Homework #9
12.1
(a)
Compute the electrical conductivity of a 7.0-mm (0.28-in.) diameter cylindrical silicon specimen 57 mm
(2.25 in.) long in which a current of 0.25 A passes in an axial direction.
A voltage of 24 V is measured across two
probes that are separated by 45 mm (1.75 in.).
(b)
Compute the resistance over the entire 57 mm (2.25 in.) of the specimen.
This problem calls for us to compute the electrical conductivity and resistance of a silicon specimen.
Solution
(a)
We use Equations 12.3 and 12.4 for the conductivity, as
σ
=
1
ρ
=
Il
VA
=
Il
V
π
d
2
2
Here
d
is the specimen diameter.
Now, incorporating values for the several parameters provided in the problem
statement, leads to
σ
=
(0.25 A)
(
45
×
10
−
3
m
)
(24 V)(
π
)
7.0
×
10
−
3
m
2
2
= 12.2 (
Ω
- m)
-1
(b)
The resistance,
R
, may be computed using Equations 12.2 and 12.4, as
R
=
l
σ
A
=
l
σπ
d
2
2
=
57
×
10
−
3
m
12.2 (
Ω −
m)
−
1
[
]
(
π
)
7.0
×
10
−
3
m
2
2
= 121.4
Ω
12.6
(a)
Calculate the number of free electrons per cubic meter for silver, assuming that there are 1.3 free
electrons per silver atom.
The electrical conductivity and density for Ag are 6.8 × 10
7
(Ω
-m)
–1
and 10.5 g/cm
3
,
respectively.
(b) Now compute the electron mobility for Ag.
Solution

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