I am a bit puzzled about this subject myself, what do you guys think of this line of reasoning?
electrons and protons attract each other, by convention 1 electron has a charge of -1 and a proton has a charge of +1.
(wikipedia: elementary charge)
This attraction is a force, which can be denoted in Newton (force required to give 1 kg an acceleration of 1 m/s^2).
1 joule = 1 N * M, in other words the amount of energy to accelerate an object with a force of 1 Newton, over a distance
of 1 meter. (of course if the actual object you apply the force is heavier than 1 kg you will not get the 1 m/s^2
acceleration, but if the object is in fact 1 kg, you will)
and if you keep on supplying energy to fuel your force application you can express this in watts (1 w = 1 joule /s)
now note that the charge of 1 coulomb equals the charge of 6.25 * 10^18 electrons and that 1 volt equals 1 joule / 1 coulomb.
since 1 electron has a given charge, so do 6.25 * 10^18 electrons, but what can be different is the amount of force applied to them;
this is determined by the existence of an equal or unequal amount of protons on the other size of the conduit, this is what determines
the amount of potential energy of a given charge point. (in other words the number of joules per coulomb).
"One Coulomb (C) is the amount of charge such that a force of 9.0×10^9 N occurs between two point like objects with charges of 1 C separated by a distance of 1 m."
(from wikipedia)
So if you look at 1 joule / 1 coulomb = 1 volt, what are we talking about if we talk about 14 volts potential difference between points A and B?
I guess we talk about 12 joules of potential energy spread out over 6.25 * 10^18 electrons caused by a surplus of electrons at 1 of the points
relative to the number of protons at the other point. In really the point probably will not contain exactly 6.25 * 10^18 electrons, but are we only talking
about a fraction of joules per coulomb which yields the same voltage.
Also note that this indicates that given a fixed number of elektrons in a given point the voltage associated with that point is strictly relative to any other point.
In other words: the number of joules per coulumb of a given point is different given the charge of whichever other point you compare that point with.
I guess the wikipedia definition is talking about the situation where 1 point has 6.25 * 10^18 electrons and the other has 6.25 * 10^18 protons. Apparently this
generates 9.0×10^9 N of force. Quite massive, so I guess in normal electronics we are talking about much lower potential differences.