Question

calculate the resistivity of the material of wire 1.0m long and 0.4mm in diameter and having a resistance of 2 ohm

Answer 1

R=(resistivity)xlength/areaResistivity=RA/L
=R x $\\ \pi r^{2}$/L
=1.256 x $10^{-3}$ Ohm-m

Answer 2

"The resistivity of the material is $\rho \quad =\quad 2.512\times { 10 }^{ -7 }\Omega m$

Solution:

Given,

Length of the wire l = 1m

Diameter d = 0.4mm

Therefore radius r = d/2 = 0.2mm

By converting mm to m

We get, $r\quad =\quad 2\quad \times \quad { 10 }^{ -4 }m$

Resistance R = 2ῼ

We know that $ρ\quad =\quad R\quad \times \quad \frac { A }{ l }$

$=\frac { 2\pi { r }^{ 2 } }{ l }$

$=2\quad \times \quad 3.14\quad \times \quad { (2\quad \times \quad { 10 }^{ -4 }) }^{ 2 }$

By simplifying we get, $\rho \quad =\quad 2.512\times { 10 }^{ -7 }\Omega m$"