Consider a resistor of resistivity 4.12 × 10 − 8 Ω ⋅ m. If an electric field of 19 V/m is applied across the resistor and the electron volume concetration in the conductor is 5.82 × 10 28 / m 3 , determine the drift velocity, in mm/s, of the free electron constituting the current.

Question

Consider a resistor of resistivity   4.12  ×      10          −      8        Ω  ⋅  m. If an electric field of 19 V/m is applied across the resistor and the electron volume concetration in the conductor is   5.82  ×      10          28            /        m    3  , determine the drift velocity, in mm/s, of the free electron constituting the current.

Frances Dodson · Accepted Answer

Electric field and resistivity relation is  E  =  ρ  JHere   ρ is resistivity, E is electric field and J is current density.The drift velocity is defined as      v    d    =      J          n      e      Here J is current density, n is electron concentration and e is electric charge.Since resistivity   ρ is   4.12  ×      10          −      8        Ω  ⋅  m and electric field E is 19 V/m. The current density J is  E  =      ρ    J    J  =      E    ρ      =            19             V              /            m              4.12      ×              10                  −          8                    Ω      ⋅      m          =  4.61  ×      10    8       A      /        m    2  The carrier concentration n is   5.82  ×      10          28            /        m    3   and electric charge e is   1.6  ×      10          −      19        C. The drift velocity       v    d   is      v    d    =      J          n      e          =            4.61      ×              10        8                   A              /                    m        2                    (      5.82      ×              10                  28                            /                    m        3            )      (      1.6      ×              10                  −          19                           C      )          =  0.05     m      /    s

Consider a resistor of resistivity 4.12 xx 10^(-8) Omega * m. If an electric field of 19 V/m is applied across the resistor and the electron volume concetration in the conductor is 5.82 xx 1028 per m3, determine the drift velocity, in mm/s, of the free electron constituting the current.

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