When a $5\,\text{V}$ potential difference is applied across a wire of length $0.1\,\text{m}$, the drift speed of the electrons is $2.5\times10^{-4}\,\text{m s}^{-1}$. If the electron density in the wire is $8\times10^{28}\,\text{m}^{-3}$, calculate the resistivity of the material of the wire.

$\rho\approx 1.56\times10^{-5}\,\Omega\,\text{m}$.

CBSE Class 12 · 2016 · All India · Current ElectricityShort Answer

When a

5 V

potential difference is applied across a wire of length

0.1 m

, the drift speed of the electrons is

2.5 \times 1 0^{- 4} m s^{- 1}

. If the electron density in the wire is

8 \times 1 0^{28} m^{- 3}

, calculate the resistivity of the material of the wire.

Answer: $ρ \approx 1.56 \times 1 0^{- 5} Ω m$ .

J = n e v_{d}

and

J = σ E = \frac{E}{ρ} = \frac{V}{ρ ℓ}

, so

ρ = \frac{V}{n e v _{d} ℓ}

ρ = \frac{5}{8 \times 1 0 ^{28} \times 1.6 \times 1 0 ^{- 19} \times 2.5 \times 1 0 ^{- 4} \times 0.1} = 1.5625 \times 1 0^{- 5} Ω m .

CBSE Class 12 Board · 2016 · All India · Subjective