Husain, Zeena – Homework 5 – Due: Feb 23 2004, 4:00 am – Inst: Sonia Paban
1
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printout
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38
questions.
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Central time.
001
(part 1 of 2) 10 points
A strong lightning bolt transfers an electric
charge of about 11 C to Earth (or
vice versa
).
How many electrons are transferred?
Correct answer: 6
.
86566
×
10
19
.
Explanation:
Given :
q
= 11 C
and
q
e
=

1
.
60218
×
10

19
C
.
The charge is proportional to the number of
electrons, so
q
=
n q
e
n
=
q
q
e
=

11 C

1
.
60218
×
10

19
C
=
6
.
86566
×
10
19
.
The charge on the electron is negative.
The direction of current flow in lightning
can be either from Earth to the clouds or
vice
versa
.
002
(part 2 of 2) 10 points
Assume:
One mole of water has a mass of
18
.
1 g
/
mol.
If each water molecule donates one electron,
how much water is ionized in the lightning?
Correct answer: 0
.
00206353 g.
Explanation:
Given :
M
= 18
.
1 g
/
mol
and
N
a
= 6
.
02214
×
10
23
/
mol
Mass is proportional to the number of atoms
in a substance, so for
m
grams in
N
atoms in
the water and
M
grams in
N
a
atoms in one
mole, we have
m
M
=
N
N
a
N
=
m
M
N
a
Hence the total mass
M
total
of the water ion
ized by the lightning bolt is give by
M
total
=
n
H
2
O
m
H
2
O
=
n
e
M
H
2
O
N
A
=
(
6
.
86566
×
10
19
)
(18
.
1 g
/
mol)
(6
.
02214
×
10
23
/
mol)
=
0
.
00206353 g
,
Since every water molecule donates one elec
tron to the discharge, the total number of
transferred electrons
n
e
equals the total num
ber
n
H
2
O
of
ionized
water
molecules,
so
n
e
=
n
H
2
O
.
003
(part 1 of 2) 10 points
The quantity of charge passing through a sur
face of area 2
.
89 cm
2
varies with time as
q
=
q
1
t
3
+
q
2
t
+
q
3
,
where
q
1
= 4
.
9 C
/
s
3
,
q
2
= 6
.
1 C
/
s,
q
3
= 7
.
4 C,
and
t
is in seconds.
What is the instantaneous current through
the surface at
t
= 0
.
9 s?
Correct answer: 18
.
007 A.
Explanation:
Given :
q
1
= 4
.
9 C
/
s
3
,
q
2
= 6
.
1 C
/
s
,
q
3
= 7
.
4 C
,
and
t
= 0
.
9 s
.
I
≡
d q
dt
= 3
q
1
t
2
+
q
2
= 3
(
4
.
9 C
/
s
3
)
(0
.
9 s)
2
+ 6
.
1 C
/
s
= 18
.
007 A
.
004
(part 2 of 2) 10 points
What is the value of the current density at
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Husain, Zeena – Homework 5 – Due: Feb 23 2004, 4:00 am – Inst: Sonia Paban
2
t
= 0
.
9 s?
Correct answer: 62308 A
/
m
2
.
Explanation:
Given :
a
= 2
.
89 cm
2
= 0
.
000289 m
2
and
t
= 0
.
9 s
.
J
≡
I
A
=
18
.
007 A
0
.
000289 m
2
= 62308 A
/
m
2
.
005
(part 1 of 5) 10 points
The mass density of Cu is 8
.
92 g
/
cm
3
, its
molar mass is 63
.
5 g
/
mol, and Avogadro’s
number is 6
.
02214
×
10
23
atoms
/
mole.
The
electron mass is 9
.
10939
×
10

31
kg, and the
resistivity of copper is 1
.
7
×
10

8
Ω
·
m.
A current of 25 A exists in a copper (Cu)
wire which has a diameter of 5 mm.
Assume:
Each atom of copper has one
conduction band, and the average thermal
speed of an electron (in the free electron model
of conductivity
v
=
r
k T
m
) = 1
×
10
6
m
/
s
.
What is the current density,
J
?
Correct answer: 1
.
27324
×
10
6
A
/
m
2
.
Explanation:
Given :
I
= 25 A
and
r
= 2
.
5 mm = 0
.
0025 m
.
The current density is given by
J
≡
I
A
=
I
π r
2
.
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 Spring '08
 Turner
 Work, SEPTA Regional Rail, Correct Answer, JenkintownWyncote, Husain, Sonia Paban

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