CBSE Class 12 · 2023 · Current ElectricityShort Answer

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Define current density and relaxation time. Derive an expression for the resistivity of a conductor in terms of the number density of charge carriers and the relaxation time.

Solution

\textbf{Current density} is the current per unit cross-sectional area perpendicular to the flow,

J = \frac{I}{A}

. \textbf{Relaxation time} is the mean time between two successive collisions of a free electron. With

I = n e A v_{d}

and

v_{d} = \frac{e E}{m} τ

, and using

E = \frac{V}{ℓ}

with Ohm's law

R = \frac{V}{I}

, one gets

R = \frac{m ℓ}{n e ^{2} τ A}

; comparing with

R = ρ \frac{ℓ}{A}

ρ = \frac{m}{n e ^{2} τ} .

CBSE Class 12 Board · 2023 · Subjective

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