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ECE 2300 -- Exam #1
October 10, 2009
Keep this exam closed until you
are told to begin.
1. This exam is closed book, closed notes. You may use one 8.5” x 11”
crib sheet, or its equivalent.
2. Show all work on these pages. Show all work necessary to complete
the problem. A solution without the appropriate work shown will receive no
credit. A solution that is not given in a reasonable order will lose credit.
Clearly indicate your answer (for example by enclosing it in a box).
3. It is assumed that your work will begin on the same page as the
problem statement. If you choose to begin your work on another page, you
must indicate this on the page with the problem statement, with a clear
indication of where the work can be found. If your work continues on to
another page, indicate clearly where your work can be found. Failure
to indicate this clearly will result in a loss of credit.
4. Show all units in solutions, intermediate results, and figures. Units in
the exam will be included between square brackets.
5. Do not use red ink. Do not use red pencil.
6. You will have 90 minutes to work on this exam.
1. ________________/30
2. ________________/30
3. ________________/20
4. ________________/30
Total = 110
ECE 2300 Exam 1 – October 10, 2009 – Page 2
Room for extra work
ECE 2300 Exam 1 – October 10, 2009 – Page 3
1. {30 Points} A device can be modeled as a current source in parallel with a
resistance. The device is shown in Figure 1. When the device is left by itself, it
has a voltage at a with respect to b of 5.310[V].
Three identical versions of this device are connected in parallel, and
connected to a voltmeter, as shown in Figure 2.
The voltmeter has a resistance of 20[k], and a full scale reading of
10[V]. Stated in a different way, the voltmeter can read negative and positive
voltages in the range from -10[V] to +10[V]. In the connection shown in Figure 2,
the voltage reading is vM = 5.516[V].
Find all the possible readings of the voltmeter when the voltmeter described
is connected to just one of these devices. Please give your answer(s) with at least
4 significant figures.
a
a
a
a
+
vM
Device
Device
Device
Device
b
b
b
b
Figure 1
Figure 2
Voltmeter
-
ECE 2300 Exam 1 – October 10, 2009 – Page 4
Room for extra work
ECE 2300 Exam 1 – October 10, 2009 – Page 5
2. {30 Points} Use the circuit shown below to solve this problem. Find the power
delivered by the 10[V] voltage source. Show your steps in some clear fashion.
You are strongly encouraged to redraw the diagram as needed to make your work
more clear.
R7 = 4.7[k]
10[V]
+
iX
-
R1 =
1.7[k]
5iX
R2 =
2.2[k]
R3 =
6.8[k]
R6 = 1.9[k]
R8 =
3.5[k]
R4 =
2.7[k]
R9 =
7.5[k]
R10 =
8.2[k]
R5 =
8.9[k]
R11 =
22[k]
R12 =
39[k]
R13 = 33[k]
R14 =
47[k]
R15 =
56[k]
ECE 2300 Exam 1 – October 10, 2009 – Page 6
Room for extra work
ECE 2300 Exam 1 – October 10, 2009 – Page 7
3. {20 Points} It is given that a AA battery can be modeled as a voltage source in
series with a resistor.
a) Assume that you have n AA batteries connected in series, where the polarity
of each battery is arbitrary. Assume that the series combination of batteries
is connected to a 10[k] resistor. Determine the number of possible
solutions for the power absorbed by the 10[k] resistor, as a function of the
number of batteries, n. (Hint: you may wish to consider the cases of n
being odd and even separately.)
b) Assume that you have n AA batteries connected in parallel, where the
polarity of each battery is arbitrary. Assume that the parallel combination of
batteries is connected to a 10[k] resistor. Determine the number of
possible solutions for the power absorbed by the 10[k] resistor, as a
function of the number of batteries, n.
ECE 2300 Exam 1 – October 10, 2009 – Page 8
Room for extra work
ECE 2300 Exam 1 – October 10, 2009 – Page 9
4. {30 Points} For the given circuit, use the Node-Voltage method to write a
complete set of independent equations that could be used to solve this circuit. Do
not simplify the circuit. Do not attempt to solve or simplify your equations.
Define all variables.
6[S]vX
2[]
-
25[A]
+
22[V]
3[]
4[]
13[]
+
8[]
vW
-
14[]
vW
7[]
iX
20[V]
10[]
11[]
+
9[]
+
-
12[]
+
21[]
5[]iX
16[]
vX
+
26[A]
21[V]
[]iQ
24[A]
17[]
-
-
+
-
-
+
+
27[V]
13[]
iQ
-
29[A]
+
15[]
23[V]
ECE 2300 Exam 1 – October 10, 2009 – Page 10
Solutions:
1. {30 Points} A device can be modeled as a current source in parallel with a
resistance. The device is shown in Figure 1. When the device is left by itself, it
has a voltage at a with respect to b of 5.310[V].
Three identical versions of this device are connected in parallel, and
connected to a voltmeter, as shown in Figure 2.
The voltmeter has a resistance of 20[k], and a full scale reading of
10[V]. Stated in a different way, the voltmeter can read negative and positive
voltages in the range from -10[V] to +10[V]. In the connection shown in Figure 2,
the voltage reading is vM = 5.516[V].
Find all the possible readings of the voltmeter when the voltmeter described
is connected to just one of these devices. Please give your answer(s) with at least
4 significant figures.
a
a
a
a
+
vM
Device
Device
Device
Device
b
b
b
b
Figure 1
Figure 2
Voltmeter
-
ECE 2300 Exam 1 – October 10, 2009 – Page 11
ECE 2300 Exam 1 – October 10, 2009 – Page 12
ECE 2300 Exam 1 – October 10, 2009 – Page 13
2. {30 Points} Use the circuit shown below to solve this problem. Find the power
delivered by the 10[V] voltage source. Show your steps in some clear fashion.
You are strongly encouraged to redraw the diagram as needed to make your work
more clear.
ECE 2300 Exam 1 – October 10, 2009 – Page 14
ECE 2300 Exam 1 – October 10, 2009 – Page 15
3. {20 Points} It is given that a AA battery can be modeled as a voltage source in
series with a resistor.
a) Assume that you have n AA batteries connected in series, where the polarity
of each battery is arbitrary. Assume that the series combination of batteries
is connected to a 10[k] resistor. Determine the number of possible
solutions for the power absorbed by the 10[k] resistor, as a function of the
number of batteries, n. (Hint: you may wish to consider the cases of n
being odd and even separately.)
b) Assume that you have n AA batteries connected in parallel, where the
polarity of each battery is arbitrary. Assume that the parallel combination of
batteries is connected to a 10[k] resistor. Determine the number of
possible solutions for the power absorbed by the 10[k] resistor, as a
function of the number of batteries, n.
ECE 2300 Exam 1 – October 10, 2009 – Page 16
ECE 2300 Exam 1 – October 10, 2009 – Page 17
4. {30 Points} For the given circuit, use the Node-Voltage method to write a
complete set of independent equations that could be used to solve this circuit. Do
not simplify the circuit. Do not attempt to solve or simplify your equations.
Define all variables.
ECE 2300 Exam 1 – October 10, 2009 – Page 18