Answer
${2}\times{10}^{-8}$ $\Omega$$m$
Work Step by Step
The formula connecting Resistance (R), Resistivity ($\rho$), Length (m) and Area (A) is as follows:
$R$=$\frac{\rho \times L}{A}$
According to the data provided in the question,
R= 50m$\Omega$ = 0.050 $\Omega$
L= 2m
D= 1 mm which means radius r is 0.5mm or 0.0005m
First, we will find the cross sectional area of the wire using the formula
A= $\pi$ $r^{2}$
Substituting the values of $\pi$ and r, A is calculated to be 0.00000079 $m^{2}$
Then, we make $\rho$ the subject of the first formula,
$\rho$= $\frac{R \times A}{L}$
Substituting the values of R,A and L into this formula, we find the Resistivity $\rho$ to be
$\rho$ = ${1.963}\times{10}^{-8}$ $\Omega$$m$
This can be approximated as ${2}\times{10}^{-8}$ $\Omega$$m$.
