Question

Deduce the relation between the current flowing through a conductor and drift velocity of electrons in it.

Answer 1

Let:

n = number of free electrons per unit volume

A = cross-sectional area

v_d = drift velocity

e = charge of electron

In time dt, electrons move a distance:

dx = v_ddt

Volume crossing area:

dV = A . dx = Av_ddt

Number of electrons = nAv_ddt

Charge (d_q) = neAv_ddt

I = `(dq)/dt`

= neAv_d