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Current and Resistance
93
17.57
The current in the wire is
15.0 V
150 A
0.100
V
R
I
∆
==
=
Ω
Then, from
d
vI
n
q
=
()
A
, the density of free electrons is
(
)
(
)
2
2
41
9
150 A
3.17
10
m s
1.60
10
C
5.00
10
m
d
I
n
ve
r
π
−−
×××
3
−
or
28
3
3.77
10
m
n
=×
17.58
At temperature
T
, the resistance of the carbon wire is
( )
00
1
cc
c
RR
TT
α
=+−
, and that
of the nichrome wire is
( )
0
1
nn
n
0
. When the wires are connected end to
end, the total resistance is
( )( )
0
T
0
0
c n
c
n
R
R
R
αα
+
+
+
k
cn
RR R
R
T
=+=
−
If this is to have a constant value of 10.0
Ω
as the temperature changes, it is necessary
that
(1)
and
10.0 k
+=
0
Ω
+
1
0
.
0
k
0
.
4
Ω−
=
10.0 k
=Ω
−
0
.
5
01
0 C
R
−
×
°
+
(2)
From equation (1),
, and substituting into equation (2) gives

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