Exam June 2017, questions and answers PDF

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ENGG1300

Mid-Semester Examination, Semester 2 2017

THE UNIVERSITY OF QUEENSLAND School of Information Technology and Electrical Engineering Mid-Semester Examination

ENGG1300 Introduction to Electrical Systems Time: TEN (10) minutes for perusal NINETY (90) minutes for working

THIS EXAM CONSISTS OF THIRTY (30) MULTIPLE CHOICE QUESTIONS. ANSWER EACH QUESTION ON THE MULTIPLE CHOICE ANSWER SHEET PROVIDED. During perusal, you are permitted to write on the rough paper provided. This examination is closed book – No materials permitted. No electronic aids are permitted (e.g. laptops, phones). A UQ approved calculator (with label), or a casio FX-82 series calculator is allowed. Each question is worth ONE (1) mark each. For each question, choose the one answer which is most correct. In a question requiring a numerical answer where "none of the above" is the correct answer option, the associated numerical answer will be different to any of the provided numerical answers by at least +/-5%.

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ENGG1300

Mid-Semester Examination, Semester 2 2017

Question 1. Consider the one-port network shown below.

What is the equivalent conductance of this network? A. 5670  B. 176 µS C. 479.17  D. 2.09 mS E. None of the above. Question 2. Consider the one-port network shown below.

What is the equivalent resistance of this network? A. 2740  B. 2.740 M C. 111.8 k D. 1.773  E. None of the above.

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Mid-Semester Examination, Semester 2 2017

Question 3. Consider the one-port network shown below. The open switch should be treated as an open circuit.

What is the equivalent resistance of this network? A. 3220  B. 920  C. 334.2  D. 657.1  E. None of the above.

Question 4. Which of the following is a unit of capacitance? A. B. C. D. E.

Ohms Siemens Henries Farads None of the above

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Mid-Semester Examination, Semester 2 2017

Questions (5)−(15) all refer to solution of the circuit below in Figure 1. You are advised to carefully read the questions; then solve the circuit and check your working to make sure it is correct; and finally answer each of the questions. In all cases be very careful about the sign of the answers.

Figure 1: Circuit Schematic for Question (5)-(15) Space for working

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Mid-Semester Examination, Semester 2 2017

Space for working

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Mid-Semester Examination, Semester 2 2017

Question 5 One way to solve linear circuits is the method of superposition. When using the method of superposition, which of the following schematics in the figure below is a correct representation of the circuit when the 18V voltage source is set to zero? A. Figure (A) B. Figure (B) C. Figure (C) D. Figure (D) E. It is not possible to solve this circuit using superposition.

Question 6 With reference to Figure 1, which of the following is a correct Kirchoff’s Voltage Law Equation? A. 870𝐼3 = 1200𝐼1 + 4800𝐼2 B. 4800𝐼2 = 1200𝐼1 + 870𝐼3 C. 1200𝐼1 = 870𝐼3 + 4800𝐼2 D. 1200𝐼1 + 870𝐼3 + 4800𝐼2 = 0 E. None of the above.

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Mid-Semester Examination, Semester 2 2017

Question 7 With reference to Figure 1, which of the following is a correct Kirchoff’s Current Law Equation? A.

𝑉𝐵 −𝑉𝐴

+

870 𝑉𝐵 −𝑉𝐴 + B. 870 𝑉 −𝑉 C. 𝐵 𝐴 + 870 𝑉 −𝑉 D. 𝐵 𝐴 + 870

𝑉𝐶 −𝑉𝐴 4800 𝑉𝐴 −𝑉𝐶 4800 𝑉𝐴 −𝑉𝐶 4800 𝑉𝐶 −𝑉𝐴 4800

+ + + +

𝑉𝐴 −𝑉𝐷 4200 𝑉𝐴 −𝑉𝐷 4200 𝑉𝐷 −𝑉𝐴 4200 𝑉𝐷 −𝑉𝐴 4200

=0 =0 =0 =0

E. None of the above.

Question 8 With reference to Figure 1, which of the following is a correct Kirchoff’s Current Law Equation at node D? A. 𝐼6 = 𝐼4 + 𝐼5 B. 𝐼5 = 𝐼4 + 𝐼6 C. 𝐼4 + 𝐼5 + 𝐼6 = 0 D. It is impossible to write this equation because the current entering the earth connection is unknown. E. None of answers (A)-(C) are correct, but it is possible to write a correct Kirchoff’s Current Law Equation at node D Question 9 In the circuit shown in Figure 1, what is the value of Current I5? A. 11 mA B. -11 mA C. 6 mA D. -6 mA E. None of the above. Question 10 In the circuit shown in Figure 1, what is the value of current I3? A. 1.54 mA B. 8.21 mA C. -8.21 mA D. 11 mA E. None of the above.

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Mid-Semester Examination, Semester 2 2017

Question 11 In the circuit shown in Figure 1, what is the value of node voltage VC? A. -24.87 V B. 18.00 C. 14.61V D. 28.29 V E. None of the above Question 12 In the circuit shown in Figure 1, what is the value of branch voltage V3? A. 18.00 V B. -18.00 V C. 1.324 V D. -1.324 V E. None of the above.

Question 13 In the circuit shown in Figure 1, what is the value of the power consumed by the 11mA current source? A. 33.2 mW B. 0 mW C. 311.2 mW D. -311.2 mW E. None of the above Question 14 In the circuit shown in Figure 1, what is the value of the power consumed by the 4.2kΩ resistor? A. 0 W B. 3.16 mW C. 43.93 mW D. 66.07 mW E. None of the above Question 15 In the circuit shown in Figure 1, what is the value of the total power consumed by all the resistors in the circuit (i.e. including the 870Ω, 1.2kΩ, 4.2kΩ and 4.8kΩ resistors)? A. 0 W B. 14.77 mW C. 184.6 mW D. 6.240 W E. None of the above.

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Mid-Semester Examination, Semester 2 2017

Questions (16)−(21) all involve analysis of the one−port network shown below in Figure 2. In particular, you will be asked to calculate the Thevenin and Norton equivalent circuits.

Figure 2: Circuit Schematic for Question’s (16)-(21) Space for working

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Mid-Semester Examination, Semester 2 2017

Question 16 If the one-port network of Figure 2 is replaced by its Thevenin Equivalent Circuit, what is the value of the voltage source (VTH) in that equivalent circuit? A. 0.5641 V B. 12.42 V C. 9.329 V D. 22.00 V E. None of the above. Question 17 If the one-port network of Figure 2 is replaced by its Norton Equivalent Circuit, what is the value of the current source (IN) in that equivalent circuit? A. 30.56 mA B. 5.767 mA C. -30.56 mA D. -5.767 mA E. None of the above. Question 18 If the one-port network of Figure 2 is replaced by its Norton Equivalent Circuit, what is the value of the parallel resistor (RN) in that equivalent circuit? A. 720  B. 522.77  C. 2152.77  D. 910  E. None of the above.

Space for working

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Mid-Semester Examination, Semester 2 2017

For Questions (19)-(21), a non-linear light emitting diode (LED) is placed across the terminals of the one port network shown in Figure 2 to give the circuit of Figure 3. The I−V characteristic of the diode is shown in Figure 4.

Figure 3: Circuit Schematic for Questions (19)-(21)

Figure 4: The I-V characteristics of the LED described in questions (19)-(23) Space for working

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Mid-Semester Examination, Semester 2 2017

Question 19 Which of the following equations must the solution to the circuit in Figure 3 satisfy? Note, RN refers to the Norton resistance as calculated in Question (18); VTH refers to the Thevenin Voltage calculated in Question (16); VD refers to the voltage across the diode, and ID refers to the current through the diode (as labelled in Figure 3). A. 𝑉𝐷 = 𝑉𝑇𝐻 −𝑅𝑁 𝐼𝐷 B. 𝐼𝐷 = 𝑅𝑁 𝑉𝐷 − 𝑉𝑇𝐻 1

C. 𝐼𝐷 = 𝑅 𝑉𝐷 − 𝑉𝑇𝐻 𝑁

D. 𝑉𝐷 = 𝑅𝑁 (𝑉𝑇𝐻 − 𝐼𝐷 ) E. It is not possible to express the solution to this circuit as a linear relationship between ID and VD because the diode is a non-linear component. Question 20 Given the circuit in Figure 3, and the diode I−V characteristic of Figure 4, which of the following is closest to the value of VD? A. VD is 2V or less B. 3 V C. 5 V D. 8 V E. VD is 10V or greater. Question 21 Given the circuit in Figure 3 and the diode I−V characteristic of Figure 4, which of the following is closest to the value of ID? A. ID is 1 mA or less B. 2 mA C. 3.5 mA D. 5 mA E. ID is 6 mA or greater. Space for working

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Mid-Semester Examination, Semester 2 2017

Questions 22 and 23 refer to the I−V characteristic of the diode as shown in Figure 4 above. These questions introduce a new design problem and DO NOT require information provided in either of Figure 2 or Figure 3. Question 22 You are designing an LED light. This will consist of a 15V lithium-ion battery connected in series with a single resistor and the LED characterised in figure 4 above. The battery can be modelled as a 15V ideal voltage source. To achieve the desired light intensity the current through the diode should be set to 6mA. Which of the following values for the series resistor will result in a current through the diode (ID) that is closest to 6mA? A. 1400Ω B. 2400Ω C. 3400Ω D. The resistor should be less than 800Ω, or greater than 4500Ω E. It is not possible to estimate the required resistor value with the information provided Question 23 The LED characterised in figure 4 can be assumed to be 100% efficient (i.e. all power dissipated by the LED is converted to light). Which of the following is the closest to the overall efficiency of the circuit described in Question (22) when the series resistor is chosen such that the current through the diode is set to 6mA (i.e. what percentage of total power supplied by the battery is converted to light)? A. 24.2% B. 46.7% C. 70.5% D. 100% E. The overall efficiency of the circuit cannot be estimated with the information provided.

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Mid-Semester Examination, Semester 2 2017

Question 24 A sinusoidal voltage is displayed in the figure below.

Which of the following equations best models the sinusoidal voltage displayed? A. 𝑉𝑠(𝑡) = 100𝐶𝑜𝑠(100𝑡 − 0.002) B. 𝑉𝑠(𝑡) = 200𝐶𝑜𝑠(628𝑡 + 1.05) C. 𝑉𝑠(𝑡) = 200𝐶𝑜𝑠(100𝑡 − 0.002) D. 𝑉𝑠(𝑡) = 100𝐶𝑜𝑠(628𝑡 + 1.05) E. 𝑉𝑠(𝑡) = 100𝐶𝑜𝑠(628𝑡 − 1.05) Space for working

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Mid-Semester Examination, Semester 2 2017

Question 25. Consider the circuit below where L1 = 1.8mH, R2 = 1.2k, C3 = 0.22F.

At a particular instant of time, vc = -12V, ic = -6.2A, vL = 4.6V, iL = 4.7A. At that instant of time, how much energy is stored in the capacitor? A. 15.84 µJ B. –15.84 µJ C. 4.223 µJ D. -4.223 µJ E. None of the above

Question 26. Which of the following expressions correctly models the voltage v(t) across an inductor (with inductance L) to the current i(t) through the inductor? A. 𝑣(𝑡) = 𝐿 × 𝑖(𝑡) 1

B. 𝑣(𝑡) = 𝐿 × 𝑖(𝑡) C. 𝑣(𝑡) = 𝐿

𝑑𝑖(𝑡) 𝑑𝑡

D. 𝑖(𝑡) = 𝐿

𝑑𝑣(𝑡) 𝑑𝑡

E. None of the above

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Mid-Semester Examination, Semester 2 2017

Question 27. Consider the one-port network shown below.

If the frequency of operation is 10kHz, what is the equivalent impedance of this network? A. 4313.4 + j2445.7  B. 5700 + j0.160  C. 5700 + j10053  D. 0.15999  E. None of the above Question 28. Consider the one-port network shown below.

If the frequency of operation is 1000Hz, what is the equivalent impedance of this network? A. 21.000022  B. 22.21𝑒 𝑗0.332  C. 22.21𝑒 −𝑗0.332  −6 D. 21.00𝑒 −𝑗1.47×10  E. None of the above

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Mid-Semester Examination, Semester 2 2017

Questions (29)-(30) refer to the schematic in Figure 5 below, where:  VS = 120ej0 V, f = 10kHz  R = 5.1 k  C = 4.7 nF  L = 47 mH

Figure 5: Circuit Schematic for Questions (29)-(30) Question 29. In the circuit shown in Figure 5 with the component values listed above, what is the value of the phasor current I? A. 23.53 mA B. 19.3𝑒 𝑗0.668 mA C. 12.6𝑒 𝑗0.91 mA D. 23.44𝑒 𝑗0.0847 mA E. It is impossible to calculate the phasor current with the provided information. Question 30. In the circuit shown in Figure 5 with the component values listed above, what is the value of the phasor voltage across the inductor, VL? A. 1.106 mV B. 69.24𝑒 𝑗1.6555 V C. 1.49𝑒 𝑗0.668 V D. 1.49𝑒 −𝑗0.668 V E. It is impossible to calculate the phasor voltage across the capacitor with the provided information.

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Mid-Semester Examination, Semester 2 2017

SPACE FOR WORKING

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Mid-Semester Examination, Semester 2 2017

SPACE FOR WORKING

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