EE211_212_Fall2023_Sample_Exam_4_Solution (1)

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Pennsylvania State University *

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Electrical Engineering

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Jan 9, 2024

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page 1/13 The Pennsylvania State University Department of Electrical Engineering EE 211/EE 212 Sample Exam #4 Student Name: PSU ID #: NOTE: 1. You have 110 minutes to complete this exam. 2. The exam consists of 20 multiple-choice questions (2 points each), and two workout problems (30 points each). 3. You are only allowed to have one 8.5” x 11” handwritten note sheet (front and back) and a calculator. 4. You are NOT allowed any other notes, textbooks, or other electrical devices. 5. You must show all intermediate steps and calculations clearly. Answers without derivations may receive no credit. Circle the correct answer on the exam booklet, and fill in the answer sheet. 6. During the exam, you may not communicate with anyone other than the instructor. 7. Turn in your note sheet and this exam booklet. 8. ANY cheating will be reported to the university and result in failing the course.

page 2/13 Multiple choice questions; only one correct answer for each question. 1. Let ? = 7.2 − ? 9.2 and ? = 5.3 ∠ 38°. Find ? =A/B. A. ? = 11.7 ∠ − 90° B. ? = 4.11 ∠ − 51.95° C. ? = 11.7 ∠ 52° D. ? = 2.2 ∠ − 90° E. ? = 0.45 ∠ 90° 2. Find the amplitude of the voltage 𝑣(?) = 25sin (35t+60  ) V. A. 60  B. 25 V C. 30  D. 60 rad/s E. 35 rad/s 3. Given the complex numbers a = − j 6 and b = 20  36.9  , compute c = a + b and give the result in rectangular form. A. 0.8 − j 5.4 B. 4 − j 2 C. 16 + j 6 D. 4 + j 10.8 E. 10 + j 6

page 3/13 4. Let ? ( ? ) = 7 cos (50 ? − 12°) A. Determine 𝐼 ̃ , the phasor representation of ? ( ? ). A. 𝐼 ̃ = 7 ∠ − 12° A B. 𝐼 ̃ = 7 ∠ 12° A C. 𝐼 ̃ = 50 ∠ -12° A D. 𝐼 ̃ = 7 ∠ 50° A E. 𝐼 ̃ = -7 ∠ 12° A 5. A circuit’s impedance is found to be 𝑍 = (5 + ? 4) Ω. Which of the following circuits could have this impedance? A. B. C. D. Circuits A. and B. E. Circuits B. and C.

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page 4/13 6. A circuit element has an impedance of Z = j25  at an angular frequency of 1000 rad/s. Determine the type and the value of the circuit element. 1) 25-  resistor 2) 40- μH inductor 3) 25- mH inductor 4) 40- μF capacitor 5) 25- mF capacitor 7. Determine the equivalent impedance at 1000 rad/s at terminals A-B in the circuit below. A. 25 ( 1 − j )  B. 25 ( 1 + j )  C. 50 ( 1 − j )  D. 50 ( 1 + j )  E. 50 ( 2 − j ) 

page 5/13 8. For the circuit shown below, find the impedance Z. A. (17.5 – ? 3.4) Ω B. (23.8 + ? 12.2) Ω C. (14.9 + ? 7.7) Ω D. (23.8 - ? 12.2) Ω E. (17.5 + ? 3.4) Ω 9. Assume the circuit below is in the sinusoidal steady state and that 𝑣 ? ( ? ) = 25 cos(500 ? + 30°) V. Determine 𝑣 𝑅 ( ? ). A. 22.4 cos(500 ? + 3.4°) V B. 11.2 cos(500 ? + 93.4°) V C. 11.2 cos(500 ? + 3.4°) V D. 1.6 cos(500 ? + 36.7°) V E. 11.2 cos(5000 ? + 93.4°) V

page 6/13 10. Use the following circuit for the next two problems and assume that the source current is ? ? ( ? ) = 10 cos( 𝜔? + 40°) mA and that the circuit is in the sinusoidal steady state. At what frequency would ? ? ( ? ) and 𝑣 𝑅 ( ? ) be in phase? A. 0.2 rad/s B. 0.4 rad/s C. 2 rad/s D. 10 rad/s E. 100 rad/s 11. Given that ? ? ( ? ) = 25 sin(10,000 ? − 50°) mA and that the circuit below is in the sinusoidal steady state, Determine the inductor current ? 𝐿 ( ? ). A. 25 cos(10,000 ? − 140°) mA B. 10 cos(10,000 ? − 70°) mA C. 15 cos(10,000 ? + 50°) mA D. 50 cos(10,000 ? − 140°) mA E. 50 cos(10,000 ? − 50°) mA

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page 7/13 12. Determine the phasor current 𝐼 𝑥 ̃ in the sinusoidal steady state circuit below. A. √10  18.4  A B. 5 √2  135  A C. 5  90  A D. 3 √5  63.4  A E. 3 √2 − 8.2  A 13. Determine the RMS value of this periodic signal. A. √10 V rms B. 3 V rms C. 4 √2 V rms D. √80 8 V rms E. 4 V rms

page 8/13 14. Suppose that the maximum amplitude of the sinusoidal voltage source is 67 V and its frequency is 1,493 rad/s. Find the RMS value of the voltage. A. 47.4 V B. 67 V C. 94.8 V D. 134 V E. 32 V 15. The voltage across a load in an AC circuit is given by: 𝑣 𝐿 ( ? ) = 10 cos(100 ? + 90°) 𝑉 . The current through the same load is given by: ? 𝐿 ( ? ) = 4 cos(100 ? + 36.9°) ? . Determine the average power absorbed by the load. A. 12 W B. 16 W C. 20 W D. 24 W E. 32 W 16. Assume that V ̃ 𝑠 = 20 ∠ 74° V rms . Determine the RMS value of I ̃ 𝑠 . A. 2 A B. 1 A C. 4 A D. √2 A E. 2 √2 A

page 9/13 17. Assume that the frequency of V Th (t) is 𝜔 = 2500 rad/s. Determine which load below will allow maximum power transfer to the load. 18. If the load impedance in the circuit below is Z L = 30 + j50 Ω, determine the average power absorbed by the load. A. 0.6 W B. 1.2 W C. 2.4 W D. 3.2 W E. 4.8 W

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page 10/13 19. Determine I 2 in the circuit shown below: A. 4  20° A B. 8  20° A C. 8  −160° A D. 10  20° A E. 10  −160° A 20. The load power is 1MW at pf = 0.8 lagging. Find the apparent power. A. 1.25  36.9° MVA B. 0.8  36.9° MVA C. 1.25  53.1 MVA D. 0.8  53.1° MVA E. 1.0  53.1° MVA

page 11/13 Student Name: PSU ID #: Answer Sheet for Multiple Choice Questions: Your grades are determined using this answer sheet. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Grade: Problems 1-20 ______________ / 40 Problem 21_______________ / 30 Problem 22_______________ / 30 TOTAL__________ /100

page 12/13 of your approach, draw the phasor-domain circuits, and appropriately label each component. 21. (30 points) Solve for i 1 (t) and i 2 (t). To get the full credit, you need to provide a comprehensive explanation

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page 13/13 22. (30 points) 1) Find the impedance value, Z L , that maximizes the average power delivered to the load. 2) Once Z L is determined, compute the maximum power that can be transferred to the load. 3) Determine the average power supplied by the source in the given circuit configuration.

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