When $5\ V$ potential difference is applied across a wire of length $0.1\ m$, the drift speed of electrons is $2.5 \times 10^{-4}$ $ms^{-1}$ . If the electron density in the wire is $8 \times 10^{28}$ $m^{-3}$ the resistivity of the material is close to
JEE MAIN 2015, Medium
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$V=I R=\left(n e A v_{d}\right) \rho \frac{\ell}{A}$
$\therefore \quad \rho=\frac{\mathrm{V}}{\mathrm{V}_{\mathrm{d}} \mathrm{lne}}$
Here $\mathrm{V}=$ potential difference
$\mathrm{I}=$ length of wire
$\mathrm{n}=\mathrm{no} .$ of electrons per unit volume of conductor.
$\mathrm{e}=\mathrm{no.}$ of electrons
Placing the value of above parameters we get resistivity
$\rho=\frac{5}{8 \times 10^{28} \times 1.6 \times 10^{-19} \times 2.5 \times 10^{-4} \times 0.1}$
$=1.6 \times 10^{-5} \,\Omega m$
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