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
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If E be electric field, then current density $j = \sigma \mathbf{E}$
Also we know that current density $j = \frac{i}{A}$
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 $v_d$ is given by $\mathbf{v_d} = \frac{j}{ne} =$ different for different j values.
Hence only current i will be constant.
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