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VERSION 00000001 ELECTENG 101
ELECTRICAL AND ELECTRONIC ENGINEERING
Electrical and Digital Systems
(Time Allowed: TWO hours)
NOTE:
Answer ALL questions.
This exam is in TWO parts:
MULTIPLE CHOICE QUESTIONS (40 marks):
 20 questions, 2 marks per question
 Answers to be entered on the Teleform sheet provided
 Use a dark pencil to mark your answers in the answer boxes
 Do NOT cross out answers on the Teleform sheet – if you change your mind, you must
completely erase one answer before you choose another one
 If you spoil your sheet, ask the supervisor for a replacement
 There is only ONE correct answer per question
LONG ANSWER QUESTIONS (60 marks):
 4 questions, 15 marks per question
 You must show ALL working to obtain full credit for each solution
 Answers to be entered in the spaces provided in the detachable Answer Booklet
 If you believe you need further information than that provided, make some appropriate
engineering assumption(s), state them clearly, and continue with your answer
Before answering any questions, please fill in your name and I.D. on the provided Teleform sheet AND
on the detachable Answer Booklet.
Compare the exam Version number on the Teleform sheet supplied with the Version number above. If
they do not match, ask the exam supervisor for a new Teleform sheet.
For all questions requiring calculations of voltages or currents, you must clearly indicate their polarity
or direction, respectively.
A table of formulae and constants is provided in the Appendix on Page 15.
MULTIPLE CHOICE QUESTIONS
(Answers to be entered on the Teleform Sheet)
1. In the circuit shown, if the voltage at Node is 6 V, the
voltage at Node is
2 Ω
3 Ω
4 V
X
A
(a) −6 V
(b) 3 V
(c) 9 V
(d) 14 V
2. In the circuit shown, the current source
R
VS IS
(a) is supplying energy
(b) is receiving energy
(c) is neither supplying nor receiving energy
(d) could be supplying or receiving energy depending
on the circuit parameters
3. If the power absorbed by the 3 Ω resistor in the circuit
shown is 48 W, the resistance of the resistor is
3 Ω R6 A
(a) 4 3⁄ Ω
(b) 3 Ω
(c) 6 Ω
(d) 12 Ω
4. In the portion of the circuit shown, the value of the
voltage source ௌ is
2 Ω
VS
2 V 2 A
−2 V
2 A
(a) −2 V
(b) 2 V
(c) 4 V
(d) 6 V
5. The equivalent resistance of the resistive network shown,
as seen from terminals - is
6 Ω
2 Ω
3 Ω
a
b
(a) 0 Ω
(b) 1.5 Ω
(c) 2 Ω
(d) 6 Ω
6. For the circuit shown, when the switch is closed
(i.e., moved to Position ), what happens to the
total power delivered by the source?
R1
R2
R3
Is
A
(a) It will increase
(b) It will decrease
(c) It will remain unchanged
(d) Cannot say without the specific parameters
7. A strain gauge ௫() is attached to a structural beam and placed in a Wheatstone bridge
so that the output voltage ୭୳୲ can be used to track the strain of the beam. Which of the
following statements is true regarding the output voltage of this sensor circuit?
(a) ୭୳୲ is positively correlated to strain
Rx(ε) R1
R2 R3
voutIS
(b) ୭୳୲ is negatively correlated to strain
(c) ୭୳୲ is roughly independent of the strain
because the current through ௫() is inversely
proportional to the changes in ௫() and
thereby cancelling out its effect on ୭୳୲
(d) the correlation between ୭୳୲ and strain depends
on the other resistances as the current through
each branch also depends on their values
8. The equivalent circuit of an interconnection between a sensor, an amplifier, and a load
is shown. If the voltage across the load is 2.7 V, then the input resistance ௜௡ of the
amplifier is
(a) 834 Ω
(b) 27953 Ω
(c) 3311 Ω
(d) 108 Ω
9. The output voltage ௢௨௧ of the
amplifier circuit shown is
(a) 2.25 V
(b) 2.75 V
(c) 1.375 V
(d) 1.125 V
10. The decimal equivalent of the octal (base 8) number 233.14 is
(a) 155.1875
(b) 1240.1875 (c) 155.023438
(d) 1240.023438
11. The following program code is to be run on a microcontroller. The expected value
stored in the variable Z after the code is run is
(a) 366 uint8_t x = 139;
uint8_t y = 228;
uint8_t z = 0;
z = y+x;
(b) 367
(c) 112
(d) 111
12. A temperature sensor is connected to a microcontroller that has a 12-bit ADC with a
reference voltage of 3.3 V. When the voltage at the output of the temperature sensor is
2.121 V, the ADC will output a value with a decimal equivalent of
(a) 2633
(b) 2631
(c) 2482
(d) 2632
13. The output signal of a sensor varies over the range 0 V to 2.72 V. If this signal is to be
quantised by an ADC with a resolution of 340 mV, the minimum number of bits the
ADC must have is
(a) 3
(b) 4 (c) 8
(d) 10
14. The following short section of a program has been written to control a number of LEDs.
Which LED(s) will be ON after the code has run? (Assume all variables are declared
and all LEDs have been set up to be OFF by default.)
int a = 10;
int b = 5;
int c = 0;
if (a > b && b > 5) then {
digitalWrite(RED_LED,HIGH);
}
if (a > 5 && b < a) then {
digitalWrite(ORANGE_LED,HIGH);
}
if (a > 5 || b > 5) {
digitalWrite(GREEN_LED,HIGH);
}
(a) The red LED
(b) The green LED
(c) The orange LED
(d) All of the LEDs
15. Which of the following is a correct Boolean expression describing the ON/OFF state of
the LED as a function of the ON/OFF state of the switches , , , , and ?
(a) + + + +
(b) ⋅ ⋅ ⋅ ⋅
(c) ⋅ ⋅ ̅ ⋅ ഥ ⋅ ത
(d) + + ̅ + ഥ + ത
16. The RMS value of a constant voltage signal of () = 1 V is
(a) 1 √2⁄ V
(b) 1 V
(c) √2 V
(d) Undefined
17. The voltage across and current through a load is given by
() = 2 cos(250 − 30∘) V and () = 0.5 cos(250 + 330∘) A.
The power factor of the load is
(a) 0.5 leading
(b) 0.5 lagging (c) 1
(d) 0
18. A load connected to an AC supply develops 5 kVA of apparent power at a leading
power factor of 0.6. The reactive power of the load is
(a) −4 kVAR
(b) 3 kVAR
(c) 4 kVAR
(d) 6.25 kVAR
19. In a step-up transformer, the primary current is
(a) higher than the secondary current
(b) lower than the secondary current
(c) equal to the secondary current
(d) always zero
20. Three-phase electricity is delivered to a factory 7 km from a distribution company. The
factory receives a total of 2000 kW of power at a voltage of 10.98 kV (rms) per phase.
If the transmission cable in each phase has a resistance of 1.8 Ω per 10 km, then the
total power lost in the cables of this three-phase system is
(a) 4.645 W
(b) 13.93 W (c) 4.645 kW
(d) 13.93 kW
21. A lighting system with an equivalent input resistance of ௅ = 2 Ω is powered by a
supply circuit as shown in Fig. 21.
4 Ω
5 Ω
3 A
6 V
2 Ω
Lighting System
vL
a
b
Supply Circuit
(1)
(2)
(3)
RL
Fig. 21: An electrical lighting system.
(a) There are three nodes in the circuit of Fig. 21 labelled (1), (2), and (3).
Choose one of these nodes as ground and write down the node-voltage equation(s)
necessary to determine the voltage ௅ across the lighting system.
Note: You do NOT need to solve the equation(s). [4 marks]
(b) (i) By means of superposition, determine the contribution and its polarity made
by the 3 A current source to the voltage ௅ across the lighting system.
[2 marks]
(ii) By means of superposition, determine the contribution and its polarity made
by the 6 V voltage source to the voltage ௅ across the lighting system.
[2 marks]
(iii) Based on your answers to Q21(b)(i) and Q21(b)(ii), determine the voltage ௅
and its polarity across the lighting system. [1 mark]
(c) (i) Determine (and sketch) the Thevenin equivalent of the supply circuit shown
in Fig. 21 as seen by the lighting system. [4 marks]
(ii) Based on the Thevenin equivalent circuit found in Q21(c)(i), determine the
voltage ௅ across the lighting system to verify your answer to Q21(b)(iii).
[2 marks]
22. (a) A resistance thermometer ௫ is placed in an interface circuit shown in Fig. 22(a)
so that the output voltage ௌ can be used to monitor the temperature of a kiln
electrically. From prior testing, the resistance of ௫ is 1000 Ω at the nominal
operating temperature of the kiln, and it varies between 600 Ω and 1500 Ω for the
sort of temperature variations expected in the kiln.
R1
250 Ω
Rx
5 V
vS
Fig. 22(a): A sensor interface circuit for monitoring temperature.
(i) Briefly explain why the correlation between the output voltage ௌ and the
temperature of the kiln is negative, i.e., an increase in ௌ corresponds to a
decrease in temperature, and vice versa. [3 marks]
(ii) Determine the resistance ଵ if, for the expected temperature variations in the
kiln, the maximum output voltage of the sensor circuit is to be 2 V.
[3 marks]
(b) The output of a sensor circuit, identical to that of Fig. 22(a), used to monitor the
temperature of a different kiln varies between 0.75 V ≤ ௦ ≤ 2 V. In order for this
sensor signal to be logged and processed by a microcontroller, it needs to be
conditioned into the range 1 V ≤ ௠ ≤ 4.25 V. Additionally, since ௌ is negatively
correlated to temperature, this needs to be corrected so that ௠ is positively
correlated to temperature, i.e., an increase in ௠ corresponds to an increase in
temperature, and vice versa. A signal conditioning circuitry therefore needs to be
designed, and placed in between the sensor output and the microcontroller input.
(i) Determine the input-output relationship that the signal conditioning circuitry
needs to have in order to map the output of the sensor circuit, ௦, to the desired
input for the microcontroller, ௠. Express your answer in the form
௠ = − ௌ
for some constant > 0 and > 0. [3 marks]
(ii) A signal conditioning circuitry that can be used to implement the operation
determined in Q22(b)(i) is shown in Fig. 22(b).
150 Ω
vs
+
−
Vref vm
Thevenin Equivalent
of Sensor Circuit
R
Signal Conditioning Circuitry
4 kΩ
Fig. 22(b): A signal conditioning circuitry.
Analyse the circuit shown in Fig. 22(b) and show that the output of the circuit,
௠, is given by
௠ = ൬1 +
൰ ୰ୣ୤ − ൬
൰ ௌ ,
for some constant , and state the value of . [4 marks]
(iii) Based on the output behaviour of the signal conditioning circuitry given in
Q22(b)(ii), determine the value of the resistance , and the reference voltage
୰ୣ୤ in the circuit shown in Fig. 22(b) for it to produce the desired output ௠
satisfying the operation you have found in Q22(b)(i). [2 marks]