Final answer:
The drift velocity of electrons is inversely proportional to the cross-sectional area of the wire for a given current, expressed by the equation I = nqAvd.
Step-by-step explanation:
The relationship between the drift velocity of electrons and the area of cross-section of a wire is quantified through the formula I = nqAvd, where I represents the electric current, n is the number density of free charges, q is the charge of each carrier (electron), A is the cross-sectional area, and vd is the drift velocity.
As the cross-sectional area (A) of the wire increases, for a constant current (I), the drift velocity (vd) must decrease correspondingly. Conversely, for a decrease in the area of cross-section, the drift velocity must increase to maintain the same current level. This is due to the fact that current is the charge moved per unit time, and vd is dependent on the number of charges moving through the cross-section of the wire within a given time frame.