c08_sol_exam3

c08_sol_exam3 - ECE Box # MULL— Mia-W 5 5’- 5’...

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Unformatted text preview: ECE Box # MULL— Mia-W 5 5’- 5’ Problem Score Points MED/I?!“ g? 1 $30.6 30 2 [9. a. 15 g D. 520 Li 3 /5"5' 20 4 [‘7- a 35 AVE t, 45:! ECE 2011 - Term C - 2008 Introduction to Electrical and Computer Engineering Exam 3 5g. . 1 H l . 0 You may use calculators. 0 Show all work. Partial credit may be given. 0 When in doubt, let common sense prevail. Don’t get entangled in unnecessary algebra. 0 As in real life, problems may include more information than required. 0 You will have 50 minutes to complete this exam. 1. First Order Transient Response |30| a) In the RC circuit below, determine expressions for the voltage across the capacitor vc(t) and the current i(t) as a function of time, after the switch closes at t=0. NOTE: The initial voltage on the capacitor vc(0) = 0V. [6] SW1 R1 tzo 2.5m 12V C1 GENEML SOLUTIoA): _. t 7):: (f) = VFW“: (Vflmm. " vl/Vt "413 C /2 UV out. M55: t/ t/ " - , (3v .. 11¢“) = la-(Ia «fie, z UNICRIZ .. 0—(0 ._ e Z Acmu FoIL 5(9): -t/z =7 :0:an ‘ (IF/Am. “ I‘lmflfl-B C I 2-“ J'S'KJ‘L _, "Vans? 5 - -t/o.ar A Uc[e)_. [2—126 CV] =o.2£.2‘q .‘ C(t): 4,8e CM b) NEATLY plot vc(t) and i(t) TO SCALE on the axes below. Be sure to indicate any key features of your plot. NOTE: Please plot your graphs out to at least 5 time constants. [10] oar 0.9 0.1? /,00 I.)( 864cm“ '6 (.347 “(0.5%)2 .7 0.17M c) The RC circuit of pan (a) is being used in the design below to create a time delay (after the switch is closed) before turning on an LED. If VREF equals 8V, solve for the time delay. NOTE: The op-amp is being used as a voltage comparator, similar to the “Clapper Lab ”. Be sure to show work for partial credit. [10] 'F’ND t amt/v Dc, (0’— 8V 1 ' FROM PM (0») ) -tol Uclt) = la—Iae /2r -t/l iv = IR-lQe “r - SOLVL pm t». / - __. -[ Time Delay: “A4 v/L‘a if /0'2r hat-mas = Ofiém A (1) As a designer, identify at least three ways of exte@1g the time delay in this circuit. [4] 119a? Wm Wm M (“WWW a: < 15w) 2 2. Steady State DC Analysis [151 Determine the indicated voltages and currents in the circuits below. You may assume that all transient behavior has died out, and that what remains is the DC steady state. NOTE: Resistor values are given in Ohms. a) cm [4] c) When analyzing linear circuits in DC steady state, what substitutions are made for inductors and capacitors? Explain why these substitutions are justified, based on the physical behavior of these devices. . [5] 3. Phasors |20| The following signal v(t) is the sum of two sinusoidal voltages having the same frequency but different magnitudes and phase shifts. NOTE: The phase shift has been given in degrees. v(t) = 7sz'n(a)t + 60‘? + 5c0s(cot +709 — 90 " a) Rewrite this equation in phasorform,%suming cos(cot) as a reference. [4] AS COSMIfl'Jt 12(6) = ’7490(wi— 30") + {500(Qéi'70“) DN/ As PHASoflJ Uswc True :0: _ r V: 74:30” + 59070" .4441 e = Coo (9-906 b) Sketch the phasor for each of the two sinusoids below, indicating the appropriate magnitudes and angles. [6] ® rec-:9 : 31‘! 4113x7530 7: 7. m 4 am" d) Express v(t) as a single cosine function, indicating its magnitude and phase shift (in degrees). [5] v[€):i/ “(wt + (a) v = Dr: W (0 7m &O(Wt+g.713°8 MM” PHM 4. Complex Impedance | 35 | a) Given the following circuit, determine an expression for the Complex Impedance (Z) connected to the ac voltage source. Express your answer in both Cartesian (a+jb) AND Polar ( I Z | 462 ) form. [6] L Cartesian: Z = v(t) = Vm sin(a)t) b) Redraw the circuit in the Phasor Domain, with the appropriate substitutions for each parameter L, R, v(t) and i(t). [4] J WL o c o .—.\ ,V e 0 l/,,1 4° c) Determine an expression for the current phasor—I-(in polar form). [5] A _> V 00 m SiM/LA—t n I = 7;:- 2‘ 4 OHM/5 um (l e2 +901 iwwfi V», '?*’ d) If Vm = 15 V(pk), L = 10mH, R = 150 Q and w = 16,000 rad/sec, determine the magnitude and phase ofT. [8] lil — V'" = " - " WNW W mar ‘ “‘3qu sum 3 __ W = _ #600 0m” __ g o 4: m z. - #7: /.06'7 e) Determine the current i (t) as a function of time, using sin(cot) as a reference. [4] 6&3 = K237 4m; {wi —- 644.85%?“47 M w: mka i(t) = ( 651.301 m (of — 94.27:") [M t) On the axes below, plot the current i (t) as a function of time. NOTE: Be sure to label your axes and indicate any key features of your plot. The source voltage, has been plotted as a reference. [8] 7‘ 97/6 ...
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c08_sol_exam3 - ECE Box # MULL— Mia-W 5 5’- 5’...

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