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^{-3}m

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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