EE215 Winter 2003
Final Exam Solutions
Monday, March 17, 2003, 2:30 – 4:20pm
Name: ______________________________ ID#: ________________ Section: ___
Please show all steps in solving the problem. Clearly mark your final answers and don’t forget
the units.
Problem 1 (20 points)
Consider the wireframe tetrahedron to the
right. Each resistor has a value of 1
Ω
. What is
the equivalent resistance between nodes
a
and
d
?
(Note: a tetrahedron is a pyramid with 4
triangular sides.)
Answers and grading guide:
This is similar but less complicated than
Homework 3, Problem 10.
We can use the same approach as in the
homework solution (node voltage method), by
setting
v
a
= 0V and
v
d
= 1V. Then we can write the equations for nodes
b
and
c
:
c
: (
v
c
–
v
a
)+(
v
c
–
v
b
) + (
v
c
–
v
d
) = 3
v
c
–
v
b
– 1 = 0
b: 3
v
b
–
v
c
– 1 = 0
Solving these equations yields
v
b
=
v
c
= ½V.
Thus the currents are
i
ba
=
i
ca
=
i
db
=
i
dc
= ½A, and
i
da
= 1A and
i
bc
= 0A.
So the total current is 2A, and the equivalent resistance
R
eq
= ½
Ω
.
Solution shortcuts:
Because of the symmetry of the tetrahedron, it is easy to see that
v
b
=
v
c
= ½V, without using any
analysis. Also note that this is essentially a Wheatstone Bridge with equal resistors (plus another
resistor
R
ad
in parallel).
Alternative solution:
It is also possible to use a deltawye transform, for example on the resistors abc. The three new
resistors have the value
R
1
=
R
2
=
R
3
= 1/3
Ω
. The resulting circuit can be reduced by serial and
parallel transforms: (
R
1
+ (
R
2
+
R
cd
)(
R
3
+
R
bd
))
R
ad
= (1/3 + 4/34/3)1 =
½
Ω
.
If node voltage method is used: Each correct node voltage equation: 5 points. Correct values for
v
b
and v
c
: 5 points.
If circuit transforms are used: Correct deltawye transform: 10 points. No deltawye transform:
0 points.
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View Full DocumentProblem 1* (20 points)
Consider the wireframe tetrahedron to the
right. Each resistor has a value of 1
Ω
. What is
the equivalent resistance between nodes
a
and
b
?
(Note: a tetrahedron is a pyramid with 4
triangular sides.)
Answers and grading guide:
This is similar but less complicated than
Homework 3, Problem 10.
We can use the same approach as in the
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 Spring '05
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 Electrical Engineering, Inductance, Inductor, Node Voltage Method

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