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?