Question

The resistivity of a conductor with a current density of $2.5Am$${}^{-2}$ when an electric field $5\times {10}^{-8}V{m}^{-1}$ is applied to it, is

• A. $1.0\times {10}^{-8}\Omega m$
• B. $2.0\times {10}^{-8}\Omega m$
• C. $0.5\times {10}^{-8}\Omega m$
• D. $12.5\times {10}^{-8}\Omega m$

Answer 1

The correct option is B $2.0\times {10}^{-8}\Omega m$

$\text{Step 1:}$ $\text{Relation between Electric field(E), Resistivity and Current density(J)}$

Suppose length of conductor $=l$

We know that, Potential difference, $V=E.l$

$\text{\&}$ Current Density $J=I/A$
So, $I=JA$

and $R=\frac{\rho l}{A}$
From $V=IR$
$\Rightarrow E.l=JA\times \frac{\rho l}{A}$
$\Rightarrow E=J\left(\rho \right)$

$\therefore \rho =\frac{E}{J}$

$\text{Step 2: Putting the values in above equation}$

$\Rightarrow \rho =\frac{E}{J}=\frac{5\times {10}^{-8}V{m}^{-1}}{2.5A{m}^2}$ $=2\times {10}^{-8}\Omega m$

Hence, Option B is correct