Rough surfaces show a load-dependent electrical constriction resistance. Here, using a recent analogy due to Barber [Proc. R. Soc. London A 459 (2003) 53] between the incremental stiffness and the conductance in the elastic regime, and the Archard hypothesis to solve the multiscale contact problem, the conductance is found for the profile defined by the Weierstrass series. The analysis is also approximately valid, neglecting thermal effects on the contact area, for the thermal conductance
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