current is just number of electrons (times its charge) passing by in a given time (in seconds for amps).
say you have a volume filled with moving electrons (ignore the inner shell electrons since they stay put) if this volume is constantly moving, the current is just the total charge of this moving volume divided by the total time it takes to pass a certain surface. total charge is e*n*A*L where l is the length (this is just total volume*charge density*charge/electron) the time it takes this to move a distance L is the time for all the charges to move across some 'measuring' surface, time=distance/velocity=L/v
Current=total charge/total time=enAL/[L/v]=nAve
this is one way to think about it...
I hope I helped! ☺️
