As we know that the current entering in a conductor is equal to the current leaving the conductor. Which is based on the conservation of the charge. As, drift velocity of electrons, vd=
eEτ
m
⇒vd∝E Where, e= charge of electron, τ= relaxation time and m= mass of electron and E= electric field inside a conductor. Since, drift velocity depends on the electric field inside a conductor, so it varies with change in cross-section of conductor. Hence, only current is constant in such conductor.