Q. 64.0( 6 Votes )

A wire of length 1 m and radius 0.1 mm has a resistance of 100 Ω. Find the resistivity of the material.

Answer :

Given,


Length of wire, l = 1m


Radius of wire, r=0.1mm=0.1×10-3m


Resistance of the wire, R =100 Ω


Formula used,


The resistivity, ρ, of a wire with cross-sectional area A and length l is expressed as



Where R is the resistance offered by the wire.


Solution,


Firs, we find the area of cross-section of the wire as,



By substituting the value of r, Area becomes



Now substitute all the given values in the expression for resistivity. So, ρ is





So, the resistivity of the material is π×10-6 Ωm


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