Derive I = nAVe

Over 1 second, electrons with drift velocity V travel through a wire of  cross sectional area A. Distance Vt (t = 1) multiplied by area A gives a volume AV. This volume multiplied by the electron density of the material n, gives the number of electrons in volume V, nAV. The charge in the volume of material is found by multiplying the number of electrons by the elementary charge e, nAVe. This is the amount of charge passing through the wire every second, or current I. Therefore, I = nAVe