Download 2300 Exam 1 Spring 2003

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ECE 2300 – FINAL EXAM
December 8, 2003
1. This exam is closed book, closed notes. You may use one 8.5” x 11” crib
sheet, or its equivalent. You may use any calculator. Turn all cell phones or other
communications devices off.
2. Show all work on these pages. Show all work necessary to complete the
problem. If you go on to another page, indicate clearly where your work can
be found. A solution without the appropriate work shown will receive no credit.
Clearly indicate your answer (for example, by enclosing it in a box).
3. Show all units in solutions, intermediate results, and figures. Units in the exam
will be included between square brackets.
4. Use appropriate notation in all places. Be sure to make a clear distinction
between time domain and phasor domain quantities.
4. Do not use red ink. Do not use red pencil.
5. You will have 180 minutes to work on this exam.
1. ________________/1
2. ________________/5
3. ________________/17
4. ________________/13
5. ________________/15
6. ________________/20
7. ________________/15
8. ________________/15
Total = 101
ECE 2300 Final Exam – December 8, 2003 – Page 2
1) {1 Point} On the front page, circle your class time.
Room for extra work
ECE 2300 Final Exam – December 8, 2003 – Page 3
2) {5 Points} For the circuit shown calculate the power delivered to the circuit by
the independent voltage source.
R1= 20[]
R2 =
40[]
R6 =
30[]
+
-
R7 =
50[]
R3 =
60[]
vS =
120[V]
R8 =
70[]
R5 = 100[]
R4 =
80[]
ECE 2300 Final Exam – December 8, 2003 – Page 4
3) {17 Points} Use the node-voltage method to write a complete set of equations
that could be used to solve the circuit shown. Do not simplify the circuit. Do not
attempt to solve the equations. Define all node voltages.
30vX
- +
20[V]
vX
22[V]
3[]
+
-
-
24[A]
+
31iX
2[]
-
++
vW
+
7[]
iX
iQ
4[]
21[V]
5[]
6[]
34[]iQ +
23[V]
+
32[S]vW
9[]
10[]
-
13[]
12[]
11[]
ECE 2300 Final Exam – December 8, 2003 – Page 5
4) {13 Points} For the circuit shown find the Thévenin equivalent circuit with
respect to resistor R4. Draw this Thévenin equivalent. On the diagram that you
draw, show the values of the Thévenin voltage and resistance, indicate the
reference polarity for the Thévenin voltage, and label the locations of terminals a
and b.
vS2=
200[V]
iS1=
-0.1[S]vX
R1= 10[]
R2= 20[]
+
a
vS1=
100[V]
+
vY
+
+
iS2=
5[A]
vX
R4=
40[]
R3=
30[]
b
iS3=
1[S]vY
ECE 2300 Final Exam – December 8, 2003 – Page 6
5) {15 Points} Before t = 0 the circuit shown in Figure 1 had iS(t) = 0, and the
switch closed, for a long time. Then, at t = 0, the switch opened. The plot for iS(t)
for 0 < t < 7[ms] is shown in Figure 2.
a) Find the energy stored in the capacitor at t = 5[ms].
b) Find the energy stored in the inductor at t = 5[ms].
R1= 1[k]
t=0
+
C1=
50[F]
iS(t)
L1=
3.7[mH]
Figure 1
iS(t), [mA]
8
4
0
t, [ms]
1 2 3 4 5 6 7
Figure 2
-
vS1=
10[V]
ECE 2300 Final Exam – December 8, 2003 – Page 7
6) {20 Points} In the circuit shown the switch was in position a for a long time.
At t = 0 the switch is moved to position b, and at t = 0.1[s] is moved back to
position a, and remains there.
For the time intervals 0 < t < 0.1[s] and t > 0.1[s], find the numerical expressions
for the current iX flowing in resistance R1, and for the terminal voltage vY of the
resistance R4.
The reference polarity for iX and vY are shown on the circuit.
For each answer clearly specify for which time interval your answer is valid.
C1= 50[F]
R2= 40[k]
t = 0.1[s]
a
+
- vS1=
100[V]
R1=
60[k]
iX
b R3= 20[]
t=0
+
-
vS2=
200[V]
R4= 30[]
+
L1=
1.2[H]
vY
-
vS3= +
300[V]
ECE 2300 Final Exam – December 8, 2003 – Page 8
7) {15 Points} The circuit shown is in steady state. Calculate the numerical
expression for the inductor L2 terminal voltage, vL2(t).
R1= 200[]
L2=
0.5[H]
L1=
0.2[H]
+
R2=
500[]
iS(t)

vL2(t)

iS (t )  20cos 1000  rad  t  60  A 
 s


vS (t )  100sin 1000  rad  t  45  V 
 s
C1= 2[F]
vS(t)
+
-
ECE 2300 Final Exam – December 8, 2003 – Page 9
8) {15 Points} Four loads are connected in parallel across a voltage source that
has an rms voltage of 100[Vrms] and a frequency of 30[Hz]. The circuit is in
steady state.
The first load absorbs 1500[W] and delivers 2000[VAR].
The second load absorbs 900[VA] at 0.8 pf lagging.
The third load is purely resistive, and draws an rms current of 3[Arms].
The fourth load can be modeled as a 5[] resistor in series with a 2[mF] capacitor.
a) Find the average power delivered by the voltage source.
b) Find the reactive power delivered by the voltage source.
c) Find the power factor for the four loads in parallel.
ECE 2300 Final Exam – December 8, 2003 – Page 10
2) {5 Points} For the circuit shown calculate the power delivered to the circuit by
the independent voltage source.
R1= 20[]
R2 =
40[]
R6 =
30[]
+
-
R7 =
50[]
R3 =
60[]
vS =
120[V]
R8 =
70[]
R5 = 100[]
R4 =
80[]
ECE 2300 Final Exam – December 8, 2003 – Page 11
ECE 2300 Final Exam – December 8, 2003 – Page 12
3) {17 Points} Use the node-voltage method to write a complete set of equations
that could be used to solve the circuit shown. Do not simplify the circuit. Do not
attempt to solve the equations. Define all node voltages.
30vX
- +
20[V]
vX
22[V]
3[]
+
-
-
24[A]
+
31iX
2[]
-
++
vW
+
7[]
iX
iQ
4[]
21[V]
5[]
6[]
34[]iQ +
23[V]
+
32[S]vW
9[]
10[]
-
13[]
12[]
11[]
ECE 2300 Final Exam – December 8, 2003 – Page 13
ECE 2300 Final Exam – December 8, 2003 – Page 14
ECE 2300 Final Exam – December 8, 2003 – Page 15
4) {13 Points} For the circuit shown find the Thévenin equivalent circuit with
respect to resistor R4. Draw this Thévenin equivalent. On the diagram that you
draw, show the values of the Thévenin voltage and resistance, indicate the
reference polarity for the Thévenin voltage, and label the locations of terminals a
and b.
vS2=
200[V]
iS1=
-0.1[S]vX
R1= 10[]
R2= 20[]
+
a
vS1=
100[V]
+
vY
+
+
iS2=
5[A]
vX
R4=
40[]
R3=
30[]
b
iS3=
1[S]vY
ECE 2300 Final Exam – December 8, 2003 – Page 16
ECE 2300 Final Exam – December 8, 2003 – Page 17
ECE 2300 Final Exam – December 8, 2003 – Page 18
ECE 2300 Final Exam – December 8, 2003 – Page 19
5) {15 Points} Before t = 0 the circuit shown in Figure 1 had iS(t) = 0, and the
switch closed, for a long time. Then, at t = 0, the switch opened. The plot for iS(t)
for 0 < t < 7[ms] is shown in Figure 2.
c) Find the energy stored in the capacitor at t = 5[ms].
d) Find the energy stored in the inductor at t = 5[ms].
R1= 1[k]
t=0
+
C1=
50[F]
iS(t)
L1=
3.7[mH]
Figure 1
iS(t), [mA]
8
4
0
t, [ms]
1 2 3 4 5 6 7
Figure 2
-
vS1=
10[V]
ECE 2300 Final Exam – December 8, 2003 – Page 20
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ECE 2300 Final Exam – December 8, 2003 – Page 22
ECE 2300 Final Exam – December 8, 2003 – Page 23
6) {20 Points} In the circuit shown the switch was in position a for a long time.
At t = 0 the switch is moved to position b, and at t = 0.1[s] is moved back to
position a, and remains there.
For the time intervals 0 < t < 0.1[s] and t > 0.1[s], find the numerical expressions
for the current iX flowing in resistance R1, and for the terminal voltage vY of the
resistance R4.
The reference polarity for iX and vY are shown on the circuit.
For each answer clearly specify for which time interval your answer is valid.
C1= 50[F]
R2= 40[k]
t = 0.1[s]
a
+
- vS1=
100[V]
R1=
60[k]
iX
b R3= 20[]
t=0
+
-
vS2=
200[V]
R4= 30[]
+
L1=
1.2[H]
vY
-
vS3= +
300[V]
ECE 2300 Final Exam – December 8, 2003 – Page 24
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ECE 2300 Final Exam – December 8, 2003 – Page 31
7) {15 Points} The circuit shown is in steady state. Calculate the numerical
expression for the inductor L2 terminal voltage, vL2(t).
R1= 200[]
L2=
0.5[H]
L1=
0.2[H]
+
R2=
500[]
iS(t)

vL2(t)

iS (t )  20cos 1000  rad  t  60  A 
 s


vS (t )  100sin 1000  rad  t  45  V 
 s
C1= 2[F]
vS(t)
+
-
ECE 2300 Final Exam – December 8, 2003 – Page 32
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ECE 2300 Final Exam – December 8, 2003 – Page 34
ECE 2300 Final Exam – December 8, 2003 – Page 35
8) {15 Points} Four loads are connected in parallel across a voltage source that
has an rms voltage of 100[Vrms] and a frequency of 30[Hz]. The circuit is in
steady state.
The first load absorbs 1500[W] and delivers 2000[VAR].
The second load absorbs 900[VA] at 0.8 pf lagging.
The third load is purely resistive, and draws an rms current of 3[Arms].
The fourth load can be modeled as a 5[] resistor in series with a 2[mF] capacitor.
d) Find the average power delivered by the voltage source.
e) Find the reactive power delivered by the voltage source.
f) Find the power factor for the four loads in parallel.
ECE 2300 Final Exam – December 8, 2003 – Page 36
ECE 2300 Final Exam – December 8, 2003 – Page 37
ECE 2300 Final Exam – December 8, 2003 – Page 38