What would happen with the drift velocity of a cylindrical resistor's diameter increases, with a given voltage between its terminals? According to the expression: R = ρ L A I = n e A v d Δ V = I R v d = Δ V ρ L n e The resistivity does not change, neither does the length of the resistor nor the term ne but the resistance does change as well as the current, so the area is eliminated from the expression. I wonder if the drift velocity would be the same after increasing the diameter or if my derivation is wrong.

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What would happen with the drift velocity of a cylindrical resistor&#039;s diameter increases, with a given voltage between its terminals? According to the expression:                    R                            =        ρ                  L          A                                    I                            =        n        e        A                  v          d                                    Δ        V                            =        I        R                                      v          d                                    =                              Δ            V                                ρ            L            n            e                              The resistivity does not change, neither does the length of the resistor nor the term ne but the resistance does change as well as the current, so the area is eliminated from the expression. I wonder if the drift velocity would be the same after increasing the diameter or if my derivation is wrong.

Emmy Sparks · Accepted Answer

The drift velocity is the average velocity due to an applied electric field. In a conductor, electrons scatter around at the Fermi velocity but have a net zero average (i.e., equal scattering in all directions). When the electric field is applied, the electrons are given a small velocity in one direction. Thus, we can say,      v          drift        =  η  Ewhere   η is some constant. Since the electric field comes from a gradient in a potential, which changes as a function of the length of the bar,   L. This approximates to      v          drift        ≃  η      V    L  which is similar to what you have. Since there is no factor of   A in the latter equation (not in my   η here), then increasing the area (by increasing the diameter) should not change the drift velocity.

What would happen with the drift velocity of a cylindrical resistor's diameter increases, with a giv

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