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

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

THE UNIVERSITY OF MELBOURNE

Midsemester Test
11th September 2018

Department of Electrical and Electronic Engineering

ELEN20005 Foundations of Electrical Networks

This paper has 10 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
(/21) (/20) (/24) (/20) (/15) (/100)
ELEN20005 Foundations of Electrical Networks, 11th September 2018

Question 1: (21 marks = 9 + 7 + 5 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. All five resistors have value 300 Ω.

(a) First, draw the equivalent circuit schematic of the breadboard circuit, then calculate the current
flowing out of +Ch1 of the power supply.

(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.

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ELEN20005 Foundations of Electrical Networks, 11th September 2018

Question 1 (Continued)

(c) Ignore the previous breadboard circuit and now consider the new breadboard circuit below.

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 150 Ω.

An ammeter is then connected to the circuit as follows: The + terminal is connected at point A and
the − terminal at point B. Estimate the reading that the ammeter will give. Show all of your work.

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ELEN20005 Foundations of Electrical Networks, 11th September 2018

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.

3ix

+
=
= +

ix

2A 10 ⌦

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ELEN20005 Foundations of Electrical Networks, 11th September 2018

Question 2 (Continued)

(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.

3ix

+
=
= +

ix

2A 10 ⌦

5
ELEN20005 Foundations of Electrical Networks, 11th September 2018

Problem 3: (24 marks = 16 + 8 marks)

(a) Consider the below circuit operating at steady state. The source voltage vs (t) = 8 cos (500t) V

Determine both vc (t) and i1 (t). Show all of your work.

vC (t)
+ _

200 µF
10 ⌦
vs (t) +
= 20 ⌦ i1 (t)

20 mH

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ELEN20005 Foundations of Electrical Networks, 11th September 2018

Question 3 (Continued)
(b) Consider the below capacitor along with a plot of its current i(t) versus time t. Assume this
capacitor is connected to some network, but that network is not being shown here for space reasons.
Further assume the top plate of the capacitor holds a net charge of zero at time t = 0.

i(t) (Amps)

1.5
i(t)
+
8
vC (t)
2 5 6 t (seconds)
_

Determine and list the time intervals when the capacitor is supplying energy to the network it is
connected to. You must show all of your work/reasoning that supports your answer. Unjustified
answers will not receive marks.

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ELEN20005 Foundations of Electrical Networks, 11th September 2018

Question 4 (20 marks = 9 + 11 marks)

(a) Find and draw the Thévenin equivalent network at the output terminals for the below circuit.
Show all of your work. 30 ⌦ 15 ⌦
a

8V +
= 10 ⌦

(b) 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. The measurement results are shown below the corresponding circuit experiment. Note
that AM refers to ammeter and VM refers to voltmeter.

“Black Box” 2 k⌦
“Black Box”
a a
Linear circuit of + Linear circuit of +
sources and AM sources and VM
resistances _ resistances _
b b

Measurement #1: AM reads 1 mA Measurement #2: VM reads 2.5 V

Find and draw the Thévenin equivalent circuit for the block box at its output terminals.
Show all of your work and reasoning.

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ELEN20005 Foundations of Electrical Networks, 11th September 2018

Problem 5: (15 marks = 5 + 5 + 5)

(a) Consider the circuit below that contains one diode that follows the simple piecewise-linear diode
model with Vf = 0.7 V. A plot of this diode model is shown below and to the right.

Determine vD and iD when (i) vs = −2 V , and (ii) vs = 1.5 V.

5 k⌦ iD

iD
+
vs + vD vD
= 0.7
_

(b) Now consider the modified circuit shown below where another resistor has been added. The diode
follows the same model as in part (a). Determine vD and iD when vs = 3 V.

5 k⌦

iD
+
vs + vD 1 k⌦
=
_

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ELEN20005 Foundations of Electrical Networks, 11th September 2018

Problem 5 (Continued)

ADVANCED
(c) The below circuit contains two Zener diodes, D1 and D2 , which both follow the simple piecewise-
linear model shown below. vD and iD are defined using the standard reference labelling (anode to
cathode) for a diode as discussed in lecture. You are given: R1 = 1 kΩ and R2 = 2 kΩ.

Assuming that the DC power supply vs can only take on values in the range of 0 V to +15 V, plot
v1 versus vs , and plot i versus vs . You must show your work that supports your plots.

D1 iD

R1
5V
vs + vD
=
+ 1V
D2 R2 v1
_

END OF MID-TEST

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