2017 Test

Student Number: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Workshop Day and Time: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
THE UNIVERSITY OF MELBOURNE
Midsemester Test
8th September 2017
Department of Electrical and Electronic Engineering

ELEN20005 Foundations of Electrical Networks
This paper has 11 pages (not including the separate formula sheet )
The test is printed single-sided.
Authorised materials:
Only Casio FX-82 (any suffix) or Casio FX-100 (any suffix) electronic calculators are permitted.
Instruction to students:
Attempt ALL questions.
The questions carry weight in proportion to the marks in brackets after the question numbers.
These marks total 100 marks. You must show your work in order to receive credit!
Write your WORKSHOP DAY and TIME at the top right where indicated.
Use the back of the previous page if you need more space for writing your work.
For examiners’ use only.
Q1 Q2 Q3 Q4 Q5 TOTAL
(/25) (/20) (/24) (/24) (/7) (/100)
ELEN20005 Foundations of Electrical Networks, 8th September 2017
Question 1: (25 marks = 10 + 6 + 3 + 6 marks)

Consider the breadboard circuit shown below with five resistors. Channel 1 of the DC power supply
is connected as labeled and set to a DC voltage of 12 V.
You are given that all five resistors are 300 Ω.
(a) Draw the equivalent circuit schematic of the breadboard circuit.
(b) A voltmeter is connected to the circuit as follows: The + terminal is connected at point A and
the − terminal at point B. Estimate the reading that the voltmeter will give. Show all of your work.
2
Question 1 (Continued)
(c) Explain the steps you would take to connect an ammeter with the breadboard circuit to measure
the current through R2 in the direction from its top terminal to its bottom.
The breadboard circuit is copied below, and you should add labels to this image to support your
explanation.
(d) The DC power supply voltage has now been changed to an unknown voltage. An ammeter is
then connected to the circuit as follows: The + terminal is connected at point C and the − terminal
at point A. The reading on the ammeter is −8.666 mA. Determine the source voltage applied to the
circuit. Show all of your work.
3
Question 2 (20 marks = 10 + 10 marks)

(a) Consider the circuit shown below. Apply only node voltage analysis (NVA) to this circuit to
generate a system of equations where the variables are all node voltages in the circuit. Be sure to
add all necessary labeling on the circuit below.
Write your equations in the box provided below and label what each equation represents (e.g.,
Node 1, etc.). Do NOT simplify your equations. Do NOT put them into standard form. Do NOT
solve your system of equations.
2A
5Ω
+
=
+
=
40 Ω
4
(b) Consider the circuit shown below. Apply only mesh current analysis (MCA) to this circuit
to generate a system of equations where the variables are all mesh currents in the circuit. The three
mesh currents have been labeled for you already on the circuit below.
Write your equations in the box provided below and label what each equation represents (e.g.,
Mesh 1, etc.). Do NOT simplify your equations. Do NOT put them into standard form. Do NOT
solve your system of equations.
5Ω
+=
i2
(4 A/V) vx
10 Ω
+ vx _
40 Ω 2A
i1 i3
5
Question 3 (24 marks = 6 + 6 + 12 marks)

(a) Find and draw the Thévenin equivalent network at the output terminals for the below circuit.
Show all of your work.
40 Ω 15 Ω
a
+
2A 10 Ω
_
b
(b) Consider the below circuit containing a diode with the current-voltage characteristic plot shown
in the below right. Find iD and vD for this circuit. Show all work that supports your answer.
iD
iD (Amps)
+
120 mA 25 Ω vD
_
vD (Volts)
6
(c) A black box with output terminals a and b is known to be a linear circuit containing only resistors
and sources. Two measurements are made with the black box in hopes to determine its Thévenin
equivalent.
• Measurement #1: An ideal ammeter (AM) is connected directly to the output terminals as
shown below. The reading on the ammeter shows 50 mA.
• Measurement #2: A resistor R = 400 Ω is connected to the output terminals and an ideal
voltmeter (VM) is used to read the voltage across the resistor. The reading on the voltmeter
shows 12 V.
“Black Box” “Black Box”

a a
Linear circuit of
+ Linear circuit of
+
sources and AM sources and R VM
resistances _ resistances _
b b
Find and draw the Thévenin equivalent circuit for the block box at its output terminals.
Show all of your work and reasoning.
7
Question 4 (24 marks = 12 + 4 + 8 marks)
Consider the above circuit at sinusoidal steady state. You are given the impedances of the four passive
elements in the circuit, but the sources voltage magnitude, frequency and phase are unknown.
(a) Find numerical values for the resistive and reactive components of Ztotal , which is the impedance
seen by the sinusoidal voltage source.
8
Question 4 (Continued) An oscilloscope is used to measure vC(t) , the voltage signal across the
capacitor. The oscilloscope settings were VOLTS/DIV = 500 mV and SEC/DIV = 1 μs. Shown
below is the resulting screen capture at steady state.
(b) Estimate the angular frequency ω of the sinusoidal source.
(c) Sketch a plot of vR(t) directly onto the scope plot above as if both vR(t) and vC(t) were captured
simultaneously on the scope. Briefly explain your plot using reasoning and/or maths. Unjustified
plots will be considered guesses and receive zero marks.
9
Question 4 (Continued) Here is a copy of the oscilloscope figure in case you need to redo the plot
for (c) because you didnt bring a pencil! (Bring one for the final exam though!)
10
Question 5 (7 marks)
The below circuit contains a Zener diode that has a strict requirement that its power cannot exceed
6 mW without risk to the diode being burnt out and no longer usable. The diode is modeled by the
simple piecewise-linear diode model shown below, where vD and iD are defined using the standard
reference labeling for a diode (as discussed in lecture).
Find and write a condition on the values of vs , the input voltage, that results in the the diode
exceeding the 6 mW power restriction. Show all of your work.
END OF MID-TEST
11
ELEN20005 Foundations of Electrical Networks (FoEN)
Formulae for the Mid-Semester Test
1. Current, Voltage, Power, Energy

t1
dq dw dw
i(t) = , v(t) = , p(t) = = v(t)i(t), w= p(t) dt
dt dq dt t0
2. Ohm’s Law and Kirchoff ’s Laws

N
M
v = iR, in = 0, vn = 0
n=1 m=1
3. Resistive DC circuits
v2 1
p = vi = = i2 R Req = R1 + R2 + R3 (series) Req = 1 1 1 (parallel)
R R1
+ R2
+ R3
1
G= (conductance in Siemens)
R
4. Thévenin and Norton Equivalent dc Circuits

voc
vT = voc , RT = , iN = isc , RL = Rt (max power transfer)
isc
5. Capacitors
dv 1
i(t) = C , q(t) = Cv(t), w(t) = Cv 2 (t), τ = RC,
dt 2
1
Ceq = C1 + C2 + C3 (parallel) Ceq = 1 1 1 (series)
C1
+ C2
+ C3
6. Inductors
di 1
v(t) = L , w(t) = Li2 (t), τ = L/R
dt 2
1
Leq = L1 + L2 + L3 (series) Leq = 1 1 1 (parallel)
L1
+ L2
+ L3
12
7. First Order differential equations

dx
+ a0 x = a1 has general solution x(t) = K1 est + K2
dt
8. Phasors
v(t) = Vm cos(ωt + θ) ⇐⇒ V = Vm θ = Vm ejθ
i(t) = Im cos(ωt + θ) ⇐⇒ I = Im θ = Im ejθ
9. Impedances
1 j 1
ZR = R, ZC = =− = −90◦ , ZL = jωL = ωL 90◦
jωC ωC ωC
V 1
V = IZ Z= Y = (admittance)
I Z
10. Thévenin and Norton Equivalent ac Circuits

Voc
VT = Voc , Zt = , IN = Isc
Isc
11. Some Useful Sinusoid Identities
sin(z) = cos(z − 90◦ ), − cos(z) = cos(z ± 180◦ ),
12. 2 by 2 matrix inverse

a b 1 d −b
=
c d ad − bc −c a
13. Resistor Colour Codes
Black = 0 Brown = 1 Red = 2 Orange = 3 Yellow = 4

Green = 5 Blue = 6 Purple = 7 Grey = 8 White = 9
Silver = 10% Gold = 5 % Red = 2% Brown = 1%
13

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Student Number: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Workshop Day and Time: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

THE UNIVERSITY OF MELBOURNE

Department of Electrical and Electronic Engineering

For examiners’ use only.

Question 1: (25 marks = 10 + 6 + 3 + 6 marks)

You are given that all ﬁve resistors are 300 Ω.

(a) Draw the equivalent circuit schematic of the breadboard circuit.

Question 2 (20 marks = 10 + 10 marks)

Question 3 (24 marks = 6 + 6 + 12 marks)

“Black Box” “Black Box”

Question 4 (24 marks = 12 + 4 + 8 marks)

(b) Estimate the angular frequency ω of the sinusoidal source.

ELEN20005 Foundations of Electrical Networks (FoEN)

Formulae for the Mid-Semester Test

1. Current, Voltage, Power, Energy

2. Ohm’s Law and Kirchoﬀ ’s Laws

4. Thévenin and Norton Equivalent dc Circuits

7. First Order diﬀerential equations

i(t) = Im cos(ωt + θ) ⇐⇒ I = Im θ = Im ejθ

10. Thévenin and Norton Equivalent ac Circuits

11. Some Useful Sinusoid Identities

sin(z) = cos(z − 90◦ ), − cos(z) = cos(z ± 180◦ ),

12. 2 by 2 matrix inverse  

13. Resistor Colour Codes

Black = 0 Brown = 1 Red = 2 Orange = 3 Yellow = 4

Silver = 10% Gold = 5 % Red = 2% Brown = 1%

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12. 2 by 2 matrix inverse