Electric Current

Electric current is the movement of mobile charge carriers. It is measured in amperes — coulombs per second. With positive and negative charge carriers we have to take into consideration the total charge going in each direction. So, if we have a conductor with:

A - cross-sectional area in m²,
n - number of mobile charge carriers per m²,
v - drift velocity of the mobile charge carrier in ms^-1,
t - time in s, and
q - the charge of a mobile charge carrier in C

then for positive charge we have:

Q⁺=q_pn_pv_pΔtA

coulombs of charge passing a point in one second. Similarly for negative charge we have:

Q^-=-q_nn_n-v_nΔtA

This gives us in total:

Q⁺+Q^- = (q_pn_pv_p + -q_nn_n-v_n)ΔtA

Now, current is the rate of charge flow, so:

I = (Q⁺+Q^-)/Δt = (q_pn_pv_p + -q_nn_n-v_n)A

Note that in a metal, we only have one type of mobile charge carrier, the electron, so:

I = Q^-/Δt = -q_nn_n-v_nA

The current divided by the area (I/A in our notation) gives us what is known as the current density.

References

Fischer-Cripps. A.C., The Electronics Companion. Institute of Physics, 2005.