The resistivity dont depends on length and thickness but we know P(resistivity)=RA/l Its sholud be directly proportional to area and inversely to length.
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Resistivity is a property of material it is not dependant on the length and the area of cross-section. It is constant for a particular meatrial irrespective of its dimensions and when the material changes so does the resistivity, other than that it remains constant with the lenght and the area of the corss-section of the conductor.
It is the resistance of the conductor that is dependant on parameters like the length and the area of cross-section of the conductor.
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