Question

2 wires a and b have same resistivity but different resistance.what do you infer from this?

Answer 1

t must be assumed that these are pure resistances (neither inductive nor capacitive), and that the materials are homogeneous.

Joule power, at constant voltage, is inversely proportional to the resistance of the conductor, whose general formulation is:

Resistance = Resistivity * L / S

If the resistivities and lengths of the two conductors are equal and the ratio of the sections are in a 1:6 ratio, the Joule powers will be in a 6:1 ratio.

This is of course a valid ratio in DC or AC under the conditions of strict covariance current / voltage, in a stationary state.