Electrical Engineering ⇒ Topic : Relation Between Current and Drift Velocity

Relation Between Current and Drift Velocity

Consider a portion of a copper wire through which current I is flowing as shown in Fig.(a).Clearly, copper wire is under the influence of electric field.

Let    A = area of X-section of the wire

         n = electron density, i.e., number of free electrons per unit volume

         e = charge on each electron

       V_d = drift velocity of free electrons

                                          figure (a)

In one second, all those free electrons within a distance v_d to the right of cross-section at P (i.e., in a volume Av_d) will flow through the cross-section at P as shown in Fig.(a). This volume contains n Av_d electrons and, hence, a charge (nAv_d)e . Therefore, a charge of neAv_d per second passes the crosssection at P.

                          I = n e A v_d.

Since A, n and e are constant, I α V_d

Hence, current flowing through a conductor is directly proportional to the drift velocity of free electrons.

The drift velocity of free electrons is very small. Since the number of free electrons in a metallic conductor is very large, even small drift velocity of free electrons gives rise to sufficient current.

The current density J is defined as current per unit area and is given by

The SI unit of current density is amperes/m²