as part of a mathematical model of things observed. It turns out to be a useful mathematical model.

Aside from being something that behaves as the mathematical model predicts, no-one knows what voltage "really" is. No one knows whether it is even meaningful to ask.

You may find this situation unsatisfactory. You would not be alone. Unfortunately, our need for a certain type of explanation is insufficient cause for such an explanation to exist.

We observe that there are forces in our world. We give them names like gravity or magnetic-attraction. As Richard Feynman noted, giving things names does not do anything at all to explain them or understand them.

To explain what voltage is the only language available is mathematics.

in terms of electric fields and charges, what exactly is voltage

There are some answers in Physics.Stackexchange which might be useful:

• Unfortunately, our need for a certain type of explanation is insufficient cause for such an explanation to exist. Only gave you +1, +10 if I could. – Neil_UK Feb 20 '18 at 11:20

The 'currency' of physics is energy. Fortunately, most people have a gut feeling for what energy is, or is like. It's the stuff that you need to make changes happen. One joule is needed to lift an apple vertically through 1m. You wouldn't want all the kinetic energy of a speeding car deposited in you in one go, though if you're careful, you can cope with all the energy of a speeding baseball or cricket ball.

When a current flows, the moving charge can do work. If it does a small amount of work, let's say 1 coulomb flows from an AA battery to heat a resistor, then it does 1.5J of work, and we say it comes from a low voltage of 1.5v. If it does a lot of work, say 1 coulomb flows from a 400kV overhead line, then it does 400kJ of work, and we say it comes from a high voltage of 400kV.

Putting numbers on 'voltage' like this wouldn't be worth doing unless we found it to be useful. As it turns out, if we put two AA batteries in series, and let 1 coulomb flow into an external circuit, it does twice as much work as from a single battery. The energy is additive, the voltage is additive, which means we can work with voltage, rather than the more clumsy energy-per-unit-charge ratio.

• I now can calculate the mass of an average apple and will be complaining at my grocer's if this is not true +1 – Andy aka Feb 20 '18 at 13:28
• @Andyaka I don't recall when I first came across the 1 apple = 1N approximation. For discussions of larger amounts of energy in earth's gravity, we can use the more conventional 'blue whale' = 1MN equivalance. – Neil_UK Feb 20 '18 at 14:01
• Best answer IMHO. – ultimA Feb 22 '18 at 10:22

There are a few ways to understand voltage from a high level, and all of them are rather insightful. Taken together, I think you get a good idea of what's going on.

There are some assumptions we need to make unless we want to really dive into quantum field theory. Here are the assumptions:

1. There exists a physical field called the electric field which can translate force between particles that interact with it. All particles that interact with the field interact with all other particles in the field, regardless of distance.
2. The electric field exists in all points in space, even if it has a value of zero at that point in space.
3. There are particles that interact with the electric field.
4. Some particles are "positively charged" and release energy by moving from more positive to more negative values of the electric field. Some particles are "negatively charged" and do the opposite.
5. Positively charged particles impart a positive value to the field around them. Negatively charged particles do the opposite.

With that said, we can address what voltage is. Taking a positive point charge for example, and assuming a present electric field with some gradient value (this could be achieved any number of ways e.g. with a smattering of other point charges, but isn't important for understanding), we say that the particle "releases energy" as it transmits from the higher valued point of the field to the lower valued point. This is the particle doing work, and is indeed how we draw energy from electricity.

Now, play that motion back again to where the particle was first located, and we know that we can release energy by allowing it to move from one end to the other. The term for this possible, but yet unreleased, energy is "potential energy". The difference between the potential energy of the first point and the second point (per Coulomb of charge) is the voltage difference. Make sure to note that the point charge located at the second point still has potential energy, it just has less.

Taken from a more mathematical perspective, the voltage difference between two points is the negative of the line integral of the electric field between two points in space. You can imaging moving a point charge between two points and using energy to do it. The negative of that energy is therefore the potential energy difference between those points i.e. the voltage.

One thing that is incredibly important to understand is that there is no such thing as "zero voltage". We can arbitrarily define some point in our system (usually ground) as zero voltage, and measure everything in respect to that, but that only applies to our system. So when we say something is at "five volts", what we mean is it is five volts above wherever we decided was zero volts in our system. We are fully capable of measuring voltage differences, but not absolute voltage.

The most concise definition that is even accurate is:

Voltage is the difference between two electrical potentials.

• About as useful as "the most accurate watch is one that does not go : it is precisely correct twice a day" – Solar Mike Feb 20 '18 at 14:16
• I admit that my answer is not very useful when you explain voltage the first time to somebody. What you forget though is that the OP explicitly asked for what „what is IS” in terms of „fields and charges”, and asked us not to explain „what it is LIKE” and to not provide any more analogies. Defining voltage in terms of potentials is thus exactly what he wanted. As opposed to other answers here that describe why they are unable to explain or that give yet another analogy. Mine also explains what others posts do not, such as why is voltage relative. I do really like Neil_UK's answer though. – ultimA Feb 22 '18 at 10:19
• I didn’t downvote as somewhere I think you are correct as well. – Solar Mike Feb 22 '18 at 12:28