Departement Elektriese, Elektroniese en Rekenaar-Ingenieurswese Semestertoets 1 Kopiereg voorbehou Module EIR221 Elektriese Ingenieurswese 20 Augustus 2010 Department of Electrical, Electronic and Computer Engineering Semester Test 1 Copyright reserved Module EIR221 Electrical Engineering 20 August 2010 Toetsinligting: Test information: Maksimum punte: Maximum marks: Duur van vraestel: Duration of paper: 60 90 minute 90 minutes Totale aantal bladsye (hierdie blad ingesluit): Total numer of pages (including this page): 11 Volpunte: Full marks: Oopboek / toeboek: Open / closed book: 60 Toeboek Closed book BELANGRIK- IMPORTANT 1. Die eksamenregulasies van die Universiteit van Pretoria geld. The examination regulations of the University of Pretoria apply. 2. Hierdie vraestel mag slegs in Afrikaans of Engels beantwoord word. This question paper may only be answered in Afrikaans or English Dosent(e): 1 Mr JH van Wyk Lecturer(s): 2 Groephoof: Ek bevestig dat die vraestel die uitkomstes toets soos gespesifiseer in die studiehandleiding. Group head: I confirm that the question paper evaluates the outcomes as specified in the study guide. Groephoof: Group Head: Handtekening: Signature:
Afdeling A / Section A Vir Afdeling A kan die rofwerkboek(e) vir berekenings gebruik word. ALLE ANTWOORDE MOET NA DIE ANTWOORDBLAD OORGEDRA WORD. Moet nie die krammetjie verwyder nie. For Section A you can use the script(s) for calculations. ALL ANSWERS MUST BE TRANSFERRED TO THE ANSWER SHEET. Do not remove the stapler. Vraag 1 Question 1 n Sinusvormige spanning v(t) het n wgk waarde A sinusoidal voltage v(t) has a rms value of 20V, a van 20V, n periode van 100µs, en bereik n period of 100µs, and reaches a positive peak at positiewe piek by 20µs. Skryf n uitdrukking vir 20µs. Write an expression for v(t). v(t) neer. Dra antwoord oor Carry over answer [3] Vraag 2 Question 2 Vind die wgk waarde vir die sein getoon. Find the rms value for the signal shown. Dra antwoord oor Carry over answer [3] Vraag 3 Question 3 Reduseer die volgende vergelyking na die vorm Vm.cos(ωt+θ) deur van fasors gebruik te maak. 5cos(ωt+75 ) - 3cos(ωt-75 ) + 4sin(ωt) Reduce the following equation to the form Vm.cos(ωt+θ) by using phasors. Dra antwoord oor Carry over answer [3] EIR221-Semester Test 1 2010 2
Vraag 4 Question 4 Beskou die fasors getoon. Beskryf die verwantskap (voor of agter) tussen al die fasors. Consider the phasors shown. Indicate the relationship (leading or lagging) between all the phasors. V 1 V 2 met/by grade/degrees V 2 V 3 met/by grade/degrees V 3 V 1 met/by grade/degrees Dra antwoorde oor Carry over answers [3] Vraag 5 Question 5 Die fasorspanning oor n sekere las is V = 1500 2-120 en die fasorstroom I = 15 2 75. Die stroomrigting se verwysing wys uitwaarts vanaf die The phasor voltage across a certain load is V = 1500 2-120 and phasor current I = 15 2 75. The current direction is referenced pointing positiewe spanningsterminaal. Bepaal die outwards from the positive voltage terminal. lasimpedansie, drywingsfaktor, drywing, die Determine the load impedance, the power factor, reaktiewe drywing en die skyndrywing van die las. the power, the reactive power and the apparent power delivered to the load. Dra antwoorde oor Carry over answers [5] EIR221-Semester Test 1 2010 3
Vraag 6 Question 6 Vir die grafiek hieronder getoon, bepaal die waardes van die stroombaankomponente hieronder getoon. For the graph shown below, determine the values of the circuit elements shown. X v(t) i(t) Dra antwoorde oor Carry over answers [6] Vraag 7 Question 7 Bepaal die fasors vir die spanning en al die strome in die stroombaan getoon. Teken die fasordiagram vir die spanning en al die strome. Find the phasors for the voltage and all currents shown in the circuit. Construct a phasor diagram of the voltage and all currents. Teken die fasordiagram op die antwoordblad Draw the phasordiagram on the answer sheet. [4] EIR221-Semester Test 1 2010 4
Vraag 8 Question 8 Vind die Thevenin ekwivalente baan (V th, Z th ) vir die stroombaan getoon. Find the Thevenin equivalent circuit (V th, Z th ) for the circuit shown. Dra antwoorde oor Carry over answers [4] Vraag 9 Question 9 Vir die stroombaan getoon, wil ons n las oor a en b verbind, wat bestaan uit n weerstand en n kapasitor in parallel, sodanig dat die drywing in die weerstand gemaksimeer word. Vind die waarde van die weerstand en die kapasitor. For the circuit shown, we wish to connect a load across a and b, consisting of a resistance and a capacitance in parallel, such that the power delivered to the resistance is maximized. Find the value of the resistance and the capacitance. Dra antwoorde oor Carry over answers [4] EIR221-Semester Test 1 2010 5
Vraag 10 Question 10 By t=0 word n voltmeter oor n gelaaide kapasitor verbind, soos hieronder getoon. By t=0 is die meterlesing 50V. By t=30s is die meterlesing 25V. Bepaal die weerstand van die voltmeter. At t=0, a voltmeter is connected across a charged capacitor as shown below. At t=0, the meter reads 50V. At t=30s, the meter reads 25V. Find the resistance of the voltmeter. Dra antwoorde oor Carry over answers [2] Vraag 11 Question 11 Vir die stroombaan getoon, bepaal n uitdrukking vir die stroom i L (t) vir t>0. For the circuit shown, determine an expression for the current i L (t) for t>0. Dra antwoorde oor Carry over answers [3] SUBTOTAL: [40] EIR221-Semester Test 1 2010 6
Afdeling B / Section B Hierdie afdeling moet op die optiese merkblad voltooi word (KANT 1) This section should be completed on the optical marksheet (SIDE 1) Vraag 1 Question 1 Beskou n sinusvormige spanning v(t)=v m.cos(ωt+θ). As Vm gehalveer word, sal die grafiek: a) skuif na links b) skuif na regs c) vertikaal saamgedruk word d) horisontaal saamgedruk word Vraag 2 Question 2 Vir n suiwer induktor, is die spanning die stroom met grade: a) voor, 90 b) agter, 90 c) voor, 180 d) agter, 180 Vraag 3 Question 3 Vir n suiwer kapasitiewe las is die drywing en die reaktiewe drywing a) nul, positief b) nie-nul, positief c) nul, negatief d) nie-nul, negatief e) geen van die boegenoemde Consider a sinusoidal voltage v(t)=v m.cos(ωt+θ). If Vm is halfed, the graph of v(t): a) shifts to the left b) shifts to the right c) is compressed vertically d) is compressed horizontally For a pure inductance, the voltage the current by degrees: a) leading, 90 b) lagging, 90 c) leading, 180 d) lagging, 180 For a pure capacitance, the power is and the reactive power is a) zero, positive b) non-zero, positive c) zero, negative d) non-zero, negative Vraag 4 Question 4 Die eenheid vir reaktiewe drywing is: a) W b) VA c) VAR d) RP The unit for reactive power is: a) W b) VA c) VAR d) RP EIR221-Semester Test 1 2010 7
Vraag 5 Question 5 Vir n RLC baan, wat is die komplementêre oplossing vir n ondergedempde stelsel: a) x c (t) = K 1 e s 1t + K 2 e s 2t b) x c (t) = K 1 e s 1t + K 2 te s 1t c) x c (t) = K 1 e t cos ω n t + K 2 e t sin ω n t d) x c (t) = A. cos ω n t + B. sin ω n t For a RLC circuit, what is the complementary solution for an underdamped system: a) x c (t) = K 1 e s 1t + K 2 e s 2t b) x c (t) = K 1 e s 1t + K 2 te s 1t c) x c (t) = K 1 e t cos ω n t + K 2 e t sin ω n t d) x c (t) = A. cos ω n t + B. sin ω n t Vraag 6 Question 6 Vir n RLC baan in die algemeen, is: a) n Kapasitor n kortsluiting b) n Induktor n kortsluiting c) n Kapasitor n opebaan d) (b) en (c) For a RLC circuit in general: a) A capacitor is a short b) A inductor is a short c) A capacitor is an open circuit d) (b) and (c) Vraag 7 Question 7 Vir n parallel RLC baan, is die dempingskoëffisient (α): a) R/L b) L/R c) L/(2R) d) R/(2L) e) 1/ LC Vraag 8 Question 8 For a parallel RLC circuit, the damping coefficient (α) is: a) R/L b) L/R c) L/(2R) d) R/(2L) e) 1/ LC Vir die stroombaan getoon, wat is die waarde van die stroom i L (t) net nadat die skakelaar oopgemaak is? a) i L (0 + ) = 4A b) i L (0 + ) = 19.9mA c) Geen stroom sal vloei, i L (t) = 0mA d) Oneindige stroom sal vloei, i L (t) = For the circuit shown, what is the current i L (t) just after the switch is opened? a) i L (0 + ) = 4A b) i L (0 + ) = 19.9mA c) No current will flow, i L (t) = 0mA d) Infinite current will flow, i L (t) = EIR221-Semester Test 1 2010 8
Vraag 9 Question 9 n Gebalanseerde Y-verbinde driefase bron het lyntot-neutraal spannings van 440V rms. Wat is die lyntot-lyn spannings? a) 622 V rms b) 762 V rms c) 311 V rms d) 254 V rms Vraag 10 Question 10 v an (t) = 100cos (ωt 60 ) V v bn (t) = 100cos (ωt + 60 ) V v cn (t) = 100cos (ωt) V A balanced Y-connected three-phase source has line-to-neutral voltages of 440V rms. What are the line-to-line voltages? a) 622 V rms b) 762 V rms c) 311 V rms d) 254 V rms Is hierdie n positiewe fasesekwensie? a) JA e) NEE Is this a positive phase sequence? a) YES e) NO Vraag 11 Question 11 Die gemiddelde drywing van n driefase stelsel is: a) 3V Yrms. I Yrms cos(θ) b) 3V Yrms. I Yrms cos(θ) c) 3V Yrms. I Lrms cos(θ) d) 3V Yrms. I Lrms cos(θ) Vraag 12 Question 12 Die reaktiewe drywing van n driefase stelsel is: a) 3V Y. I Y sin(θ) b) 3V Y. I Y cos(θ) c) 3 2. V Y. I L sin(θ) d) 3V Yrms. I Lrms cos(θ) Vraag 13 Question 13 Vir n kapasitor C, is die impedansie: a) Z C = jωc b) Z C = jωc c) Z C = j/ωc d) Z C = 1/ωC e) Z C = 1/jωC The average power of a three phase system is: a) 3V Yrms. I Yrms cos(θ) b) 3V Yrms. I Yrms cos(θ) c) 3V Yrms. I Lrms cos(θ) d) 3V Yrms. I Lrms cos(θ) The reactive power of a three phase system is: a) 3V Y. I Y sin(θ) b) 3V Y. I Y cos(θ) c) 3 2. V Y. I L sin(θ) d) 3V Yrms. I Lrms cos(θ) For a capacitor C, its impedance is given by: a) Z C = jωc b) Z C = jωc c) Z C = j/ωc d) Z C = 1/ωC e) Z C = 1/jωC EIR221-Semester Test 1 2010 9
Vraag 14 Question 14 As n stelsel twee lasse (A en B) en een bron het, is die gekombineerde drywing van die bron P A P B. If a system has two loads (A and B), and one power source, the combined power of the source is P A P B. Vraag 15 Question 15 n Y-verbinde las en n Δ-verbinde las is dieselfde as: a) Z Y = Z b) Z Y = 3Z c) Z Y = Z / 3 d) Z Y = Z /3 Vraag 16 Question 16 Vir n spesifieke RC baan is die oplossing v C (t)=20-10exp(-20t) V. Die geforseerde waarde is 10V. A Y-connected load and a Δ-connected load is the same when: a) Z Y = Z b) Z Y = 3Z c) Z Y = Z / 3 f) Z Y = Z /3 d) none of the above For a specific RC circuit the solution is v C (t)=20-10exp(-20t) V. The forced value is 10V. Vraag 17 Question 17 Vir n spesifieke RC baan is die oplossing v C (t)=20-10exp(-50t) V. As die waarde van C 10µF is, is R 20kΩ. For a specific RC circuit the solution is v C (t)=20-10exp(-50t) V. If the value of C is 10µF, R is 20kΩ. EIR221-Semester Test 1 2010 10
Vraag 18 Question 18 Vir die stroombaan getoon is die ekwivalente kapasitansiewaarde wat die 200kΩ weerstand sien, wanneer die skakelaar toe is, 25µF. For the circuit shown, the equivalent capacitance value seen by the 200kΩ resistor after the switch is closed, is 25µF. Vraag 19 Question 19 Vir maksimum drywingsoordrag moet die las wat tussen die twee terminale verbind word, Z load = 100Ω. For maximum power transfer, the load connected between the two terminals should be Z load = 100Ω. Vraag 20 Question 20 Vir n parallel RLC baan, is die partikulêre oplossing altyd v P (t) = 0 For a parallel RLC circuit, the particular solution is always v P (t) = 0 SUBTOTAL: [20] EIR221-Semester Test 1 2010 11