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THE UNIVERSITY OF MELBOURNE
Semester 1 Assessment
June 2020
Department of Electrical and Electronic Engineering
ELEN20005 FOUNDATIONS OF ELECTRICAL NETWORKS
Writing Time: 180 minutes
Reading time: 15 minutes
Scan and upload time: 30 minutes
This examination paper has 8 pages.
Instruction to students:
Attempt ALL questions. Write your test answers using pens and A4 paper. Tablets
and other electronic software may not be used for writing your test answers. Start each
question on a new sheet of paper. Only write on one side of each sheet of paper.
The questions carry weight in proportion to the marks in brackets after the question num-
bers. These marks total 100 marks. You must show your work in order to receive credit!
The format of the test is open book, meaning that students may have unlimited access to
printed or online materials.
Students may use any computational software for numerical calculations, however the marking
scheme will require that students show the details of their calculations as if a CASIO FX-82
or CASIO FX-100 calculator had been used.
Your work must be scanned and uploaded to CANVAS as a single pdf file. This must be done
by 6.45 p.m. Late submissions will not be marked
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 1 (10 marks)
(a) [7 marks] In the following circuit, use Node Voltage Analysis to find the node voltages
v1 and v2. Hence find the current ix.
2A
SQ IOQ
2A 20Q IA
-
(b) [3 marks] Is the 1 A current source generating or consuming power? Justify your answer.
Question 2 (12 marks)
Consider the following circuit, with output terminals a and b.
(a) [8 marks] Find the The´venin equivalent circuit.
(b) [4 marks] Now assume a 20 Ω load resistor is attached across the output terminals of the
circuit. Find the power of the 2 A current source. It is generating or consuming power?
Page 2 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 3 (16 marks)
In the circuit below, a sinusoidal voltage source VS(t) = Vm cos(ωt) V is applied to a load
consisting of an inductance L, resistance R and capacitance C, connected in series. VR(t) is
the resistor voltage.
PSfrag replacements VS
i L
C
R
+
−
+
VR
_
(a) [2 marks] Obtain an expression for the total impedance Z in terms of R, L, C and ω.
(b) [2 marks] Use your answer to part (a) to obtain an expression for the transfer function
HR(ω) that is defined to be the ratio of the resistor voltage phasor VR to the source
voltage phasor VS:
HR(ω) =
VR
VS
In the following questions, assume that L = 2 H, R = 18 Ω and C = 50 mF .
(c) [4 marks] Find the value of ω that will ensure the source voltage and resistor voltage
are in phase.
(d) [2 marks] Assume the magnitude of the source voltage is Vm = 5 V . For your value of
ω in part (c), what is VR(t)?
(e) [4 marks] Find a value of ω that will ensure the source voltage and resistor voltage have
a phase difference of 45◦.
(f) [2 marks] For your value of ω in part (e), explain whether the resistor voltage leads or
lags the source voltage.
Page 3 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 4 (12 marks)
In the following dc circuit, the switch has been open for a long time. The switch is closed at
t = 0 s.
+
−
3 kΩ3 kΩ 6 kΩ
2 H
100 µF
24 V
i1 i2
t = 0
+
v1
-
(a) [2 marks] Determine the current i1(0
−) immediately before the switch is closed.
(b) [2 marks] Determine the capacitor voltage v1(0
−) immediately before the switch is closed.
(c) [2 marks] Determine the current i1(0
+) immediately after the switch is closed.
(d) [2 marks] Determine the capacitor voltage v1(0
+) immediately after the switch is closed.
(e) [2 marks] Determine i1(∞), the steady state value for i1 after the switch has been closed
for a long time.
(f) [2 marks] Determine v1(∞), the steady state value the capacitor voltage after the switch
has been closed for a long time.
Explain and justify your answers by drawing appropriate circuit diagrams and by referring to
known dc transient and steady-state behaviour of capacitors and inductors.
Page 4 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 5 (14 marks)
In the following circuit a sinusoidal source voltage V has rms amplitude Vrms, phase angle
θv = 0
◦, and angular frequency ω. The load consists of a resistor R and capacitor C connected
in series. It consumes real power P with leading power factor PF%.
Load+−
L
I
V
Assume initially that the inductor is not connected to the circuit.
(a) [6 marks] Write down nested formulae for the following:
(i) The power angle θ, in degrees;
(ii) The rms current Irms;
(iii) The reactive power Q of the load;
(iv) R and X, the real and complex components of the load impedance Z = R + jX;
(v) The capacitor C;
(vi) The phasor current I.
Note: By nested formulae we mean that the variables used in each formula can only
include any variables that have been previously defined. Thus θ may be defined in terms
of Vrms, P , ω, and PF, while Irms may be defined in terms of Vrms, P , ω, PF and θ, etc.
Now assume Vrms = 1000 V rms, ω = 1000 rad/s, P = 4000 W and PF = 50%.
(b) [3 marks] If the inductor is added to the load in parallel as shown, find the inductor
value that will yield a load power factor of 100%.
(c) [5 marks] Find the range of inductor values that will yield a load power factor of 90 %
or better. State which inductor values will yield an inductive load and which will give a
capacitive load.
Page 5 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 6 (12 marks)
A balanced Wye-Delta three-phase power circuit has line-to-neutral source voltages of 220 V
rms. The source angular frequency is 1000 rad/s, and the source voltages follow a positive phase
sequence. The load impedances each consist of a 30 Ω resistor in series with a 5 mH inductor.
The line impedances can be modeled as a 1 Ω resistor in series with a 0.5 mH inductor.
(a) [4 marks] Find the line current phasor IbB and load current phasor IBC . Support your
calculations with an appropriate circuit diagram.
(b) [3 marks] Find the real and reactive power of the Wye source.
(c) [3 marks] Find the total real and reactive power of the line impedances, and the real
and reactive power consumed by the Delta load.
(d) [2 marks] Confirm that your answers in parts (b) and (c) are consistent with the con-
servation of energy.
Question 7 (8 marks)
This question has been removed as it is no longer part of FoEN.
Page 6 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 8 (6 marks)
Page 7 of 8
This question has been removed as it is no longer
part of FoEN.
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 9 (10 marks)
The diode in the following circuit has a simple piecewise linear current-voltage relationship
with a threshold value vf = 0.6 V . The dc battery has a fixed voltage of 3.4 V . The variable
resistor RL can take values in the range [0, 100 Ω]. The constant input voltage is 8 V .
PSfrag replacements
8 V
iD
v1
50 Ω
RL
3.4 V
+
+
−
−
(a) [4 marks] What is the smallest value of RL for which the diode is on? Justify your
answer.
(b) [6 marks] Let iD be the current through the diode. Express iD in terms of RL and hence
plot the graph of iD against RL, for RL in the range [0, 100 Ω].
END OF EXAMINATION
Page 8 of 8
Semester 1 Assessment
June 2020
Department of Electrical and Electronic Engineering
ELEN20005 FOUNDATIONS OF ELECTRICAL NETWORKS
Writing Time: 180 minutes
Reading time: 15 minutes
Scan and upload time: 30 minutes
This examination paper has 8 pages.
Instruction to students:
Attempt ALL questions. Write your test answers using pens and A4 paper. Tablets
and other electronic software may not be used for writing your test answers. Start each
question on a new sheet of paper. Only write on one side of each sheet of paper.
The questions carry weight in proportion to the marks in brackets after the question num-
bers. These marks total 100 marks. You must show your work in order to receive credit!
The format of the test is open book, meaning that students may have unlimited access to
printed or online materials.
Students may use any computational software for numerical calculations, however the marking
scheme will require that students show the details of their calculations as if a CASIO FX-82
or CASIO FX-100 calculator had been used.
Your work must be scanned and uploaded to CANVAS as a single pdf file. This must be done
by 6.45 p.m. Late submissions will not be marked
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 1 (10 marks)
(a) [7 marks] In the following circuit, use Node Voltage Analysis to find the node voltages
v1 and v2. Hence find the current ix.
2A
SQ IOQ
2A 20Q IA
-
(b) [3 marks] Is the 1 A current source generating or consuming power? Justify your answer.
Question 2 (12 marks)
Consider the following circuit, with output terminals a and b.
(a) [8 marks] Find the The´venin equivalent circuit.
(b) [4 marks] Now assume a 20 Ω load resistor is attached across the output terminals of the
circuit. Find the power of the 2 A current source. It is generating or consuming power?
Page 2 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 3 (16 marks)
In the circuit below, a sinusoidal voltage source VS(t) = Vm cos(ωt) V is applied to a load
consisting of an inductance L, resistance R and capacitance C, connected in series. VR(t) is
the resistor voltage.
PSfrag replacements VS
i L
C
R
+
−
+
VR
_
(a) [2 marks] Obtain an expression for the total impedance Z in terms of R, L, C and ω.
(b) [2 marks] Use your answer to part (a) to obtain an expression for the transfer function
HR(ω) that is defined to be the ratio of the resistor voltage phasor VR to the source
voltage phasor VS:
HR(ω) =
VR
VS
In the following questions, assume that L = 2 H, R = 18 Ω and C = 50 mF .
(c) [4 marks] Find the value of ω that will ensure the source voltage and resistor voltage
are in phase.
(d) [2 marks] Assume the magnitude of the source voltage is Vm = 5 V . For your value of
ω in part (c), what is VR(t)?
(e) [4 marks] Find a value of ω that will ensure the source voltage and resistor voltage have
a phase difference of 45◦.
(f) [2 marks] For your value of ω in part (e), explain whether the resistor voltage leads or
lags the source voltage.
Page 3 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 4 (12 marks)
In the following dc circuit, the switch has been open for a long time. The switch is closed at
t = 0 s.
+
−
3 kΩ3 kΩ 6 kΩ
2 H
100 µF
24 V
i1 i2
t = 0
+
v1
-
(a) [2 marks] Determine the current i1(0
−) immediately before the switch is closed.
(b) [2 marks] Determine the capacitor voltage v1(0
−) immediately before the switch is closed.
(c) [2 marks] Determine the current i1(0
+) immediately after the switch is closed.
(d) [2 marks] Determine the capacitor voltage v1(0
+) immediately after the switch is closed.
(e) [2 marks] Determine i1(∞), the steady state value for i1 after the switch has been closed
for a long time.
(f) [2 marks] Determine v1(∞), the steady state value the capacitor voltage after the switch
has been closed for a long time.
Explain and justify your answers by drawing appropriate circuit diagrams and by referring to
known dc transient and steady-state behaviour of capacitors and inductors.
Page 4 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 5 (14 marks)
In the following circuit a sinusoidal source voltage V has rms amplitude Vrms, phase angle
θv = 0
◦, and angular frequency ω. The load consists of a resistor R and capacitor C connected
in series. It consumes real power P with leading power factor PF%.
Load+−
L
I
V
Assume initially that the inductor is not connected to the circuit.
(a) [6 marks] Write down nested formulae for the following:
(i) The power angle θ, in degrees;
(ii) The rms current Irms;
(iii) The reactive power Q of the load;
(iv) R and X, the real and complex components of the load impedance Z = R + jX;
(v) The capacitor C;
(vi) The phasor current I.
Note: By nested formulae we mean that the variables used in each formula can only
include any variables that have been previously defined. Thus θ may be defined in terms
of Vrms, P , ω, and PF, while Irms may be defined in terms of Vrms, P , ω, PF and θ, etc.
Now assume Vrms = 1000 V rms, ω = 1000 rad/s, P = 4000 W and PF = 50%.
(b) [3 marks] If the inductor is added to the load in parallel as shown, find the inductor
value that will yield a load power factor of 100%.
(c) [5 marks] Find the range of inductor values that will yield a load power factor of 90 %
or better. State which inductor values will yield an inductive load and which will give a
capacitive load.
Page 5 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 6 (12 marks)
A balanced Wye-Delta three-phase power circuit has line-to-neutral source voltages of 220 V
rms. The source angular frequency is 1000 rad/s, and the source voltages follow a positive phase
sequence. The load impedances each consist of a 30 Ω resistor in series with a 5 mH inductor.
The line impedances can be modeled as a 1 Ω resistor in series with a 0.5 mH inductor.
(a) [4 marks] Find the line current phasor IbB and load current phasor IBC . Support your
calculations with an appropriate circuit diagram.
(b) [3 marks] Find the real and reactive power of the Wye source.
(c) [3 marks] Find the total real and reactive power of the line impedances, and the real
and reactive power consumed by the Delta load.
(d) [2 marks] Confirm that your answers in parts (b) and (c) are consistent with the con-
servation of energy.
Question 7 (8 marks)
This question has been removed as it is no longer part of FoEN.
Page 6 of 8
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 8 (6 marks)
Page 7 of 8
This question has been removed as it is no longer
part of FoEN.
ELEN20005 Foundations of Electrical Networks Semester 1 Exam 2020
Question 9 (10 marks)
The diode in the following circuit has a simple piecewise linear current-voltage relationship
with a threshold value vf = 0.6 V . The dc battery has a fixed voltage of 3.4 V . The variable
resistor RL can take values in the range [0, 100 Ω]. The constant input voltage is 8 V .
PSfrag replacements
8 V
iD
v1
50 Ω
RL
3.4 V
+
+
−
−
(a) [4 marks] What is the smallest value of RL for which the diode is on? Justify your
answer.
(b) [6 marks] Let iD be the current through the diode. Express iD in terms of RL and hence
plot the graph of iD against RL, for RL in the range [0, 100 Ω].
END OF EXAMINATION
Page 8 of 8
