homework 14 – LEE, BENJAMIN – Due: Oct 6 2007, 4:00 am
1
Question 1, chap 28, sect 4.
part 1 of 3
10 points
Twelve resistors, each of equal value 75 Ω,
are connected so that each is along one edge
of a cube, as shown in the Fgure below. A
current of 13
.
3 A is introduced at point “a”.
The current will be allowed to exit only along
a wire at point “e”, as drawn.
a
d
e
h
g
b
c
f
6
12
10
7
3
5
8
1
2
4
11
9
I
I
Which one of the following conditions is
correct concerning the electric potential at
the various nodes in the circuit above?
1.
V
c
=
V
d
and
V
g
=
V
h
correct
2.
V
b
=
V
g
and
V
d
=
V
f
3.
V
c
=
V
g
and
V
d
=
V
h
4.
V
b
=
V
f
and
V
c
=
V
g
5.
V
h
=
V
b
and
V
f
=
V
d
6.
V
c
=
V
h
and
V
d
=
V
g
7.
V
b
=
V
d
and
V
f
=
V
h
8.
V
d
=
V
b
and
V
f
=
V
g
9.
V
b
=
V
f
and
V
d
=
V
g
10.
V
f
=
V
b
and
V
d
=
V
h
Explanation:
Consider the Fgure in the question. The
current
I
is introduced into node “a”. Three
independent resistors of equal value are acces
sible via this node, namely, resistor
R
1
,
R
2
,
and
R
3
.
Neglect resistor
R
3
for the moment, which
is parallel with the rest of the resistors in the
network.
Because resistors
R
1
and
R
2
are equal and
the remainder of the circuit is symmetric, the
current will split equally between these two
paths.
Thus, the electric potential across
each of the resistors
R
1
and
R
2
is equal and
V
c
=
V
d
.
The same argument can be made for
R
5
and
R
6
, thus
V
g
=
V
h
Question 2, chap 28, sect 4.
part 2 of 3
10 points
What is the equivalent resistance of the
resistor network shown in the Fgure?
Correct answer: 43
.
75 Ω (tolerance
±
1 %).
Explanation:
Let :
R
= 75 Ω
.
We wish to calculate the equivalent resis
tance of our cubic setup. To assist in this
endeavor, recall the following facts derived in
Part 1. Since
I
1
=
I
2
and
I
4
=
I
5
, we have
V
c
=
V
d
and
V
g
=
V
h
.
Note:
We can achieve the
identical
cur
rent distribution if we rearrange the twelve
resistors in the following conFguration let
ting nodes “c” and “d” be one node
and nodes “g” and “h” be one node.
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View Full Documenthomework 14 – LEE, BENJAMIN – Due: Oct 6 2007, 4:00 am
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7
9
11
12
5
4
8
10
6
3
1
2
a
e
f
b
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 Fall '07
 Turner
 Current, Work, Resistor, Correct Answer, Electric power transmission

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