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Unformatted text preview: University of Caiifomia San Diego
Department of Electrical and Computer Engineering ECE 35 Final Exam
Winter 2009 Name (Last, First) Student ID Number Signature 50 L” T70 0 S This is a closed book exam, but you are allowed a single 8.5” x 11” page sheet of notes.
You can use a nongraphing calculator, but cellphones and computers are forbidden. Write clearly: work which is not legible will not count towards your grade. Numeric answers MUST HAVE UNITS to be correct (Le, 30, 2A, 4mV) You must show your work to receive credit on any problem. Grade Key Good exam policy: ASK FOR CLARIFICATION IF THE QUESTION ASKED IS NOT CLEAR
 READ THROUGH THE ENTIRE EXAM BEFORE BEGINNING
 WORK ON THE SIMPLER PROBLEMS FIRST  TRY TO ANSWER ALL PROBLEMS Problem 1 (10 pts): stillaluunlillqul
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I ——_+_.__ e($cm) 0 I! we'll? . or brieﬂy explain why it can not be represented that way.
"c J 2 + 2cos(4rr t + m4) [v(t) is in Volts, t is in seconds I (t) v? (t) = v(t)  2 as a phasor in angle notation, or brieﬂy explain why it can not be represented that way.
IL
K :2. (ll Cﬂ‘d'HlUﬁ kc»: hr» ‘91 u (be sure to label and scale the axes)
B) Either represent v(t) as a phasor in angle notation A) Graph the voltage as a function of time if v C) Either represent v’ Problem 2 (20 pts): Find the Thevenin and Norton equivalents to the DC circuit below for two cases. SWITCH OPEN:
A Vt“: O
Rm: 3.9.
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switch
SWITCH CLOSED: ‘lV
vm=
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’frLszﬁffH U0 foggy“ abqut. ‘" VA : I“ r. 0
R = 5/16 = if; = 3,5;
‘1. 6+6 :L. .. v \Q—Ua “ :2. 1H ' 3
2. vﬁ—UL~ {2. F2. = ‘iv rape _
(Siting: e3) 5 Kg; ‘ 2”? +‘{//2 Cﬁnﬁuizvbu'zﬁgo“ £3— 1_e:__f_i= 9?!)—
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Aifmmled . Problem 3 (20 pts): The circuit of problem 2 is now connected to a capacitor and resistor in series.
The switch is open for a long time, then close at time = zero. Answer the following questions: A 29 49 2F V switch 12V 1l3 Q
4Q 29 24 ﬂeet: Ln:H/ §_
? 313 RIL —ZF' ‘lv V“ ”3.12.. guikﬁL‘ DP‘ht CA?“L;“‘°’ 1') AFSGLatFLJ. Shitck 'Jusl'ctoscal' MFAcHor 5+4V+5 4" Lt“
ewahniw hack1.: Wm: Va. 'IIu—
.— V(f’°)¢ vac. l. (Vﬂraa) " Vac):
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., "( ((9. )V (A) What is Vc just before the switch is closed? V.a (t=0') = __0_
(B) What is vc just after the switch is closed? Vc (t=0*) = _i_
(C) What is Vc a long time after the switch is closed? VG (t > 00) = ‘fV
(D) What is the characteristic time of the circuit? T = G 5 . . . #6:
(E) What IS the equation for the voltage as a function of time? Vc (t>0) = "1V   C. Problem 4 (20 pt): In the circuit below, assume the opamp is ideal and answer the following questions. A) What is the voltage gain of the circuit above? [0 "' B) What is the range of INPUT voltage for which the opamp in this circuit can behave as ideal? _15v < V L S U in: C) Assuming the circuit is constructed in your lab (that is, with a real opamp connected to good but not ideal voltage
supplies) graph the approximate output voltage of the circuit as a function of the input voltage. A) Vast = ix  (it. + and
:7 51'; (10k\ 7' {DVM
Lit.
V 'l
Gu = v—“: . to
G) 09+?ui Wi'i‘m): is Laudcok b7 svpff—irS, v,.c_ vM 5 v,
=9 v.“ = 51—:— e' LSV
War:
v w
Vi“ ' = i 7: ‘.Y\/
Veal(q)
IS
l.r LT V;_'(v) A? Problem 5 (20 pt): For the circuit below, Vs(t) = Vmcos(wt). Answer the following questions. (A) Write the impedances deﬁned in_the ﬁgure at right as complex values . A _._’L. .
Z1: UL‘+F’I ’ZZ=lSuea ’23:“ we’lz4zﬂ (B) Mark the ﬁgure at right to deﬁne a supernode containing (only) the voltage Asource Vs(t), labeling the
terminals with the voltage expressed as a function of the compiex voltage Vx. (C) Write KCL for the supernode using 9; as the single variable, using the parameters (i.e. capacitance,
resistance, etc.) as deﬁned in the original circuit. ‘ ~ n 1 "l M " __ l— I'
(not: ” Zi" 3* ”ti 2:. ” it) °
1 1 l l 1
= V  v " .3— ' r R, Z. ' 4“
O ’ "wt—:35z iUL"'" “r ”at 1““ ’ “c3
(D) Write an equation for the complex voltage Vx ; you do NOT need to simplify the equation
l 1 I 4 t
d ——_— i ——'—F + q— 3/ . ——*—" 4
A9 = ' “3—. 0 .., 4—.
VX vs II. lad; JUL‘ IlR‘ ( 21 “c1 ﬂDL‘ +R‘ 1} (“Q5 A'" ~ AM; at. ‘1'6 941% ngt—rcr l.“ ‘1’“: "F ZHEQELEY Problem 6 (20 pt): For the circuit below, ﬁnd Vc(t). 20mH Mcul +0 05:. idpcr Posikan. 59hr: 'DC‘. circuH Fini b S o
V " T = 3V I" VOt+I,¢. Aiutalgy" C  ‘V I . _, =_.
21.? —_ '1 32"“ AC Circuﬂi AchA {updauccs 3.“: . .5 .
a: ‘6‘...”— =% loo263mm 1: 1}14. ~157 //(2 +5 2) sill—=1.a' 1z41"’1
.3" " «r FEB41"
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\{:(‘l’) 9 3 1 W (155(IGDE ALT") V .. 3 4' 6.3 cos(oot  lB.‘I‘)V Problem 7 (20 pt): Find the values of the circuit elements in the RLC load circuit at right that will maximize
aqu1¢ power transfer from the circuit at left, driven with either a DC or AC drive voltage source. (A) Suppose the voltage source Vs = 5 Volts (DC). Calculate the following values. RL2 2.0. 50L: 0 ILL=GU~$1 'PL= ’5.IZ5'N
(B) One of the circuit elements does not affect the power transfer. Which is it, and why?
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Us ‘ 5‘ 1
" ‘ ‘L‘L‘Cg i ‘1' ‘ (7)2
L D {,ﬁL
z '5‘
= T W (C) Now suppose the voltage source VS = 5003(100nt+rrf4) Volts. Calculate the following values. 125i. CL: 50? F . LL: 0 ﬂ: 1.59251: (D) Which of the circuit elements, if any, do not affect the power transferred? A“ how am :“tgt an HM. ecucf MK! Ltd—Lo!
=————.—.—.___—__—__—__—_— (E) What effect does the phase of the drive voltage have on the power transferred? (dour. H N * L 1: “I—" = ﬂ = FF—Eﬂﬂ
2h 7. D =9 KL: "Xe $ '4 on : ¢ u‘L (loomL2
. l1 : 5.01/4?
P — V” p“ = 5" 3* . 2? u
L. z Lﬁmleh)‘ ‘2. .11 IL Problem 8 (20 pt): In the two circuits below, two inductors are positioned so theyr are nearly touching.
The switch is closed at time t = 0, and left closed. Answer the following questions: 4. switch
0
6V 2H 1 nF Vc(t)
R1 = 10 1 Q I (A) 5 pts: What is the voltage on the capacitor after a long time? Vc (t > 00) = 0 (3)10 pts: Sketch the voltage on the capacitor as a function of time (your answer is qualitative, not numeric) Vclt) (C) With the same vertical and horizontal scale. sketch Vc(t) assuming that R2 was increased to 10!). vat?) but, Liloru ...
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 Winter '10
 JosephFord

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