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202_HW61-72Sp09

202_HW61-72Sp09 - EE202 HOMEWORK PROBLEMS SPRING 09 RAYS...

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EE202 HOMEWORK PROBLEMS SPRING 09 R AY S R EADING S UGGESTIONS FOR B ROADENING YOUR E DUCATIONAL F OUNDATION O N H ISTORY His Excellency: George Washington by Joseph J. Ellis (George was a vain man, but believed that people and nations do things that are in their best interest and are true to treaties and the like, only in so far as it is in the best interest of both groups.) Bound to Canaan by Fergus Bordewich (An excellent rendition of the origins of the underground railroad and the people who used it and the heros and heroines who became its conductors.) O N P HILOSOPHY Nonviolence: 25 Lessons from the History of a Dangerous Idea by Mark Kurlansky (Did you know that no language in the world has a word for “nonviolence” that is not a negation of violence?) Plato and a Platypus Walk into a Bar: Understanding Philosophy through Jokes by Thomas Cathcart and Daniel Klein. (Great!) On Bullshit by Harry G. Frankfurt (Professor of Philosophy Emeritus at Princeton University)— (Someone who tells a lie knows the truth and deliberately ignores it. BS is so insidious because it marginalizes, makes irrelevant both the truth and the lie—making no distinction.) S UPPLEMENTAL P ROBLEMS NOT TO BE TURNED IN: 1. Consider the RLC circuit shown below. (a) Find L eq , Y in (s) and Z in (s). (b) Find the poles and zeros of Z in (s). Find the impulse response. (c) Find the zero-input response if v C (0 - ) = 10 V with all other initial conditions zero. (d) Find the zero-state response if i in ( t ) = cos(100 t ) u ( t ) A. (e) Find the complete response of the circuit.
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page 2 Spring 09 2 ANSWERS : L eq = 0.1 H, Z in ( s ) = 5000 s ( s + 100) 2 + (200) 2 , 5000*exp(-100*t)*cos(200*t)-2500*exp(- 100*t)*sin(200*t), v out ( t ) = e ! 100 t 10cos(200 t ) ! 5sin(200 t ) ( ) u ( t ) V, -5*exp(-100*t)*cos(200*t)+55/2*exp(-100*t)*sin(200*t)+5*cos(100*t)-10*sin(100*t), Sum of prior answers 2. Figure 2 below shows the two ways to connect a pair of coupled inductors in parallel. For each case, find L eq . (a) (b) Figure 2 S OLUTION M ETHOD : Step 1: Label the currents and voltages on each circuit: V 1 , V 2 , I 1 , I 2 , V in , I in . Step 2: Write the matrix equation for coupled inductors in the s-domain. Step 3: Invert the matrix equation to obtain the currents in terms of the voltages. Step 4: Apply KVL and KCL, simplify, and produce the impedance Z in ( s ) = V in ( s ) I in ( s ) . Step 5: Identify L eq = L 1 L 2 ! M 2 L 1 + L 2 ! 2 M .
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