(5) On the basis of electron drift, derive expression
for resistivity of a conductor in terms of relaxation
time.
Answers
Answer:
As
V
d
=−
m
e
E
τ....(i)
Current flowing through the conductor ---
I=nAV
d
e....(ii)
from equation (i) and (ii).
I=nA(
m
eE
τ)e
⟹I=
m
nAe
2
Eτ
....(iii)
If V is potential difference applied across the two ends of the conductor, then
E=
l
V
Putting this E in equation (iii),
I=
ml
nAe
2
Vτ
⟹
I
V
=
ne
2
τ
m
A
l
According to ohm's law,
I
V
=R (resistance of the conductor)
R=
ne
2
τ
m
A
l
....(iv)
But, R=ρ
A
l
.....(v)
Comparing (iv) and (v)
ρ=
ne
2
τ
m
Resistivity of a conductor depends on the following factors:
(1) It is inversely proportional to the number of free electrons per unit volume (n) of the conductor.
(2) It is inversely proportional to the average relaxation time (τ) of the free electrons in the conductor.
Explanation:
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