Page 1 ECE 201 – Spring 2010 Final Exam May 7, 2010 Division 0101: Prof. Capano (9:30am) Division 0201: Prof. Tan (10:30 am) Division 0301: Prof. Jung (7:30 am) Division 0401: Prof. Capano (11:30am) Instructions 1. DO NOT START UNTIL TOLD TO DO SO. 2. Write your Name, division, professor, and student ID# (PUID) on your scantron sheet. 3. This is a CLOSED BOOKS and CLOSED NOTES exam. 4. There is only one correct answer to each question. Problem 1 is worth 5 points, Problem 2 is worth 6 points, and the rest of the problems are worth 9 points each. 5. Calculators are allowed (but not necessary). Please clear any formulas, text, or other information from your calculator memory prior to the exam. 6. If extra paper is needed, use back of test pages. 7. Formulas are given on the final page of this exam. 8. Cheating will not be tolerated. Cheating in this exam will result in an F in the course. 9. If you cannot solve a question, be sure to look at the other ones and come back to it if time permits. 10. As described in the course syllabus, we must certify that every student who receives a passing grade in this course has satisfied each of the course outcomes. On this exam, you have the opportunity to satisfy all outcomes. (See the course syllabus for a complete description of each outcome.) On the chart below, we list the criteria we use for determining whether you have satisfied these course outcomes. You only need to satisfy the outcomes once during the course, so any outcomes that you satisfied previously will remain satisfied, independent of your performance on this exam. Course Outcome Exam Questions Minimum correct answers required to satisfy the course outcome i 1, 2 1 ii 3 1 iii 4, 5 1 iv 6, 7, 8 1 v 11, 12, 13, 14, 16 2 vi 15, 17 1 vii 18, 19, 20, 21 2 viii 22, 23 1 ix 9, 10 1Page 2 1. (5pts) The current IR in the circuit below is: (1) −10A (2) 10A (3) −100A (4) 100A (5) −1A (6) 1A 2. (6 pts) If the transconductance (gm) equals 0.002 S, find the current Is. (1) 1A (2) 2mA (3) −2A (4) −4mA (5) 8mA (6) 4A (7) 0Page 3 3. (9 pts) Find the power delivered by the dependent source (in W) using nodal or mesh analysis. 1) 10 2) 20 (3) 30 (4) 40 (5) 50 (6) 60 (7) 70 4. (9 pts) Using source transformation, find the power delivered to the 12 Ω resistor (in W) (1) 1 (2) 12 (3) 0.75 (4) 48 (5) 0.5 (6) 0.0625 (7) 24Page 4 5. (9 pts) The Thevenin equivalent of the circuit below is: (1) a single 6Ω resistor (2) a short circuit (3) an open circuit (4) a single 6 A independent source (5) a single 6 V independent source 6. (9 pts) In the circuit below, the switch has been at the top position for a long time. It is suddenly opened at t = − 4 sec. The voltage vc(t) across the capacitor for t ≥ − 4 sec is (in V): (1) 4)100(t5e+− (2) 1(t 4)310e−+ (3) (t 4)5e−−− (4) 1(t 4)310e−− (5) 4)100(t5e−− (6) 3(t 4)5e−−−Page 5 7. (9 pts) Find R (in Ω) for the capacitor voltage vc(t) for t > 0 to be critically damped. (1) 20/3 (2) 2.5 (3) 3/20 (4) 0.4 (5) 5 (6) 4 (7) 1.25 8. (9 pts) The circuit below has initial conditions, iL(0−) = 8 A and vC(0−) = 20 V. Find the value of ( )cdv 0dt+ (in V/s). (1) 12 (2) −4 (3) −92 (4) 8 (5) −108 (6) 92 (7) 0Page 6 9. (9 pts) If the input voltage Vs1 = 10V and the input voltage Vs2 = 5V, then Vout is (in V): (1) 20 (2) 15 (3) −10 (4) 5 (5) 0 (6) −15 10. (9 pts) In the ideal op amp circuit, Vs(t) = 1u(t)V and vc(0) = 1V. Find vout(t) (in V). (1) −1 u(t) (2) −2 u(t) (3) −t u(t) (4) −2t u(t) (5) −2t u(t)+1 (6) −2t u(t)-1 (7) 1 + 2t u(t)Page 7 11. (9 pts) Determine the frequency ω, in rad/s, for which the input impedance Zin(jω) is purely resistive. (1) 10,000 (2) 100,000 (3) 1,000,000 (4) 316 (5) 3160 (6) 31600 (7) 25 12. (9 pts) Find Vout. (1) 50∠0° V (2) 50∠90° V (3) 100∠0° V (4) 100∠90° V (5) 150∠0° V (6) 150∠90° V (7) 200∠0° VPage 8 13. (9 pts) For the following circuit, determine the value Vth and Zth of the Thevenin equivalent network. Vth Zth (1) 60∠0° j1 (2) 60∠0° j9 (3) 60∠90° j1 (4) 90∠0° j9 (5) 90∠0° j9 (6) 90∠90° j1 (7) 110∠0° j9Page 9 14. (9 pts) Consider the following circuit. Iin and Vout are the phasor representations of input current and output voltage, respectively. The input Iin is a sinusoidal signal of frequency ω. Which of the following graphs is a correct sketch of |Vout/Iin| vs. ω in steady state? (1) 0.1 11000.40.8H ω( )ω (2) 0.11 1000.20.40.60.8H ω( )ω (3) 0.111000.40.8H ω( )ω (4) 0.11100.70.80.91H ω( )ω (5) 0.11 1000.40.8H ω( )ω (6) 0.1 1 1000.40.8H ω( )ω (7) 0.1110048H ω( )ωPage 10 15. (9 pts) The circuit below is in sinusoidal steady state. The average power absorbed by the capacitor is (in mW): (1) 0 (2) 20 (3) 50 (4) 100 (5) 200 (6) 500 (7) 1000 16. (9 pts) The current phasors in the circuit below are expressed in effective (i.e., root-mean-square) value. The value of the impedance Z is (in Ω): (1) 6 – j3 (2) 6 + j3 (3) −10 + j20 (4) −10 – j20 (5) 25 (6) j20Page 11 17. (9 pts) The load shown below consists of one resistor and one capacitor. Using the voltage and current waveforms shown below, compute the average power absorbed by the resistor in the load. Assume ω=2π rad/sec. 00.125 0.250.3750.50.625 0.75 0.875 11.125 1.251.375 1.51.625 1.75 1.875 24−2−024υ t( )i t( )t (1) 2 W (2) 4 W (3) 22W (4) 24 W (5) 2 + j2 VA (6) 2 – j2 VA (7) 4 + j2 VA (8) 4 – j2 VAPage 12 18. (9 pts) Find the complex power delivered to the load ZL. Assume IS = 30∠0° A rms. (1) 11250 + j11250 VA (2) 11250 - j11250 VA (3) 11250 + j22500 VA (4) 22500 + j11250 VA (5) 11250 - j22500 VA (6) 22500 - j11250 VA (7) 22500 + j22500 VA 19. (9 pts) Consider a source that drives an electric motor that consumes an average power of 50kW at a power factor (pf) of “21lagging”. Assume the motor needs a fixed voltage of Vm = 110∠0°. Find the complex power, Sm, delivered to the motor. Assume ω = 120π rad/sec. (1) 50 + j50 kVA (2) 50 - j50 kVA (3) 50 + j100 kVA (4) 50 - j100 kVA (5) 100 + j50 kVA (6) 100 - j50 kVA (7) 100 + j100 kVAPage 13 20. (9 pts) A voltage source rated at …
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