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benavides (jjb2356) – homework 14 – Turner – (59130)
1
This printout should have 11 questions.
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beFore answering.
001
10.0 points
Current is carried throughout the body oF a
typeII superconductor.
Assume:
The density oF superconducting
electrons is 5
×
10
27
m
−
3
.
IF a Nb
3
Sn (type II) superconducting wire
oF cross sectional area 4
.
4 mm
2
can carry a 1
×
10
5
A supercurrent, what is the average (driFt)
velocity oF the superconducting electrons?
Correct answer: 28
.
3736 m
/
s.
Explanation:
Let :
n
= 5
×
10
27
m
−
3
,
A
= 4
.
4 mm
2
= 4
.
4
×
10
−
6
m
2
,
and
I
= 1
×
10
5
A
.
The driFt velocity is
v
=
I
q
e
n A
=
1
×
10
5
A
(1
.
602
×
10
−
19
C)
×
1
(5
×
10
27
m
−
3
) (4
.
4
×
10
−
6
m
2
)
=
28
.
3736 m
/
s
.
002
10.0 points
A length oF metal wire has a radius oF 0
.
005 m
and a resistance oF 0
.
05 Ω. When the potential
di±erence across the wire is 18 V, the electron
driFt speed is Found to be 0
.
00039 m
/
s.
Based on these data, calculate the density
oF Free electron in the wire.
Correct answer: 7
.
34561
×
10
28
m
−
3
.
Explanation:
Let :
r
= 0
.
005 m
,
R
= 0
.
05 Ω
,
Δ
V
= 18 V
,
and
v
d
= 0
.
00039 m
/
s
.
The current in the wire is
I
=
Δ
V
R
=
18 V
0
.
05 Ω
= 360 A
.
²rom
v
d
=
I
n q A
, the density oF Free elec
tron is
n
=
I
v
d
q
e
(
π r
2
)
=
360 A
(0
.
00039 m
/
s) (1
.
6
×
10
−
19
C)
×
1
π
(0
.
005 m)
2
=
7
.
34561
×
10
28
m
−
3
.
003
10.0 points
At 25
◦
C, the resistance oF a segment oF gold
wire is 76 Ω. When the wire is placed in a
liquid bath, the resistance increases to 175 Ω.
The temperature coe³cient is 0
.
0034 (
◦
C)
−
1
at 20
◦
C.
What is the temperature oF the bath?
Correct answer: 414
.
64
◦
C.
Explanation:
Let :
R
1
= 76 Ω
,
R
2
= 175 Ω
,
T
0
= 20
◦
C
,
T
1
= 25
◦
C
,
and
α
= 0
.
0034(
◦
C)
−
1
.
Neglecting change in the shape oF the wire,
we have
R
1
=
R
0
[1 +
α
(
T
1

T
0
)]
R
0
=
R
1
1 +
α
(
T
1

T
0
)
and
R
2
=
R
0
[1 +
α
(
T
2

T
0
)]
,
where
T
0
= 20
◦
C
.
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 Spring '08
 Turner
 Current, Work

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