ece3337_hw4_solutions_spring_2003 - Use ECE 3456 Drop Box...

Unformatted text preview: Use ECE 3456 Drop Box in Lab (S383—D) to Turn in ECE 3337 Homeworks ECE 3337 HW 4 FASTEEV—Lxlhlé/ awe? Due April 21 Monday 5:30pm 2003 Name (Last, First) Use this sheet as cover sheet *This is a big homework, worth the credit of two homeworks. Get started early. Consider the circuit shown. The parameter values are C =1 nF and L=1mH. In each question, find iL (t). In each case (when appropriate), plot the solution use mathcad (or anything else you are familiar with). In question 1-4, find the solution use the following two ways (i) Find the solution as the response of a forced problem (force starting at t = O ). (ii) Find the solution as the sum of (l) the response of a steady—state forced problem (i.e. force started at tz—oo and continued to t=oo) and (2) the natural response of the system to the initial condition at 1:0 established by the steady state forced problem in (1). First, consider the step-DC problem, where iS(t) :u(t). The various resistor values put you through over—damped, under—damped and critically—damped situations of second order circuits. 1.R:1kQ 2. R=0.25k§2 3. R=O.SkQ Consider the step—AC problem, with ix (1) = sin(a)3t + 45° )u(t) where cos = 2x106 / sec . This problem let you get a comparison of step—DC with step-AC problems. 4. Rzle The following two problems let you get a comparison of first—order circuits with second- order circuits. 5. Repeat problem 1, taking out the capacitor. 6. Repeat problem 1, taking out the inductor. The following problem let you get a comparison of the step-DC response with the impulse response. 7. Repeat problem 1, now with the source given by i$(t)=5(t). Check to see if the impulse response is the time derivative of the stepADC response. Finally, the following problems let you apply what you have learned to circuits different from what you have seen (RLC in parallel). The idea is to convince you that you have learned enough to deal with time dependent circuit problems in general. 8. The switch in the circuit shown has been in position x for along time. At i=0, the switch is moved to position y. Find vC (t). 9. The switch in the circuit shown has been in position a for along time. At t = 0, the switch is moved to position b. Find vL (t). 10. The switch in the circuit shown has been in position a for along time. At t: 0, the switch is moved to position b. Find iL (t). 22-141 50 SHEETS 22442 100 SHEETS 22-144 200 SHEETS @111 AMPAD got 33.31? 19201:“- 33, PA: A ng/az Fkarté-QMELQ @1175; *g‘a/QQK/ £4 19%: M34104 '2‘ ’03 ‘q magi? /HJI€ Ci? GUM“; c; yiDVVVE Fix/154 01 @‘MJ‘I‘M “Hm: wésw‘svzw 09a 1%VC66! gob! C/W‘ [Fox/(5 21av¥seag ’ *‘ Fey {<o.” tail 119911961 wt? 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