Question

When $5V$ potential difference is applied across a wire of length $10cm,$ the drift speed of electrons is $2.5\times {10}^{–4}m/s.$ If the electron density in the wire is $8\times {10}^{28}/m^3$, then resistivity of the material is close to

• A. $1.6\times {10}^{-7}\Omega m$
• B. $1.6\times {10}^{-5}\Omega m$
• C. $1.6\times {10}^{-6}\Omega m$
• D. $1.6\times {10}^{-8}\Omega m$

Answer 1

The correct option is B $1.6\times {10}^{-5}\Omega m$

Clearly $J=\frac{E}{\rho }$ and $J=\eta e{v}_d$


$\eta e{v}_d=\frac{5\times 10}{\rho }$

$\Rightarrow \rho =\frac{50}{\eta e{v}_d}$

$\Rightarrow \rho =\frac{50}{8\times {10}^{28}\times 1.6\times {10}^{-19}\times 2.5\times {10}^{-4}}$

$\approx 1.6\times {10}^{-5}$