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EECS314_W08_HW7

# EECS314_W08_HW7 - EECS 314 Winter 2008 Homework set 7...

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EECS 314 Winter 2008 Homework set 7 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2008 Alexander Ganago Page 1 of 2 Scores for the HW set: Problem 1 2 3 4 5 6 7 Total Score Problem 1 Maximal power transfer to the load in AC circuits The Big Picture In the phasor form, the voltage across a circuit element and the current through it are ˆ V = V max " # V and ˆ I = I max " # I , where V max and I max are the peak amplitudes of the sinusoidal functions, and " # V and " # I are the phase angles. The complex power absorbed by the circuit element is defined as Power = 1 2 ˆ V " ˆ I * = 1 2 V max " I max # \$ V % \$ I ( ) , which emphasizes the importance of the phase shift between the current and voltage. The real part of complex power equals the average power P av = 1 2 V max " I max " cos # V \$ # I ( ) ; here cos " V # " I ( ) is the power factor, which should be maximized for optimal power transfer. The source, which is shown here in its Thevenin equivalent form, transfers maximal power to the load if the load impedance is complex conjugate of the source impedance Z L = Z T * ; complex conjugate ensures the phase matching between the voltage and current in the circuit. The maximal average power transferred to the load equals P max = 1 8 " V T 2 R T Part 1 2 3 Total

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EECS 314 Winter 2008 Homework set 7 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2008 Alexander Ganago Page 2 of 2 Problem 1, continued The Assignment In this problem, you will consider 3 circuits, which all have the same Thevenin equivalent source ˆ V T = 12 V ( ) " 0 o and the same Thevenin equivalent impedance (to the left of the terminals a and b) and the same load resistance 0.1 Ω but differ in the load impedance. By comparing these circuits, you will appreciate the role of phase matching between the voltage and the current in the circuit. Part 1 (15 points) Calculate in the phasor form the current through each circuit (in the clockwise reference direction) and the voltage across the terminals a and b . Part 2 (10 points) Calculate the maximal average power that can be transferred to the load from the given source. Your answer: _____________ W Part 3 (15 points) Calculate the complex power and the average power absorbed by the load (to the right from the terminals a and b ). Also, express the average power as percentage of the maximal value you found in Part 2. Write your results in the table below. Circuit Current, A V ab , volts Complex power P av , watts P av , % max 1 2 3 Show your work on additional pages.
EECS 314 Winter 2008 Homework set 7 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2008 Alexander Ganago Page 1 of 2 Problem 2

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