In the absence of any electric field, the free electrons of a metal are in a state of continuous random motion. At room temp. their random velocities corresponds to 10⁵ m/sec. the average fandom velocity of free electron id zero.

 Thus, there is no net flow of charges in any direction. In the presence of any external field E, each electron experiences a force –eE in the opposite direction of E and undergoes an acceleration a is given by

At any instant of time, the velocity of an electron having thermal velocity u1 will be (r₁ + aτ₁),

where aτ₁   is the time that has elapsed since its last collisions. Similarly, the velocity of other electrons are (u₂ + aτ₂), (u₃ + aτ₃),……………………….. (u_n + aτ_n) respectively. The average velocity of all the free electrons is the velocity v_d of the free electrons.

Therefore, average velocity of all the n electrons will be

The parameter V_d if the drift velocity of electrons. It may be defined as the average velocity gained by free electrons of a conductor in the opposite direction of the from equation 2, we have

V_d = 0 + aτ

Where

= average time that elapsed since each electron suffered its last collision with the ion of conductor and is called relaxation time. Its value is of the order of 10^-14 sec.