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Question

Resistance of a metal wire of length 1 m is 26Ω at 20C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature?

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Solution

Given: R=26 Ω, l=1m, d=0.3mm

Step 1: Resistivity of the metal (ρ)
We know that resistance can be given as :
R=ρ lA
ρ=R Al ....(1)

Step 2: Calculations and Substituting the values

A=πd24=3.14×(0.3×103m)24=0.071×106m2
From equation (1)
ρ=26 Ω×0.071×106 m21 m=1.85×106Ωm

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