When current flows from a wire of greater diameter to one of lesser diameter, the drift velocity of electrons increases due to the inverse relationship between drift velocity and cross-sectional area. The equation I = venA illustrates that as the area (A) decreases, the drift velocity (v) must increase to maintain a constant current (I). This phenomenon is explained by the conservation of energy rather than an external force, drawing a parallel to Bernoulli's principle in fluid dynamics. The discussion emphasizes that the increase in drift velocity is a natural consequence of the geometry of the conductor. Understanding this relationship is crucial for analyzing current flow in wires of varying diameters.