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Question : 27
Total: 35
Define current density and relaxation time. Derive an expression for resistivity of a conductor in terms of number density of charge carriers in the conductor and relaxation time.
Solution: 👈: Video Solution
Current density: Current density is the current per unit area of cross-section of a conductor.
J =
Relaxation time: Relaxation time is the time interval between two successive collisions of electrons in a conductor.
Expression for resistivity:
v d =
τ
or,v d =
τ (since, E =
)
or,V =
or,I R =
V = I R
or,R =
=
( since R =
)
ρ =
or, ρ =
(since, I = n e A v d )
∴ ρ =
Relaxation time: Relaxation time is the time interval between two successive collisions of electrons in a conductor.
Expression for resistivity:
or,
or,
or,
or,
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