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I understand that water flows because of height difference and current flows because of potential dfference. Now, in this analogy, I can understand height but I fail to realise what potential is. Is it the number of electrons? Say, A has 10 electrons, B has 20 and C has 100 electrons. So, can I say AC has more potential difference than AB and can I also say C has the highest potential?

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Potential is a measure of usable energy above some averaged background energy. So in the case of gravity, since the Earth or any other solid object has some mean radius (generally speaking), then an object on a peak that is greater then the mean radial distance from the center of the earth has some amount usable energy; one can think of the situation as also implying a low entropy condition.

Voltage is no different. When we talk of voltage one is actually talking about voltage above ground voltage, e.g. usable energy above the mean energy of the entire system one is connected with. Since electrical energy of the ground is effectively "thermal" with the rest of the Earth, we tend to use the Earth as our electrical ground state. So voltage in a circuit is a direct measure of the amount of usable energy one has (speaking very generally). A high voltage relative to ground again implies the system is in a low entropy condition.

Also the number of electrons itself does not imply a voltage difference. Only the difference in number of electrons in a system that would prefer to establish equilibrium. A battery for instance as a total system is going to have the same number of electrons at its beginning and end state. However at the beginning state, some of those electrons are concentrated on one side of the total system. So a distribution that has a bias of 100 electrons will have more potential then one with a bias of only 10 electrons.

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The potential is always measured relative to a potential in some other point. It is not an absolute value (in electronics this relative point is defined by the ground, the spot where the potential is taken to be zero). This is due to the fact that potential is related to the work which one does moving electron from one point to another. Usually, as a reference point, one take a point somewhere at infinity. Moving electron from infinity to a spot occupied by 10 electrons requires less energy than moving electron to a spot occupied by 20 electrons due to repulsion.

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I had the same problem with potential when I learned about it for the first time. I admit it is not easy to see similarity between water example and potential.

The best way I can describe it is, the potential is a measure of the internal pressure of charged particles. In other words, a measure of the intensity of pushing among charges to each other. Think of it as a group of people who don't like each other. If you put them in a small room "the tension" among them is going to rise. If they were distributed in different rooms "the tension" will go away. The "tension" in this example is somehow similar to potential.

One need to keep in mind that potential is relative. It is meaningless to speak about absolute potential. Potential difference is what matters. Charge carriers move from high potential to low potential. Just like people who hate each other would go away if they have that option which will cause the tension to go down among them. The motion of charge carrier is what is called current.

With respect to electrons as you mentioned in your question. Think of a billion of electrons confined in a cube of size 1 mm cube. The absolute potential of electrons is meaningless. However, if you brought another cube with a million electrons in it, you can define the voltage difference between the two cubes. If you connected them a huge number of electrons in more dense cube will rush to less dense cube. The quantification of the difference is called the potential difference. It is basically like a guy who lives on an island, he can't realize whether he is rich or poor unless he compares himself to somebody else.

You quite frequently hear potential without difference, the reason is that in such a case it is meant that potential is taken with respect to ground.

I hope that helped

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