A steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities constant along the length of the conductor is/are:
Let E be electric field, then current density j= σ E
Also we know that current density j=iA
Hence j is different for different area of cross-sections. When j is different, then E is also different. Thus E is not constant. The drift velocity vd is given by vd=jne= different for different j values.Hence only current i remains constant.