homework 05 – KIM, JI – Due: Feb 17 2008, 4:00 am
1
Question 1, chap 27, sect 3.
part 1 of 2
10 points
The quantity of charge passing through a
surface of area 2
.
1 cm
2
varies with time as
q
=
q
1
t
3
+
q
2
t
+
q
3
,
where
q
1
= 5 C
/
s
3
,
q
2
= 2
.
3 C
/
s,
q
3
= 8
.
5 C,
and
t
is in seconds.
What is the instantaneous current through
the surface at
t
= 1
.
5 s?
Correct answer: 36
.
05 A (tolerance
±
1 %).
Explanation:
Let :
q
1
= 5 C
/
s
3
,
q
2
= 2
.
3 C
/
s
,
q
3
= 8
.
5 C
,
and
t
= 1
.
5 s
.
I
≡
d q
dt
= 3
q
1
t
2
+
q
2
= 3
(
5 C
/
s
3
)
(1
.
5 s)
2
+ 2
.
3 C
/
s
=
36
.
05 A
.
Question 2, chap 27, sect 3.
part 2 of 2
10 points
What is the value of the current density at
t
= 1
.
5 s?
Correct answer: 171667 A
/
m
2
(tolerance
±
1
%).
Explanation:
Let :
A
= 2
.
1 cm
2
= 0
.
00021 m
2
and
t
= 1
.
5 s
.
J
≡
I
A
=
36
.
05 A
0
.
00021 m
2
=
171667 A
/
m
2
.
Question 3, chap 27, sect 2.
part 1 of 3
10 points
Consider two cylindrical conductors made
of the same ohmic material. Conductor 1 has
a radius
r
1
and length
ℓ
1
while conductor 2
has a radius
r
2
and length
ℓ
2
.
Denote:
The currents of the two conductors
as
I
1
and
I
2
, the potential di±erences between
the two ends of the conductors as
V
1
and
V
2
,
and the electric ²elds within the conductors
as
E
1
and
E
2
.
V
1
v
E
I
ℓ
r
1
b
2
r
2
b
If
ρ
2
=
ρ
1
, r
2
= 2
r
1
, ℓ
2
= 3
ℓ
1
and
V
2
=
V
1
, ²nd the ratio
R
2
R
1
of the resistances.
1.
R
2
R
1
=
2
3
2.
R
2
R
1
=
3
4
correct
3.
R
2
R
1
= 2
4.
R
2
R
1
=
3
2
5.
R
2
R
1
= 3
6.
R
2
R
1
=
4
3
7.
R
2
R
1
= 4
8.
R
2
R
1
=
1
3
9.
R
2
R
1
=
1
4
10.
R
2
R
1
=
1
2
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View Full Documenthomework 05 – KIM, JI – Due: Feb 17 2008, 4:00 am
2
Explanation:
The relation between resistance and resis
tivity is given by
R
=
ρ ℓ
A
=
ρ ℓ
π r
2
.
Then since
r
2
= 2
r
1
and
ℓ
2
= 3
ℓ
1
, the ratio
of the resistances is
R
2
R
1
=
ρ ℓ
2
π r
2
2
π r
2
1
ρ ℓ
1
=
ℓ
2
r
2
1
ℓ
1
r
2
2
=
(3
ℓ
1
)
r
2
1
ℓ
1
(2
r
1
)
2
=
3
4
.
Question 4, chap 27, sect 2.
part 2 of 3
10 points
When the two conductors are attached to a
battery of voltage V, determine the ratio
E
2
E
1
of the electric ±elds.
1.
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 Spring '08
 Turner
 Physics, Charge, Work, Resistor, Electrical resistance, E1 E2 E1

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