When 5v potential difference is applied across a wire

Asked by admin @ 17/08/2021 in Physics viewed by 484 People

When 5V potential difference is applied across a wire of length 0.1, the drift speed of electrons is 2.5× 10-4m/s if the electron density in the wire is 8× 1028m-3, calculate the resistivity of the material of wire.

Answered by admin @ 17/08/2021

resistivity of the material of wire is 1.6 × 10^-5

potential difference applied across wire, V = 5 volts

length of wire, l = 0.1 m

drift velocity, vd = 2.5 × 10^-4 m/s

electron density in the wire, n = 8 × 10^28 /m³

charge on electron, e = 1.6 × 10^-19 C

using formula, i = neAvd .......(1)

from Ohm's law, i = V/R ......(2)

and R = ρl/A......(3)

so,from equations (1), (2) and (3) we get

V/ρl = nevd

⇒ρ = V/nevd.l

= 5/(8 × 10^28 × 1.6 × 10^-19 × 2.5 × 10^-4 × 0.1)

= 5/(8 × 1.6 × 2.5 × 10⁴)

= 5/(20 × 1.6 × 10⁴)

= (1/6.4) × 10-⁴

≈ 1.6 × 10^-5 Ωm

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