Engineering physics 3(Relaxation time, Temperature dependence of Electrical Resistivity)

better understanding points on Relaxation time, Temperature dependence of Electrical Resistivity.

1. 1
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
1
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
ENGINERING PHYSICS ENGINERING PHYSICS ENGINERING PHYSICS ENGINERING PHYSICS ENGINERING PHYSICS ENGINERING PHYSICS ENGINERING PHYSICS ENGINERING PHYSICS
Mr. GouriKumar Sahu
Senior Lecturer in Physics
C.U. T. M.

2. 2
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
2
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
SESSION-4
4.1 Interpretation of Relaxation time
From eq[2.3],
],L
th
]l
ciflld
sew
,L
the
a
Let the electric field is switched off at t=0, then the drift velocity gradually falls
to zero, due to scattering by phonons. Integrating above equation
=
0 n v
yg
n v
yg
s w
=
0u

!"
n v
yg
n v
yITx g
s w
u

1-4n v
ygsn v
y
T g K
*
l
a
+3.2.
FThe relaxation time is determined by the electron p honon interaction in the
metal.
FIt is of the order of 10
-14
sec.

3. 3
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
3
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
SESSION-4
4.2
Temperature Dependence of 
Electrical Resistivity
4.2
Temperature Dependence of 
Electrical Resistivity
Kinetic energy associated with an electron is
1
2
0#1
̅%
3
s
3
2
4
56
When an electric field is applied, the resulting ac celeration 7 s
89
:
.
If the mean free path is ;, then the time between collision is
<
i
̅.
Hench the drift velocity acquired before next colli sion is
= s 7CCbd>u?(K s
)@
0
;
1
̅
Thus the average drift velocity is
=
2
s
)@
20
;
1
̅

4. 4
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
4
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
SESSION-4
4.2
Temperature Dependence of 
Electrical Resistivity
4.2
Temperature Dependence of 
Electrical Resistivity
If n is the number of electrons per unit volume, th en current density is
A
ys
")=
2
s
")
3
@
20
;
1
̅
Or
B s
A
y
@
s
")
3
20
;
1
̅
Or,
C s
20
";)
3
>
34
56
0
s
1204
56
")
3
;
wwwwwwwHOdO)
Here it is assumed that ;is independent of temperature.
Hence C ∝
6which is contradictory to the experimental fact tha t C ∝ 6.

5. 5
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
5
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
SESSION-4
4.3
Drawbacks 
of Classical free electron 
theory
4.3
Drawbacks 
of Classical free electron 
theory
1)
Cis proportional to
6. But experimentally it was found that Cis
proportional to T.
2) K/ B6= L, a constant (Wiedmann-Franz law) for all temper atures. But this is
not true at low temperatures.
3) The theoretically predicted value of specific he at of a metal does not agree
with the experimentally obtained value.
4) This theory fails to explain ferromagnetism, sup erconductivity, photoelectric
effect, Compton effect and blackbody radiation.

6. 6
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
6
ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics
.
END OF SESSION -4
SESSION-4
THANK YOU