It is easy to visualize gravitational potential energy as a function of the position of height, and a change in this potential is manifested in a change in height. Further, by the work-energy theorem any change in potential energy results in work done, which results in a corresponding change in kinetic energy.
In an electric circuit, the potential energy difference is provided by the battery. Yet it is not easy to see how a voltage drops manifests itself. When energy is lost (let's say by going through a resistor), what physically happens to the electrons.
In the case of gravitation potential energy it is easy to see that the height of the object changes. For an electron the only way I can see would have to do with its energy level. Also, by the work-KE theorem doesn't this also mean that the kinetic energy of the electron would have to change? Yet this is clearly untrue for the current before and after (assuming a simple series circuit) is the same so the drift velocity cannot have changed.
(And before this is marked as a duplicate of this question I already looked into every answer there and none of them answer my question — they merely restate the definitions of potential, voltage, and ohms law or provide an analogy to water level. In the case of a resistor I already know that the reason for energy loss can be considered at a superficial level to be due to collisions — I am instead asking for an explanation of how this loss of energy manifests itself in the electric field or electrons themselves, perhaps via a change in occupied orbital or something similar.)
Best Answer
The current in a circuit is a collective phenomenon from zillions of electrons. It appears due to conductivity, another collective phenomenon . It is a cumulative behavior of atoms and electrons in matter.
In insulators, electrons occupy energy levels and have to be actively kicked out of them, with the energy provided by an interaction. Insulators can be charged ( tribo electricity) but the potentials induced on the surface do not have sufficient energy to dislodge more electrons.
In conductors a single electron is free to move in collective energy levels of the conductor, and in metals there exist in a continuum unoccupied energy levels which an electron can move into given a very small energy. This is the band theory for solids.
A voltage drop sets up a field that individual electrons ( and ions) react to by moving according to the field. The individual motion of electrons in space is small, it is called the drift velocity.
The ensemble of motions of all outer level electrons generates the current. The drift velocity depends on the conductivity, and depends on the type of solid.
In resistors the conductivity is reduced , it takes more energy to go to the conduction band. For the same voltage drop across a resistor the drift velocity is much smaller ( depending on how resisitive it is) than for a same size conductor, which would short!
You say:
In the band model, the band is wide, it will have less kinetic energy.
Yes
It is changed from the case where that particular resistor is not added. The resistor acts as the maestro of the drift velocity. By lowering it within , conservation laws assure that it will get lower in the whole cirtuit, which is assured by the voltage drop across the resistor. The electrons in the metal see a smaller field than before the new resistor was introduced. ( I am talking of new resistor because one should always be there , otherwise one would have a short).