Maximum possible current in a Conductor

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suchith
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If we are given a metallic conductor in a given Temperature(Room temperature here), Area of cross section A, is there an upper limit to the strength of the current through such a conductor due to the upper limit for drift velocity(v)??

I=nAve

e=electron charge
n=electron density
 
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What factors lead to limiting of maximum permissible current besides limit of drift velocity?