What really is voltage, what effect does a higher voltage have on an unit of charge and what makes electrons flow? [duplicate]

I have been reading a lot about the subject, I've seen lots of videos (youtube, udemy) and even read some scholar papers about it and everyone explains the above in so many different ways. We all know what the scientific definition of what voltage is but I still don't know what effect it has on the electrons.

The water analogy which is used so much, seems to fail when we compare higher voltage vs lower voltage, because the higher the pressure of water in a tank is, the faster the water current will be once the tap is open, but the same does not apply to electrons. In fact, from what I've read, the velocity at which electrons move (drift velocity) is quite slow - small drift changes which propagate across the wire is what allow the fast delivery of electricity.

The other thing I have a problem is is how the voltage is represented in a circuit. I keep reading over and over again and seeing in the water analogy too, that voltage is what pushes the electrons, but if that's the case why is voltage lower at the negative terminal?

If I put a few springs in a box and apply pressure to close the box, some springs will contract and will probably fly away once I open the box, so using this analogy, is voltage the force necessary to keep the springs tight in the box?

The electrons don't really need a push to move across the hire, they have that desire, they are attracted to the positive side, how what is really the voltage role here?

Using another analogy, it seems that voltage is to electrons what fuel is to my car. At the end of a working day all I want to do is to drive home. I will always have the desire to reach home, but if I don't have enough fuel in the tank, I will never be able to, in the same manner, if there's no enough voltage the electrons will never reach the other end of the hire, even if that's all they want.

To me, it seems that voltage is simply the force that pushes electrons apart from each other. I also see in so many videos, electrons flowing from the beginning of the circuit to the end, when in fact the electrons barely more.

The more I read the more confused I become.

UPDATE 1

This is the best explanation I have read so far:

"A voltage appears whenever there is an imbalance of electrical charge (i.e. electrons). Since like charges repel and opposite charges attract, any collection of electrically charged particles creates some kind of force on each other. If there is an imbalance of negative to positive, a kind of "pressure" or "push" is formed. In conducting materials, electrons are free to flow through the material, as opposed to being fixed in atoms, and will therefore flow to the point of least "pressure"."

What exactly is voltage? • Comments are not for extended discussion; this conversation has been moved to chat. Jun 8 '20 at 22:33

The trick is not to use bad analogies. As you've noticed, the water analogy is bad, because "pressure" is an inherent property of a volume of material, and not something that only exist in relation to some reference pressure¹.

Instead, try to simply go by the plain definition of what voltage is, and things will get easier.

Your fuel analogy is another bad analogy, because the electrons don't leave your circuit. Your fuel does. Honestly, the model we use for basic electronics isn't that hard, analogies just make it harder.

Voltage is the amount of energy per charge. That's it!

Wait. Energy per charge? Energy – how? A charge itself doesn't work, does it?

You're right, a charge (say, a 5V-charged metal sphere floating in outer space) don't exert a force on anything or so, they don't heat up the sphere by themselves, they don't shine light...

But: if you have a second sphere with the same charge, but negative voltage, these two spheres will attract: a force is exerted on both, and that force is proportional to the voltage.

Same happens with your battery: the chemistry inside leads to a potential on the positive pole that is (say, 1.5V) more positive than on the negative pole.

That means that 1 Coulomb (that's the unit of charge, it's 1 C = 1As, the amount of charge that flows through a cable when you draw 1 ampere for 1 second) charge has 1.5 V · 1 As = 1.5 VAs = 1.5 Ws = 1.5 J energy. Done!

To me, it seems that voltage is simply the force that pushes electrons apart from each other.

pretty much, yeah.

You can think of in electrons, but you'll later learn that thinking in electrons doesn't have any more physical relevance than thinking in "missing electrons", so just think of charges, then you can say

it seems that voltage is simply the proportionality between the force that pushes charges apart or attracts them to each and the amount of charge

or really, as said,

it seems that voltage is the ability of a charge to exert work

which really is identical to saying

it seems that voltage is energy per charge.

There we are. You were right!

electrons flowing from the beginning of the circuit to the end, when in fact the electrons barely more.

Yeeeeah, long story short, making good animations is hard, and especially when you grow up with the water analogy, it's even harder.

In reality it's really more like a "potential slope". At the top of your battery, relative to the bottom / ground connection, you have a high potential. Your drawn connection is an ideal conductor, i.e. no voltage drops across it, so at the top side of your resistor, you still have +1.5V relative to the bottom side. Now, along the length of the resistor, the electrons have to logically have less and less potential – and that's exactly what happens, if you make a graph of "energy per electron" on the y-axis, and "length along the resistor" on the x-axis, it's just going to be a falling straight line from y=1.5 V at x=0 to y=0 V at x=end.

So, I think you're righter in understanding electricity than these analogies are.

Generally, analogies are rarely more useful than just as an "introduction". If something is complex in reality, then the analogous thing you use to explain it needs to be complex, too. So, what's the point of using an analogy if it's as complicated as the thing you actually want to understand?

Luckily, voltage isn't that complicated. (If you think about water circulating in pipes – hell, that is complicated. Fluid dynamics really is complicated, and also, quite different from how electricity behaves.)

¹ I really don't know why the water analogy is so commonly used. It's not really a great analogy – whenever people use it, they have to define what the water in their model does in ways that water, pipes, volumes, pumps don't really work in reality. I could rant about this for hours – but it wouldn't help you.

• When I have questions about electrons, I ask Fennmann, and sometimes it gets clearer. Whether this helps feynmanlectures.caltech.edu/II_06.html or not depends on where youŕe starting from. Apr 19 '20 at 22:03
• "making good animations is hard" ... did you mean "analogies"? Apr 19 '20 at 22:04
• @jonathanjo no, I meant animations, because OP rightfully complains about videos in which the electrons always move completely through the circuit and the speed of that is supposed to indicate the current; but it's not like that in reality. Electrons are rather slow, the speed of electricity is the speed at which the electric field propagates – and that's speed of light in free space, and lower on cables; but: the amount of current doesn't change that speed. However, it's hard to actually represent "current magnitude" in an animation without "abusing" the speed. Apr 19 '20 at 22:07
• I agree that the hydraulic analogies are often misused, but I don't think it is fair to say that the problem is because we always measure pressure with respect to some reference pressure. On the contrary, we can measure absolute pressure in a fluid...but where is your absolute zero voltage? In all practical situations we measure voltage with respect to some reference point. Apr 20 '20 at 14:37
• @ElliotAlderson fair point. Apr 20 '20 at 14:46

If you have a reservoir of immovable electrons any where and then you bring some electrons near that reservoir then the electrons you brought near the reserviors will be replelled by the reservoir of electrons.

When your electrons are repelled they will move away from the reservior of the electrons and because they are moving they have the kinetic energy.

Votage is that enery per unit coulomb that moving electrons posses. Means what energy 1 coulomb of electrons have as they move. So 1 joules per 1 coulomb of electrons is 1 volt. 2 joules per coulomb of electrons is 2 volts and so on.

Now when you connect a wire across the terminals of the battery the two terminals of battery are like the reseviors of charges. One terminal has the reservoir of negative charge and the other terminal has a reservior of positive charge. When wire is connected across the two reserviors of battery electrons from the negative terminal of the battery will move to the positive terminal through the wire.

Those electrons will have kinetic energy. If 1 coulomb of these electrons have 1 joules of kinetic energy then its 1 volt. And so on.

If there is resistance in the wire the kinetic energy of the electrons will be converted to the heat energy and the kinetic energy is lost. Thats what we call voltage drop.

• "energy that moving electrons possess"...no, the electrons have the same energy whether they are moving or not. So clearly it is not kinetic energy. Apr 20 '20 at 11:57
• Yeah, voltage is a property of the electric field, and the field is present regardless of whether it's moving anything or not. It's important not to get confused with the "electron-volt", which is a unit of kinetic energy but not relevant unless you're building a particle accelerator. Or the old domestic particle accelerator kind of television. Apr 20 '20 at 15:23
• Its the kinetic enery which is converter to heat. Electric field is not converted to heat i think.
– Alex
Apr 20 '20 at 16:06

Voltage is a slippery subject and many times I've seen answers that discourage folk from thinking of voltage as anything to do with the movement of electrons but, in it's most basic form, it is.

We all know what the scientific definition of what voltage is but I still don't know what effect it has on the electrons.

The higher the electric field between two points in a conductor, the greater the drift velocity of the carrier (electrons in conductors). This basic relationship is: -

$$v_d = \mu_e\cdot E$$

• $$\v_d\$$ is the drift velocity of electrons in m/s
• $$\\mu_e\$$ is the electron mobility in $$\m^2\$$ per volt-seconds
• E is the applied electric field in volts per metre

The above formula can be re-arranged to include conductivity ($$\\sigma\$$) because: -

$$\sigma = n\cdot e\cdot \mu_e$$

• $$\n\$$ is the carrier (electron) concentration
• $$\e\$$ is the electron charge

And, you could carry on a bit and derive ohms law (V = IR) if you wanted.

So, thinking about voltage as a mechanism of controlling drift velocity of electrons is OK in my book. If you want to imply that it's a pressure that's OK too.

Talking about voltage being energy per charge always leaves me cold. However it is true when discussing the energy (W) in a capacitor and its charge (Q): -

$$W = \dfrac{CV^2}{2}$$

Substituting with Q (= CV) we get: -

$$W = \dfrac{CQ^2}{2C^2}$$

Then differentiating energy with respect to charge we get: -

$$\dfrac{dW}{dQ} = \dfrac{Q}{C} = V$$

But what is that really telling us? If we took the mechanical analogy of a moving mass and differentiated its energy with respect to momentum (charge, Q and momentum, p are always conserved) we get: -

$$W = \dfrac{mV^2}{2}$$ $$W = \dfrac{mp^2}{2m^2}$$ $$\dfrac{dW}{dp} = \dfrac{p}{m} = \text{velocity}$$

So now, velocity is defined as work per unit of momentum. But we all understand what velocity is. We all learned that at school and we can all measure it and feel the wind in out faces in an open top car. But we don't really know what voltage is intuitively so, I go back to the original equation at the top of this answer.

• I would not say that's what voltage is "in its basic form". What you describe is a very special case of interpretation of voltage, namely in a conductor that follows Ohm's law. (Which, by the way cannot be derived correctly in classical physics, but that's irrelevant here). Sure, for an EE, how conductors responds to voltage is certainly the most important thing to know, but it's not how voltage is defined. Aug 24 '20 at 0:20

The water analogy

The water analogy does not go as far as you expect it. You should only consider that pressure differences relate to voltage differences and flow rates to currents.

It is not meant to have a perfect equivalence, but it is a great way to help visualising or starting to get a feel of what a voltage is, what current is, and what resistors, etc. are.

When the difference in pressure is higher, the flow rate is higher. The same way how higher voltage results in higher current.

There are other differences. Water will have higher flow in the center of a tube, while current will be higher on the outer edge (skin effect). So the analogy is only a way to get started.

Speed of electrons

The speed that really matters is the signal speed which is about half the speed of light in a cable or in a PCB. And signal speed is actually related to displacement of power.

So what seems strange is that electrons are so much slower.

So let's look at the water analogy.

Suppose that I have a tube with a section of 1 dm^2, which means that there is 1L in 10 cm of the tube. In order to receive 1 L, the water in the tube has to make a displacement of 10 cm.

Suppose that I then have a bigger tube, which has a section of 1m^2. In that case, to receive 1 L, I need a displacement of only 1 mm.

It is very easy with the tube of 1m^2 to have a fast fluctuation of 0 L/s to 1 L/s with very small displacements. In the small tube the water would need to move 100 times faster.

Electrons in a wire work more or less the same way - there are quite a lot of them. In fact for 1 amps in a wire with a radius of 2 mm the speed that the electrons must exhibit is only only 23μm/s (source https://en.wikipedia.org/wiki/Drift_velocity#Numerical_example).

So similary the signal can change from 0A (Coulomb/s) to 1A (Coulomb/s) very quickly with these "very low" speeds of electrons, the same way we can change from 0L/s to 1L/s in the water analogy.

Electromagnetic waves around a wire are determined by the current fluctuations in the wire. And as you can see, the speed of these fluctuations can be very high with only low displacement speeds of the electrons.

Voltage is what pushes the electrons...

Voltage is defined as the "work" (joule) needed to displace one unit of charge (coulomb), which itself is a number of electrons. In an electrical field, we can identify a voltage level at a given position that indicate how much work is needed to move a charge from 0 V to that position. These voltage levels represent the electrical field, which is an "invisible" force acting on electrons, in a analoguous way as gravity acts on water.

I prefer to think that electrons are drawn to the lower energy level, but as they loose energy they do flow to the positive potential by convention (so the higher voltage potential is in fact the lower energy level, but forget that as it makes things more awkward).

That should explain the role of "Voltage" - Voltage is a measure in the electrical field.

Why is voltage lower at the negative terminal? By convention: it could have been chosen the opposite way and the current negative terminal could have been the positive terminal. The negative terminal is called "negative" because the voltage is lower there, and that is a choice.

Analogy with springs

Comparing to strings is another ball game, and surely not the best one as springs do not seem to have something that can compare to current. Voltage could be somewhat compared to the force to keep the springs tight in the box. But there is not an "infinite" reservoir of what could represent electrons and current.

Analogy with fuel

This is even more difficult than the analogy with springs. There is a chemical reaction that results in heat and pressure that is transformed in a displacement.

The fuel is displaced to the combustion engine by succion. The tank itself does not represent the voltage.

The voltage level in the fuel is somehow in the chemical bonds. These bonds are stable enough until enough heat is applied to break them. I can't think of a proper analogy in electricity for that. I could find one with water though.

? Voltage is the force that pushes electroncs apart ?

No, from what I indicated above, voltage indicates the work that that was need to move the electrons to that voltage.

Pushing or attraction is a question of a point of view.

This is true up to a certain point - electromagnetic fields will not help keeping that true.

Remember when you have a metal tip, electrons will tend to all move towards the tip which seems difficult to explain when considering that electrons want to be distant from each other.

Final word

The reality is really a lot more complex and we are working with analogies all the time.

Even mathematics could be viewed as some kind of analogy. We can do calculations about signals "themselves" or use Fourrier, z, and other transformations to compute them.

As said, there is the question a point of view. Electrons are attracted by the holes or pushed away by other electrons.

Fact is that they can not really go anywhere if there is no hole. Electrons are attracted by the protons and any unmatched proton creates a hole. Electrons can change energy levels within the same atom and emit or absorb a photon when they do so. The scientific world has not been capable of combining the theory about photons with electromagnetic waves.

Electrons can also be entangled, which allows for teleportation. When an entangled electron absorbs a photon, the other one emits one. That is displacement of energy and hence mass without an electrical path.

So in the end, we choose the analogy that fits best to solve a given problem, and we sometimes use more than one to be confident that the problem is solved.

Electronics (as water) will tend to move in a position where they have lower potential energy.

Suppose that 1 L represents 1 J of energy. If you move 1 L horizontally, you displace 1J. If you move $$\1 m^3\$$ over the same distance you displace 1000J.

we all wish to loose energy till equilibrium and if we get a chance of loosing it with higher mobility we would definitely prefer that path.So you have 2 things one is the natural tendency to equalize the concentration gradient and another being the mobility, namely the Diffusion and Drift current. Other effects are also there which can be considered less bothering for while.

In general Voltage is definitely the energy per unit Charge(where the charge is causal charge of the Field under which the subject charge is moving). whereas in case of an Inductor its an EMF..essentially called an Energy as well as an Inertia storage.. while in case of a capacitor its only a charge(energy) storage. In case of the behavior of LC tank circuit..you can observe it