Slowly moving electrons represent electric current at DC. Electric current is amount of electric charge passing, per second. For the current to be 1 ampere electric charge of 1 coulomb (6.242 × 10^18 electrons) has to drift for 1 second (thru the plane). When electric field (voltage) changes (at AC), amount of "directed" free electrons in whole wire changes. As a result more or less electrons will cross given plane in time. Joules are just a measure of energy delivered to the load, equivalent to current of 1 ampere thru 1 ohm load for 1 second. This energy is still delivered on the outside. Power delivered by energy field is a product of electric field and magnetic field. Since electric field is proportional to voltage and magnetic field is proportional to current we say P = V x I (instead of measuring fields it is easier to measure what is causing them - voltage and current).
As I understand it, electric charge is carried by free electrons. Since free electrons always carry the same elementary charge then increase in electric charge means more electrons. Free electrons in the wire move randomly in all directions and are kept apart by repealing forces. Application of voltage directs some of them and they slowly move along the cable (overall motion of free electrons becomes less random). Applying higher voltage directs more of them in whole wire resulting in sudden change in amount of electrons crossing given plane in time (electric current). That would imply that electrons in thin wire move faster than electrons in thick wire, at the same current. I’ve read somewhere that this is the case. It is a little weird tough, because it means that electrons will accelerate thru the narrower part, like notched wire.
Again, it is how I understand it. Perhaps electricity, like a woman, exists to be loved (music) and not to be understood.
