W09 314 HW07 solution

W09 314 HW07 solution - EECS 314 Winter 2009 Homework set 7...

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EECS 314 Winter 2009 Homework set 7 Student’s name ___ PROBLEM 2 SOLUTION _____ 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 © 2009 Alexander Ganago Page 1 of 3 Solution by Idong Ebong Problem 2 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 The Assignment In this problem, you will consider 3 circuits, which all have the same Thevenin equivalent source o T V V 30 2 ˆ and the same Thevenin equivalent impedance (to the left of the terminals a and b) and the same load resistance 0.1 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 2 3 Total
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EECS 314 Winter 2009 Homework set 7 Student’s name ___ PROBLEM 2 SOLUTION _____ 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 © 2009 Alexander Ganago Page 2 of 3 Solution by Idong Ebong Part 2 Calculate the maximal average power that can be transferred to the load from the given source. ܲ ௠௔௫ | 8ൈܴ ሺ2ܸሻ 8ൈ0 .1ߗ ൌ૞ࢃ Circuit 1 Circuit 2 Circuit 3 ۱ܝܚܚ܍ܖܜ ܑܖ ܜܐ܍ ܔܗܗܘܛ ሺ܋ܔܗ܋ܓܟܑܛ܍ ܌ܑܚ܍܋ܜܑܗܖሻ ܫൌ ܸ ܼ ൅ܼ 2ס30° ܸ ሺ0.1 ൅ ݆0.3 ൅ 0.1ሻߗ ൌ 5.547ס െ 26.31° ܣ 2ס30° ܸ ሺ0.1 ൅ ݆0.3 ൅ 0.1 ൅ ݆0.3ሻߗ ൌ 3.162ס െ 41.57° ܣ 2ס30° ܸ ሺ0.1 ൅ ݆0.3 ൅ 0.1 െ ݆0.3ሻߗ ൌ 10ס30° ܣ ܄ ܉܊ ሺ܉܋ܚܗܛܛ ܔܗ܉܌ሻ ܸ ܾܽ ൌܼ ܮ ൈܫ 0.1ߗ ൈ ሺ5.547ס െ 26.31°ሻܣ ൌ 0.5547ס െ 26.31° ܸ ሺ0.1 ൅ ݆0.3ሻߗൈ ሺ3.162ס െ 41.57°ሻܣ ൌ1ס30°ܸ ሺ0.1 െ ݆0.3ሻߗൈ ሺ10ס30°ሻܣ ൌ 3.162ס െ 41.57° ܸ
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EECS 314 Winter 2009 Homework set 7 Student’s name ___ PROBLEM 2 SOLUTION _____ Discussion section # _______ (Last, First, write legibly, use ink) (use ink)
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This note was uploaded on 10/28/2009 for the course EECS 314 taught by Professor Ganago during the Winter '07 term at University of Michigan.

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W09 314 HW07 solution - EECS 314 Winter 2009 Homework set 7...

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