1 ECE 201 – Fall 2008 Final Exam December 20, 2008 Division 0101: Clark (7:30am) Division 0201: Elliott (10:30 pm) Division 0301: Capano (3:30 pm) Division 0401: Qi (4:30 pm) 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. 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, 4 2 ii 3, 7, 10, 17 2 iii 5, 8, 19, 24 2 iv 7-11 2 v 14-19 3 vi 21, 21 1 vii 22, 23 1 viii 6, 24 1 ix 12, 13 12 1. A current ( )it [in Amperes] (see Figure below) passes through an arbitrary cross-section of a wire. What is the net charge q [in Coulombs] that passes through that cross-section in the time interval 0 10t≤≤ seconds? (1) 1 (2) 6 (3) 18 (4) 12 (5) 8 (6) 24 (7) 0 (8) 12 2. For the following network of resistors, each of value R, determine the equivalent resistance Req. (1) 1R8 (2) 1R4 (3) 3R8 (4) 1R2 (5) 5R8 (6) 3R4 (7) 7R8 (8) R (9) 9R8 (10) 9R3 3. Determine the voltage Vb. (1) 1 (2) 2 (3) 3 (4) 4 (5) 5 (6) 6 (7) 7 (8) 8 4. Find Vs for the circuit below (in V): (1) 10 (2) 20 (3) 30 (4) -10 (5) -44 (6) 60 (7) 04 5. We make a series of measurements of the voltage VAB between two terminals of a box containing an electrical circuit. Each measurement is made by connecting a resister RL between the terminals, and then measuring the voltage VAB. Determine the Thévenin equivalent for the network in the box. RL VAB 50Ω 15V 100Ω 20V 250Ω 25V 500Ω 27.3V (1) th th1V 5V ; R20= = Ω (2) th thV 5V ; R 20= = Ω (3) th th1V 15V ; R20= = Ω (4) th thV 25V ; R 20= = Ω (5) th thV 15V ; R 20= = Ω (6) th thV 30V ; R 30= = Ω (7) th thV 30V ; R 50= = Ω 6. A variable resistor RL is connected to a current source (4A) and parallel resistor (20Ω), as shown. Determine the maximum power that the resistor RL can absorb. (1) 10W (2) 20W (3) 40W (4) 80W (5) 120W (6) 160W (7) 320W (8) 640W5 7. In the following circuit, the switch has been closed for a long time prior to t = 0, but opens at t = 0. Find ( )RV0+. (1) 6V (2) 4V (3) 3V (4) 2V (5) 1V (6) 0V (7) -1V (8) -2V (9) -3V (10) -4V 8. For the circuit shown, find the time constant, τ, for the exponential time dependence of the voltage Vx(t), in seconds. (1) 1 (2) 2 (3) 3 (4) 4 (5) 5 (6) 6 (7) 7 (8) 8 (9) 266 9. Find the correct RL, RC, or RLC equation which describes the behavior for the variable of interest in the circuit below for t > 0. Suppose ( )Li 0 0A−≠ and ( )cv 0 0V−≠. The switch remains open for all t > 0. (1) ( )( )cctv (t) v 0 exp V8+−= (2) ( )( )L 12ti (t) k k t exp A4−= + (3) ( )2t 4tL1 2i (t) k e k e A−−= + (4) ( )t/4 t/2c1 2v (t) k e k e V−−= + (5) ( )( )LLti (t) i 0 exp A2+−= (6) ( ) ( )c 12v (t) k k t exp t V=+− (7) ( ) ( )tL ddi (t) e Acos t Bsin t A−= ω+ ω7 10. Find the differential equation for vc(t). Note: ccdv (t)v (t)dt′=. (Hint: apply KCL at the top node.) (1) c cs sv (t) 2v (t) v (t) 0.5i (t)′+=− (2) c cs sv (t) 2v (t) v (t) 0.5i (t)′+=+ (3) ccs sv (t) v (t) v (t) 0.5i (t)′+=+ (4) ccs sv (t) v (t) v (t) 0.5i (t)′+=− (5) ccs sv (t) v (t) v (t) 0.5i (t)′−=− (6) c cs sv (t) 2v (t) v (t) 0.5i (t)′−=+ (7) cc s sv (t) 2v (t) v (t) 0.5i (t)′+ =−+ 11. For the circuit shown, the two resistors have the same value R. Find R (in Ω) that yields a critical damping condition. (1) 0.3Ω (2) 0.6Ω (3) 0.9Ω (4) 1.2Ω (5) 1.5Ω (6) 1.8Ω (7) 3Ω (8) 4Ω (9) 9Ω (10) 12Ω8 12. Determine Vout for the following op amp configuration. (1) -15V (2) -10V (3) -6V (4) -5V (5) 0V (6) +5V (7) +6V (8) +10V (9) +15V 13. inv (t)is given in the graph. The value of outv (t)at t = 2 sec, assuming ( )cv 0 0V−=, is (in V): (1) 1 (2) 2 (3) 3 (4) 4 (5) -2 (6) -4 (7) 89 14. A sinusoidal voltage of effective value 5V is applied to the input terminals A-B of the circuit inside the box shown . As the frequency of the source is varied, the effective value of the current is measured, as shown in the plot. Which of the following networks could be contained in the box?10 15. Element A in the following circuit is either a capacitor or an inductor. Determine the impedance of this element, ZA, that causes the current I to lag the source Voltage by 45° (1) -1000jΩ (2) -500jΩ (3) -250jΩ (4) -50jΩ (5) +50jΩ (6) +250jΩ (7) +500jΩ (8) +1000jΩ 16. Determine the phasor voltage VR. (1) -j5V (2) (6.25 – 2.5j) V (3) 1jV (4) -1jV (5) 1V 0∠° (6) (2 + 5j) V (7) -j2.5V11 17. Using KVL, the phasor voltage Vs, in volts, is (1) 3-4j (2) -j (3) 2-3j (4) 4-3j (5) 4+3j (6) 3+4j (7) 1 (8) 2+3j (9) j (10) 5+2j 18. The current in a circuit is represented by the following first order differential equation ( )( …
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