Best visualization of electric current and voltage

Question

I asked this exact question on the electrical engineering stack exchange, and it was suggested that I post it here:

So, I want to know what the best way to visualize what is actually happening in a circuit. I typically visualized it with the Drude model, where the electrons are like free-flowing balls and the atoms of the circuit are fixed in space. It makes sense to think of voltage as being an application of an electric field across the wire that accelerates the electrons and resistance as the atoms in the way that the electrons hit. It also makes sense that when the electrons hit the atoms, some of their energy is given to the atoms and make them move faster, thus increasing their kinetic energy, and producing heat.

So, I like the Drude model, but it leaves a lot to be desired. For example, it makes no sense to me to think of electrons as "hitting" the atoms as the nucleus of the atoms are so far away from the electron cloud, it seems counter-intuitive as to why they would "hit" the electrons.

So, I just want a better model to visualize everything in my head. Which models do you use, and what are their advantages and setbacks?

Answer 1

To suggest an answer to your specific problem with Drude's theory: it's not the nuclei that the free electrons are supposed to bump into, but the ions: nuclei surrounded by bound electrons.

Having said this, I think it's generally agreed that it's not worth trying to refine the Drude model. It can't be patched up satisfactorily to give, for example, the observed dependency of resistivity on temperature. To get significant improvement in the match between theory and observation you have to use a quantum mechanical approach. In simple terms you need to consider the wave-like nature of electrons. You find that free electrons can propagate resistance-free in a perfectly regular stationary lattice of potential wells (representing the metal ions – see Kronig-Penney model), but that irregularities in the lattice caused by thermal vibration or foreign ions cause scattering and hence electrical resistance.