When a potential difference of 5 V is applied across a wire of length 0.1 m, the drift speed of electrons is 2.5 times 10^ -4 ,text m/s . If the electron number density in the wire is 8 times 10^ 28 ,text m ^ -3 , the resistivity of the material is closest to:

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JEE MAIN Physics QUESTION #5588

Question 1

When a potential difference of 5 V is applied across a wire of length 0.1 m, the drift speed of electrons is $2.5 \times 10^{-4}\,\text{m/s}$. If the electron number density in the wire is $8 \times 10^{28}\,\text{m}^{-3}$, the resistivity of the material is closest to:

$1.6 \times 10^{-8}\,\Omega\text{m}$
$1.6 \times 10^{-7}\,\Omega\text{m}$
$1.6 \times 10^{-6}\,\Omega\text{m}$
$1.6 \times 10^{-5}\,\Omega\text{m}$✔️

Correct Answer Explanation

Electric field: $E = \frac{V}{L} = \frac{5}{0.1} = 50\,\text{V/m}$

Current density: $J = nev_d = 8 \times 10^{28} \times 1.6 \times 10^{-19} \times 2.5 \times 10^{-4} = 3.2 \times 10^{6}\,\text{A/m}^2$

Resistivity: $\rho = \frac{E}{J} = \frac{50}{3.2 \times 10^{6}} \approx 1.56 \times 10^{-5}\,\Omega\text{m}$

Closest option: $1.6 \times 10^{-5}\,\Omega\text{m}$. Answer: D.

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