This is obviously a part of the Ohm's law derivation. You can find my whole explanation here:
Is it possible to mathematically derive the formula for resistance?
And this is part I wrote about free electrons:
In material you have certain amount of almost "free" electrons. Those electrons behave like particles in the gas, they are crashing between themselves and into atom cores, bouncing back and forth and there is actually no net movement, average speed and current are zero.
You might find the whole text interesting.