I have been thinking about ways of teaching electronics and I'm wondering if the following is true...
For starters, when we talk about voltage as energy per unit charge, is this energy manifest simply as the kinetic energy of the electron?
So, all other things being equal, will the electrons coming out of a 4 volt battery will have twice the velocity of electrons coming out of a 1 volt battery because of ${1 \over 2}mv^2$?
This would seem to imply that the voltage drop across different parts of the circuit is essentially a comparison of the electron speeds at those points.
Furthermore doesn't this imply that the electrons are nearly halted by the time they reach the positive terminal of the battery? This makes intuitive sense to me, it seems pedagogically sound, and it provides an explanation for how electrons "know" to give up their energy across the circuit -- electrostatic repulsion communicates later resistances to earlier parts of the circuit.
How much of the above is correct? The one things that makes me suspicious is that, in this picture, electron density at the positive terminal of the battery is very high, and repulsive forces would prohibit this. On the other hand, if the Joules per Coulomb are not coming from kinetic energy, then what? The field? But wouldn't that just dissipate as light?
Something is wrong but I don't know what.