ELEN20005 Foundations of Electrical Networks 2021
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Midsemester Test
10th September 2021
Department of Electrical and Electronic Engineering
ELEN20005 Foundations of Electrical Networks
Question 1 (20 marks = 7 + 5 + 8 marks)
(a) Consider the breadboard circuit shown below with four resistors that is connected to a DC voltage source set to 9 V.
An ideal voltmeter is connected with the + terminal at point A and the - terminal at point B. You are given the following resistor values:
R2 = 500 Ω , R3 = 500 Ω , Other two resistors = 100 Ω each
Determine the reading on the voltmeter. SHOW ALL OF YOUR WORK, including a drawing of an equivalent circuit schematic of the breadboard circuit. You do not need to redraw the breadboard figure in your work.
Your work must support your answer. Answers without sufficient support will receive reduced or zero marks.
+ of voltage source
R2 R3
B
_ of voltage source A
(b) For the breadboard circuit in part (a) and all of the given information, determine the current flowing through the resistor R3 with the reference direction from top to bottom. Show your work.
(c) Consider the breadboard circuit shown below with six resistors that is connected to a DC voltage source with an unknown voltage Vs .
You are given that all six resistors have the value 200 Ω . Ignore the colour code on the resistors in the image.
An ideal ammeter is connected with the + terminal at point A and the - terminal at point B and gives a reading of -4.36 mA.
You are to do the following:
(i) Draw the equivalent schematic for this circuit (including the ammeter in you schematic). (ii) Determine the DC source voltage Vs .
Your work must support your answer. Answers without sufficient support will receive reduced or zero marks.
A
_ of Voltage Source
+ of Voltage Source
B
You do not need to redraw the above breadboard figure in your work.
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.
9 ⌦
6 ⌦
ia
30 V
(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 labelled 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.
6 ⌦
ia
Question 3 (20 marks = 10 + 10 marks)
(a) A black box with output terminals a and b is known to be a linear circuit containing only resistors and sources. In the hopes of determining the Th´evenin equivalent of the black box, two experiments are performed with a resistor connected across the output terminals as shown below. Measurement results are shown below the corresponding circuit experiment. Note that AM refers to an ideal ammeter and VM refers to an ideal voltmeter.
“Black Box”
Linear circuit of sources and resistances |
Measurement #1: VM reads 3.0 V
“Black Box”
Linear circuit of sources and resistances |
Measurement #2: AM reads 8.0 mA
Find and draw the Th´evenin equivalent circuit for the black box at its output terminals. Show all of your work and reasoning.
It is not required for you to redraw the above figures in your work.
(b) Consider the below circuit with output terminals a and b.
a
+
1〇〇 ⌦
2〇〇 ⌦
_
b
One resistor value is not given to you, but instead is labelled as R. Your answer may contain this R
variable, and any other calculations should be simplified as much as possible.
Find and draw the Th´evenin equivalent circuit at its output terminals. Show all of your work and reasoning.
You will need to copy the above circuit diagram
Question 4 (20 marks = 10 + 10 marks)
(a) Consider the below circuit with the voltage source v(t) that is expressed as follows:
, 5 V , t ≤ 0
( 3 V , t > 0
In other words, v(t) = 5 V for a very long time, i.e., t o (-与, 0], before it changes.
i(t)
+
100 mH
_
(i) Determine i(t) for t S 0. Sketch a rough plot.
(ii) Determine vL (t) for t S 0. Sketch a rough plot.
(b) Consider the below circuit with the DC voltage source with unknown voltage Vs and a switch. The element X in the circuit is a type of passive linear circuit element that we have studied this semester. The switch closes at time t = 0. Assume that device X has no stored energy before the switch is closed.
On the next page, a plot of the labelled current i(t) versus time t is given. Note that this current decays to 0 as t 2 与, but the plot is only up to time t = 0.018 seconds.
YOUR TASKS: (show all of your work)
(i) Determine the type of element X is. Briefly explain your reasoning.
(ii) Estimate the component value of X . State any specific data used from the plot.
(iii) Determine the value of the DC voltage source, i.e., determine Vs . Show your work.
S
t = 0
i(t)
2 k⌦
Question 5 (20 marks = 8 + 7 + 5 marks)
(a) Consider the below circuit with a zener diode (D1 ) that follows the simple-piecewise linear model (to the right of the circuit) where vD and iD are defined using the standard reference labelling (anode to cathode) for a diode as discussed in lecture.
1k⌦
D
-5 V
1 V
0D
Determine the power for the diode. Is the diode absorbing or supplying power in this circuit?
Show all of your work.
(b) Consider the below circuit which contains a zener diode (D1 ) that follows the same simple- piecewise linear model from part (a).
Determine the labelled current i in the circuit. Show all of your work.
NOTE: The value of the resistor R is not given to you, so your answer for this part may be a function of R.
1k⌦
7 V
R
(c) Consider the below circuit which contains a zener diode that follows the piecewise linear model shown to the right of the circuit, where vD and iD are defined using the standard reference labelling
(anode to cathode) for a diode as discussed in lecture.
Assume the capacitor has zero charge stored at time t = 0 − .
You are given the following circuit parameters:
● Vs = 8 V
● R1 = 400 Ω
● R2 = 150 Ω
● C = 1 µF
Determine the labelled current iR (t) in the circuit for t > 0. Show all of your work.
S
t = 0
iR (t)
R2
C
D
40 mA
-6 v -5 V
0D
1 V 2 V
-20 mA
2022-08-30