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.
Best Answer
If there was nothing in the way then an electron leaving the anode of a 4 volt battery would have a kinetic energy of 4 electronvolts by the time it reached the cathode.
However the mean free path of electrons in metal wires is exceedingly short so electrons never build up anything like this velocity. The end result is that the electron velocities are randomised but with an small average velocity from the anode to the cathode called the drift velocity. To give you a feel for the difference the electron velocity corresponding to 4eV is about a million m/sec but drift velocities are typically around 1 m/sec.
To make an analogy - suppose you are standing in a pleasant breeze of one m/sec. According to the Maxwell-Boltzmann distribution the velocity of air molecules at room temperature is 300 to 400 m/sec but their directions are random and cancel out. You're left with a net motion of the air of 1 m/sec which is analogous to the drift velocity of electrons in a circuit.
The best way to teach electronics to beginners is to use the hydraulic analogy. Even though it might seem clunky at first glance the hydraulic analogy is remarkably useful. You can even model circuit elements like capacitors.