VERSION 00000001 ELECTENG 101 Page 1 of 32 THE UNIVERSITY OF AUCKLAND SEMESTER TWO 2020 Campus: City, NZ Online, Offshore Online, UoA CLC - Northeast Forestry, UoA CLC - Southwest University 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. VERSION 00000001 ELECTENG 101 Page 2 of 32 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 VERSION 00000001 ELECTENG 101 Page 3 of 32 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 VERSION 00000001 ELECTENG 101 Page 4 of 32 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 VERSION 00000001 ELECTENG 101 Page 5 of 32 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 VERSION 00000001 ELECTENG 101 Page 6 of 32 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 VERSION 00000001 ELECTENG 101 Page 7 of 32 LONG ANSWER QUESTIONS (Answers to be entered in the Answer Booklet) 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] VERSION 00000001 ELECTENG 101 Page 8 of 32 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] (QUESTION 22 CONTINUED NEXT PAGE) VERSION 00000001 ELECTENG 101 Page 9 of 32 (QUESTION 22 CONTINUED) (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] VERSION 00000001 ELECTENG 101 Page 10 of 32 23. Two temperature sensors are used to monitor the temperature of the water inlet and the water outlet of a manufacturing plant. The sensors are connected to two 12-bit ADC inputs of a microcontroller that has a reference voltage of 1.1 V. An LED and a switch are also connected as shown in Fig. 23. The microcontroller needs to be programmed to perform the following functions: When the outlet water temperature exceeds the inlet water temperature by 4 ∘C, the warning LED must be turned on. When the switch is pressed the warning light must be turned off. The output voltage of the sensors changes linearly with respect to temperature at 10 mV ∘C⁄ , and at 0 ∘C the output is 0 V. It can be assumed that the system will only operate over the temperature range 0 ∘C to 100 ∘C. Fig. 23: An ESP32 Microcontroller. The program below is to be used to control the warning LED according to the above specifications: /***** Hardware macros *****/ #define TEMPR_WARN_PIN 18 #define SW_CANCEL_PIN 14 #define T_SEN_OUT A3 #define T_SEN_IN A4 #define TEMPR_DIFF 4 /***** Declare & initialise global variables *****/ int t_out_C = 0; int t_in_C = 0; int tempr_diff = 0; int t_sen_out_val = 0; int t_sen_in_val = 0; int sw_cancel_val = 0; (QUESTION 23 CONTINUED NEXT PAGE) VERSION 00000001 ELECTENG 101 Page 11 of 32 (QUESTION 23 CONTINUED) void setup() { pinMode(TEMPR_WARN_PIN, OUTPUT); pinMode(SW_CANCEL_PIN, INPUT_PULLUP); } void loop() { t_sen_out_val = analogRead(T_SEN_OUT); t_sen_in_val = analogRead(T_SEN_IN); sw_cancel_val = digitalRead(SW_CANCEL_PIN); t_out_C = adc_to_deg(t_sen_out_val); t_in_C = adc_to_deg(t_sen_in_val); tempr_diff = TEMPR_DIFF; tempr_diff = check_tempr_diff(t_out_C,t_in_C, tempr_diff); warning_on_control(tempr_diff); warning_off_control(sw_cancel_val); } /***** Functions to be written*****/ int adc_to_deg(int adc_val){ } int check_tempr_diff(int t_upper, t_lower, int diff){ } void warning_on_control(int val){ } void warning_off_control(int val) { } Complete (in your Answer Booklet) the code for the four functions, adc_to_deg(), check_tempr_diff(), warning_on_control(), and warning_off_control() used in the program in order for the microcontroller to control the warning LED as desired. Specifically, the functions needs to perform the following: (a) adc_to_deg() should convert the ADC reading to a numerical value that corresponds to temperature in ∘C. [5 marks] (b) check_tempr_diff() should take the two temperature measurements and a constant threshold as inputs, and return a value that is 1 if the difference between the two measurements exceeds the constant threshold, and 0 if otherwise. [4 marks] (c) warning_on_control() should take a control signal as input, and use it to turn on the warning output. [3 marks] (d) warning_off_control() should take a control signal as input, and use it to turn off the warning output. [3 marks] VERSION 00000001 ELECTENG 101 Page 12 of 32 24. (a) An electrical load requires a sinusoidal voltage (), as shown in Fig. 24(a)(i), to operate. However, an AC supply is not readily available and so a squarewave ො() is generated from a DC supply as shown in Fig. 24(a)(ii) to approximate the desired signal () and drive the load. 6 V t (ms) −4 V 4020 3010 3 V −4 V 3010 Vp 20 40 t (ms) Fig. 24(a)(i): A sinusoidal signal. Fig. 24(a)(ii): A discrete sinusoidal signal. (i) Determine the equation describing the voltage signal () in Fig. 24(a)(i) and express it in the form () = cos( + ) + for some constants > 0, > 0, > 0, and > 0. [3 marks] (ii) If the RMS value of the squarewave signal ො() in Fig. 24(a)(ii) and the sinusoidal signal () in Fig. 24(a)(i) are to be equal, briefly explain whether the peak voltage of the squarewave signal should be larger, smaller, or equal in value compared to the peak voltage of the sinusoidal signal (). Note: It is not necessary to determine the exact value of . [2 marks] (b) An electrical load is connected across a sinusoidal supply of ௌ = 250 V(rms). The load was measured to absorb 60 W of active (average) power and the phase of the current through the load was measured to lead the voltage across it by 60∘. (i) Any electrical load under AC excitation can be modelled equivalently as a resistor, a capacitor, an inductor or a subset combination of the three. Briefly explain what you would expect the equivalent composition of this electrical load to be. [2 marks] (ii) Determine the reactive power of the electrical load. [3 marks] (QUESTION 24 CONTINUED NEXT PAGE) () ො() VERSION 00000001 ELECTENG 101 Page 13 of 32 (QUESTION 24 CONTINUED) (c) An electricity transmission system consisting of two transformers is used to deliver power from a generator to a domestic load , as shown in Fig. 24(c). RL 100 Ω Generator 10 Ω Transmission System 1:10 10:1 vS 10 kV vL Fig. 24(c): An electricity transmission system. (i) Show that the voltage across the load is related to the generator voltage ௌ by = ൬ 10 10 + 1 100⁄ ൰ ௌ . [3 marks] (ii) Determine the power efficiency of the transmission system, i.e., the power received by the load as a fraction of the total power produced by the generator. [2 marks] (APPENDIX FOLLOWS) VERSION 00000001 ELECTENG 101 Page 14 of 32 Blank Page This page will NOT be marked VERSION 00000001 ELECTENG 101 Page 15 of 32 APPENDIX – Table of Formulæ and Identities (Power) () = = () ⋅ () (Current) = (Ohmᇱs law) = ⋅ (Resistance) = ⋅ (Inductor) = (Capacitor) = (Resistivity) () = ൫1 + ( − )൯ (Strain) ∆ = (KVL) = 0 ே ୀଵ (KCL) = 0 ே ୀଵ (Series Equiv. Resistance) = ே ୀଵ (Parallel Equiv. Resistance) = 1 ∑ 1/ேୀଵ (Voltage Divider) = ⋅ ∑ ேୀଵ , ∈ [1, ] (Current Divider) = ⋅ 1 ⁄ ∑ 1 ⁄ேୀଵ , ∈ [1, ] (Frequency and period) = 1 (Angular frequency) = 2 (RMS value) ୰୫ୱ = ඨ 1 න ଶ() ் (RMS of sinusoids) ୰୫ୱ = ୮ୣୟ୩ √2 (Average Power) = ୰୫ୱ୰୫ୱ cos(௩ − ) (Reactive Power) = ୰୫ୱ୰୫ୱ sin(௩ − ) (Apparent power) = ඥଶ + ଶ = ୰୫ୱ୰୫ୱ (Power factor) p. f. = cos(௩ − ) (Transformer voltage) ௦ = ௦ = (Transformer current) ௦ = ௦ = ௦ = 1 Boolean Identities Comment 1 + = + OR is commutative 2 ⋅ = ⋅ AND is commutative 3 + ( + ) = ( + ) + OR is associative 4 ⋅ ( ⋅ ) = ( ⋅ ) ⋅ AND is associative 5 ⋅ ( + ) = ⋅ + ⋅ AND distributes over OR 6 + ⋅ = ( + ) ⋅ ( + ) OR distributes over AND 7 ⋅ തതതതതത = ̅ + ത De Morgan’s Law I 8 + തതതതതതതത = ̅ ⋅ ത De Morgan’s Law II VERSION 00000001 ELECTENG 101 Page 16 of 32 Blank Page This page will NOT be marked ANSWER BOOKLET ELECTENG 101 VERSION 00000001 Page 17 of 32 THE UNIVERSITY OF AUCKLAND SEMESTER TWO 2020 Campus: City, NZ Online, Offshore Online, UoA CLC - Northeast Forestry, UoA CLC - Southwest University ELECTRICAL AND ELECTRONIC ENGINEERING Electrical and Digital Systems ANSWER BOOKLET Office Use Only Q1 – 20 Q21 Q22 Q23 Q24 Total Family Name: First Name: ID Number: ANSWER BOOKLET ELECTENG 101 VERSION 00000001 Page 18 of 32 Blank Page This page will NOT be marked ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 19 of 32 Long-answer Section NOTE: Working is required QUESTION 21 21 (a) (4 marks) 21 (b) (i) (2 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 20 of 32 QUESTION 21 CONTINUED 21 (b) (ii) (2 marks) 21 (b) (iii) (1 mark) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 21 of 32 QUESTION 21 CONTINUED 21 (c) (i) (4 marks) 21 (c) (ii) (2 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 22 of 32 QUESTION 22 22 (a) (i) (3 marks) 22 (a) (ii) (3 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 23 of 32 QUESTION 22 CONTINUED 22 (b) (i) (3 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 24 of 32 QUESTION 22 CONTINUED 22 (b) (ii) (4 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 25 of 32 QUESTION 22 CONTINUED 22 (b) (iii) (2 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 26 of 32 QUESTION 23 23 (a) int adc_to_deg(int adc_val){ } (5 marks) 23 (b) int check_tempr_diff(int t_upper,t_lower,int diff){ } (4 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 27 of 32 QUESTION 23 CONTINUED 23 (c) void warning_on_control(int val){ } (3 marks) 23 (d) void warning_off_control(int val) { } (3 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 28 of 32 QUESTION 24 24 (a) (i) (2 marks) 24 (a) (ii) (3 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 29 of 32 QUESTION 24 CONTINUED 24 (b) (i) (2 marks) 24 (b) (ii) (3 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 30 of 32 QUESTION 24 CONTINUED 24 (c) (i) (3 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 31 of 32 QUESTION 24 CONTINUED 24 (c) (ii) (2 marks) ANSWER BOOKLET / VERSION 00000001 ELECTENG 101 ID: ……………………………… Page 32 of 32 Blank Page This page will NOT be marked
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