Question

Calculate the resistivity of wire 1.0m long, 0.4mm in diameter and having a resistance of 2ohm. Answer is 2.153 × 10^-7 ohm m but I need solution.

Answer 1

resistivity= (resistance *area of cross-section)/length
=(R*A)/L

R=2
A=  3.142 r^2        [ 3.142 is the value of pi, r is radius, r=diameter/2]
=3.142 * {(0.4*10^-3)/2}^2     [ SI unit of diameter is metre, so I converted mm into m]
=1.26*10^-7
L=1

Putting all the values in the above equation, resistivity=2.513*10^-7 ohm metre

Answer 2

R = ρL / A

ρ = RA / L
= R πr²/L ………[∵ Area of cross section of wire is circular, A = πr²]
= [2 Ω × π × (0.4/2 × 10^-3 m)²] / 1.0 m
= 2.513 × 10^-7 Ω m

Resistivity of wire is 2.513 × 10^-7 Ω m