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Unformatted text preview: EECS 314 Winter 2009 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 © 2009 Alexander Ganago Page 1 of 2 Scores for the HW set: Problem 1 2 3 4 5 6 7 Total Score Problem 1 Voltage division in the phasor world The Big Picture To solve this problem, you should use the formulas for impedances Z L = j ⋅ ω ⋅ L and Z C = 1 j ⋅ ω ⋅ C at different frequencies ω = 2 π ⋅ f . The units: if capacitance is in farads, inductance in henry, and frequency ω in rad/sec, then the impedance is in ohms. If f is in kHz, then 2 π ⋅ f is in krad/sec. In all equations, the impedances are used exactly as resistances, according to the rules of complex algebra. You will obtain expressions such as Z = (5 + j ⋅ 2) Ω , and V = V MAX ∠α where V MAX is the peak voltage. The Assignment Consider the circuit shown on the diagram with the following component values: R = 40 Ω C = 300 nF L = 1 mH V S = 1 2 ⋅ cos( ω t) V . Assume sinusoidal steadystate conditions. Consider two frequencies: 2 kHz and 10 kHz. Part 1 2 3 Total EECS 314 Winter 2009 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 © 2009 Alexander Ganago Page 2 of 2 Problem 1, continued Part 1 (10 points) Use the component values on page 1; calculate the impedances in ohms. Show your work for 2 kHz. Write the results in the table below. Frequency Z L Z C 2 kHz 10 kHz Part 2 (30 points) Calculate the peak amplitude of each current in mA and each voltage in V and write your results in the table below: Frequency, kHz Capacitor current I C Capacitor voltage V C Inductor current I L Inductor voltage V L 2 10 Briefly discuss how the increase of frequency affects the magnitude of each voltage and current. Show your work on additional pages. EECS 314 Winter 2009 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 © 2009 Alexander Ganago Page 1 of 2 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 ∠ ϕ V and ˆ I = I max ∠ ϕ I , where V max and I max are the peak amplitudes of the sinusoidal functions, and ∠ ϕ V and ∠ ϕ I are the phase angles....
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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.
 Winter '07
 Ganago

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