MAE140  Linear Circuits  Fall 09
Midterm, November 10
Instructions
(i) This exam is open book. You may use whatever written materials you choose, including your class
notes and textbook. You may use a hand calculator with no communication capabilities
(ii) You have 70 minutes
(iii) Do not forget to write your
name
,
student number
, and
instructor
B
+

10 V
0.5 A
10
40
20
10
Ω
Ω
Ω
Ω
A
(a) Question 1.
A
v
S
i
S
B
D
C
R
2
R
4
R
3
R
1
i
1
i
2
(b) Question 2.
Figure 1: Circuits for questions 1 and 2.
1.
Equivalente Circuits
Part I
[4 points] Use source transformations and association of resistors to find the Thevenin equiva
lent to the circuit in Fig. 1(a) as seen from terminals A and B.
Part II
[4 points] A classmate was arguing with you that one would “extract” the most power out of
this circuit by connecting a very small resistance between terminals A and B. You argued that
he/she was wrong and that a 20
Ω
resistor would be a better choice. Who is right and why?
Hint #1: Don’t complicate: all you need to do is compare the two options!
Hint #2: Use the Thevenin equivalent computed in Part I to answer the question.
Solution:
Part I:
A possible series of source transformations is shown here:
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10 V
+

+

10 V
40
20
Ω
Ω
A
B
20
Ω
(+ 1 point)
20 V
+

40
40
Ω
Ω
A
B
Ω
40
Ω
A
B
0.5 A
40
(+ 1 point)
0.5 A
20
Ω
A
B
(+ 1 point)
Ω
+

A
B
10 V
20
(+ 1 point)
Part II:
Let’s investigate the two scenarios. In the case of a small resistance, say
R
=
Ω
, using the
Thevenin equivalent and voltage division we have that
v
R
=
20 +
10
≈
/
2 V
,
i
R
=
v
R
/
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 Spring '10
 VladoLubarda
 Thévenin's theorem, Voltage source, R Vin R

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