wilson (kw22588) – HW7 – Mackie – (20224)
1
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printout
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have
16
questions.
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before answering.
001
10.0 points
The current in a wire decreases with time
according to the relationship
I
= (2
.
15 mA)
×
e

at
where
a
= 0
.
13328 s

1
.
Determine
the
total charge
that
passes
through the wire from
t
= 0 to the time the
current has diminished to zero.
Correct answer: 0
.
0161315 C.
Explanation:
I
=
dq
dt
q
=
integraldisplay
t
t
=0
I dt
=
integraldisplay
∞
t
=0
(0
.
00215 A)
e

0
.
13328 s

1
t
dt
= (0
.
00215 A )
e

0
.
13328 s

1
t

0
.
13328 s

1
vextendsingle
vextendsingle
vextendsingle
vextendsingle
vextendsingle
∞
0
=
0
.
0161315 C
.
002
10.0 points
The total charge that an automobile battery
can supply without being recharged is given
in terms of Amperehours.
A typical 12V
battery has a rating of 42 A
·
h
.
Suppose you
forget to turn off the headlights in your parked
automobile.
If each of the two headlights draws 3
.
9 A
,
find
out
the
time
before
your
battery
is
“dead”.
Correct answer: 5
.
38462 h.
Explanation:
Let :
rating = 42 A
·
h
and
I
= 3
.
9 A
.
If only one of the two headlights is left on,
the time before the battery dies is given by
T
1
=
rating
I
=
42 A
·
h
3
.
9 A
= 10
.
7692 h
.
Thus the required time is
5
.
38462 h
.
003
(part 1 of 2) 10.0 points
The quantity of charge passing through a sur
face of area 1
.
71 cm
2
varies with time as
q
=
q
1
t
3
+
q
2
t
+
q
3
,
where
q
1
= 3
.
2 C
/
s
3
,
q
2
= 3
.
7 C
/
s,
q
3
= 5
.
1 C,
and
t
is in seconds.
What is the instantaneous current through
the surface at
t
= 0
.
7 s?
Correct answer: 8
.
404 A.
Explanation:
Let :
q
1
= 3
.
2 C
/
s
3
,
q
2
= 3
.
7 C
/
s
,
q
3
= 5
.
1 C
,
and
t
= 0
.
7 s
.
I
≡
d q
dt
= 3
q
1
t
2
+
q
2
= 3
(
3
.
2 C
/
s
3
)
(0
.
7 s)
2
+ 3
.
7 C
/
s
=
8
.
404 A
.
004
(part 2 of 2) 10.0 points
What is the value of the current density at
t
= 0
.
7 s?
Correct answer: 49146
.
2 A
/
m
2
.
Explanation:
Let :
a
= 1
.
71 cm
2
= 0
.
000171 m
2
and
t
= 0
.
7 s
.
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wilson (kw22588) – HW7 – Mackie – (20224)
2
J
≡
I
A
=
8
.
404 A
0
.
000171 m
2
=
49146
.
2 A
/
m
2
.
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 Spring '08
 Turner
 Physics, Current, Resistor, SEPTA Regional Rail, Jaguar Racing, Series and parallel circuits, JenkintownWyncote

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