Color: Ivory

Closed book/notes, calculators allowed up to level of TI89, TI Inspire CAS, HP50.

Part I: 12 questions Part II: 12 questions Part II questions are worth twice as much as Part I questions. On the SCANTRON write and bubble-in your: 1. Name (Last, first) 2. Below your first name, bubble in the color of your exam paper (A=IVORY or B=GREEN). Show your UofA picture ID card when you turn in your exam. All work should be done on the examination paper. Allow for reasonable amounts of round off error, and carefully mark one choice for each problem on the SCANTRON answer sheet. All answer sheets and examinations will be collected after 2 hours. You will be asked to stop writing and hand in your papers/answer sheets. Failure to comply promptly may result in disqualification from the exam. NAME: _________________________________ SIGNATURE: ____________________________

University of Arizona Department of Electrical & Computer Engineering

ECE 220 Basic Circuits

Final Examination December 13, 2016

Formula Sheet

𝑥𝑥(𝑡𝑡) = 𝑥𝑥(∞) + 𝐴𝐴1𝑒𝑒𝑠𝑠1(𝑡𝑡−𝑡𝑡0) + 𝐴𝐴2𝑒𝑒𝑠𝑠2(𝑡𝑡−𝑡𝑡0) 𝑥𝑥(𝑡𝑡0) = 𝑥𝑥(∞) + 𝐴𝐴1 + 𝐴𝐴2 𝑥𝑥′(𝑡𝑡0) = 𝑠𝑠1𝐴𝐴1 + 𝑠𝑠2𝐴𝐴2 𝑥𝑥(𝑡𝑡) = 𝑥𝑥(∞) + (𝐵𝐵1cos [𝜔𝜔𝑑𝑑(𝑡𝑡 − 𝑡𝑡0)] + 𝐵𝐵2sin [𝜔𝜔𝑑𝑑(𝑡𝑡 − 𝑡𝑡0)])𝑒𝑒−𝛼𝛼(𝑡𝑡−𝑡𝑡0) 𝑥𝑥(𝑡𝑡0) = 𝑥𝑥(∞) + 𝐵𝐵1 𝑥𝑥′(𝑡𝑡0) = −𝛼𝛼𝐵𝐵1 + 𝜔𝜔𝑑𝑑𝐵𝐵2 𝑥𝑥(𝑡𝑡) = 𝑥𝑥(∞) + [𝐷𝐷1(𝑡𝑡 − 𝑡𝑡0) + 𝐷𝐷2]𝑒𝑒−𝛼𝛼(𝑡𝑡−𝑡𝑡0) 𝑥𝑥(𝑡𝑡0) = 𝑥𝑥(∞) + 𝐷𝐷2 𝑥𝑥′(𝑡𝑡0) = 𝐷𝐷1 − 𝛼𝛼𝐷𝐷2

𝑠𝑠1, 𝑠𝑠2 = −𝛼𝛼 ± �𝛼𝛼2 − 𝜔𝜔02

Parallel RLC 𝛼𝛼 = 1

2𝑅𝑅𝑅𝑅

Series RLC 𝛼𝛼 = 𝑅𝑅

2𝐿𝐿

Part I.

1. Find the power delivered by the circuit element when 𝑖 5 𝑚A and 𝑣 2 V.

a) 10 Wb) 10 Wc) 10 𝑚Wd) 10 𝑚We) none of these

2. Is the circuit valid?

a) yesb) noc) depends on the value of Bd) depends on the value of De) not enough information given

3. Find 𝑅 .

a) 0.5 𝑘b) 1.0 𝑘c) 1.5 𝑘d) 2.0 𝑘e) none of these

4. What is the max power that can be delivered to the 4 resister? Hint: Don’t make hasty assumptions. a) 8 W b) 16 W c) 32 W d) 64 W e) none of these

5. Find 𝑣 . The power rails are 12 V.

a) 12 V b) 12 V c) 10 V d) 10 V e) none of these

6. Find the equivalent capacitance. a) 1.44 10 F b) 16 𝑝F c) 16 10 F d) 1440 𝑛F e) none of these

7. Find 𝑣 𝑡 𝑣 𝑡 𝑣 𝑡 .

𝑣 𝑡 3sin 200𝜋𝑡 240°

𝑣 𝑡 7cos 200𝜋𝑡 190°

a) 8.5 cos(200t + 9.4°) b) 9.9 cos(200t – 16.0°) c) 4.3 cos(200t – 176.2°) d) 6.6 cos(200t + 144.7°) e) none of these 8. By how much does 𝑣 lag 𝑖?

a) 45° b) 90° c) 90° d) 45° e) none of these

9. Find 𝑖 𝑡 .  

a) 0.8cos 10𝑡 135° A b) 0.42cos 10𝑡 13.4° A c) 8cos 10𝑡 45° A d) 0.42cos 10𝑡 103.4° A e) none of these  

10. Find 𝑣 𝑡 at 𝑡 2.5 𝑚s.

a) 59.3 V b) 0 V c) 50.1 V d) 60 V e) none of these

11. At what frequency is 𝑍 purely resistive? a) 100 𝑘Hz b) 15.9 𝑘Hz c) 1.4 𝑘HZ d) 0 𝑘Hz e) none of these

12. Find 𝑍 at terminals 𝑎 and 𝑏. a) 5 𝑗5 b) 10 c) 5 𝑗5 d) 0 e) none of these

Part II. 13. The voltage applied to a 10 𝑘 resister is shown below. Find the total energy absorbed by the resister. a) 1066.67 J b) 533.33 J c) 600 J d) 1200 J e) none of these

14. The box labeled “circuit” is the same in all three figures below. When two different voltage sources are connected at the terminals of the circuit, the currents are as shown in the first two figures below. Find the amount of power that would be delivered by the circuit to the 5 resistor in the third figure. a) 400 W b) 80 W c) 720 W d) 0 W e) none of these

15. Suppose the 10 V full scale meter shown below is used to measure the voltage across the 250 resistor. What will be the percentage error of the reading? % error = (measured – true)/true 100%. a) 1.6 % b) 2.0 % c) 2.4 % d) 2.8 % e) none of these

16. Find 𝑉 .

a) 12 V b) 16 V c) 36 V d) 52 V e) none of these

17. Find 𝑣 . The power rails are ±7 V.

a) 1.25 V b) 1.50 V c) 1.75 V d) 2.0 V e) none of these

18. The switch has been in the “left position” for a long time. Find 𝑣 𝑡 for 𝑡 40 s. a) 1.43 V b) 0.35 V c) 0.74 V d) 1.43 V e) none of these

19. Find Zab. a) 4.3 𝑗1.1 b) 3.6 𝑗0.8 c) 5.5 𝑗2.9 d) 9.8 𝑗7.9 e) none of these

20. Find 𝑉. a) 57.2 – 𝑗52 V b) 8.8 – 𝑗60 V c) 16.1 𝑗12.1 V d) 13.2 – 𝑗8 V e) none of these

21. Find 𝐼. a) 0.25 + 𝑗1.75 A b) 2 + 𝑗1 A c) 0.25 – 𝑗1.75 A d) 2 + 𝑗1 A e) none of these

22. Find 𝑉. a) 9.72∠94.30° V b) 0.45∠12.72° V c) 2.43∠4.30° V d) 5.82∠-13.59° V e) none of these

23. Which phasor diagram can be (approximately) correct?

e) none of these

24. Find 𝐼.  a) 125∠-143.13° A b) 5∠-143.13° A c) 200∠-143.13° 𝑚A d) 320∠-143.13° 𝜇A e) none of these

EXTRA CREDIT: 25. What is the ECE 220 class favorite non-ECE course? a) Psychology b) Discrete Math c) Personal and Consumer Finance d) Linear Algebra e) Conversational Spanish 26. What is Professor Marcellin’s favorite answer for the ECE 220 class favorite non-ECE course? a) Psychology b) Discrete Math c) Personal and Consumer Finance d) Linear Algebra e) Conversational Spanish

Answers

1. d 2. b 3. c 4. d 5. d 6. a 7. c 8. c 9. d 10. d 11. b 12. a 13. a 14. b 15. c 16. d 17. c 18. c 19. a 20. b 21. d 22. a 23. c 24. A 25. B 26. c