CBSE Class 12 · 2018 · Current ElectricityShort Answer

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(a) Define the conductivity of a metallic wire and write its SI unit.
(b) Using the free-electron model, derive the expression for the conductivity of a wire in terms of the number density and the relaxation time, and hence obtain the relation between the current density and the applied field

E

Solution

(a) Conductivity is the reciprocal of resistivity,

σ = \frac{1}{ρ}

; SI unit

Ω^{- 1} m^{- 1}

. (b) With

v_{d} = \frac{e E}{m} τ

, the current density is

J = \frac{I}{A} = n e v_{d} = \frac{n e ^{2} τ}{m} E

. Hence

σ = \frac{J}{E} = \frac{n e ^{2} τ}{m}

and

J = σ E,

which is the microscopic form of Ohm's law.

CBSE Class 12 Board · 2018 · Subjective

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