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ELE204-MT1(2007-8) - C f If m1(9 HACETTEPE UNIVERSITY...

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Unformatted text preview: C f? If m1 (9' HACETTEPE UNIVERSITY DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING ELE 204 CIRCUIT THEORY - II MIDTERM.1. ll Aril 2008 Student # : 1. Show all of your steps in detail and present your work clearly. 2. Write your name on all the papers you turn in. 3. Use the back side of your paper if necessary. Q1. For the circuit given in figure 1, the variable load resistor ZL is adjusted for maximum average power transfer to ZL when is(t) =8cost A. a) Find the impedance that should be connected across a, b for maximum average power transfer. b) Find the maximum average power transferred to the load of part (a), c) Find the power factor of the load found in part (a). Q2. A three-phase line has an impedance of 0.5 + j4 9/4). The line feeds two balanced three-phase loads Connected in parallel. The first load is absorbing a total of 691.20 kW and delivering 201.6 kVAR magnetizing vars. The second load is A connected and has an impedance of 622.08-j l 8 l .44 Q/q). The line to neutral voltage at the load end of the line is 7200V. What is the magnitude of the line voltage at the source end of the line? Q3. In the audio system shown in figure 2, the transformers are assumed to be ideal. The loudspeaker is represented approximately by a 4 Q resistance. a) Find the turns ratios 3 and b such that the average power delivered to the 49 loudspeaker is as large as possible. What is the maximum power? b) The turns ratiosare those determined in part (a) for maximum power transfer. Suppose that a loudspeaker with 169 resistance is used in place of the 49 speaker. What is the new power? ______. 0+ __ ____ '_______l A ’1‘? v, ~ Out .14 Sou“ Ce \Msfiwmer QMel £\ef T :?r i isEi I 5“ Q4. For the circuit given in figure3, a) Find the impedance seen by the ideal source, b) What is the complex power delivered by the source? .l./2_ 51 W956») = . fi‘ 3 5Cosimo’c 1M H Jr 3“: 2m F Q5. For the circuit given in figure 4, 3) Draw a proper tree of the circuit by including the 19 resistor into the co-tree, b) Using circuit topology, obtain the state equations (including the output equation) for the state variables order vc (t), i L(t). Use the given polarities for the capacitor voltage and given direction for the inductor current, c) Derive the state transition matrix for the state equations determined in part (b), d) For the zero input response, find a set of initial conditions (vc(0), 11(0)) such that the response will be bounded, e) For the zero state response, obtain the solutions for vc(t), iL(t) and the output for t>0 if v(t)= e" u(t), i(t)= —e" u(t) a . .— Z> ——\— 1.9.3:; 4 32.632’3—1» ”3:; + .LQCI') -1\:Q .2+_23' - 32 (323 +3 (la—"12.3 ,V—m + A. (1;-L} :0 “A“: <3+L>1&+(j—Q<€ \m: A§+H+§3-€ =(\23»A)\1 ‘gM—«w ‘ A ’ A -i E} miDa-flx iT— —L\ 2 Tax “We“ ,_ 2: ..\J 44*“; ML%‘% \J—r $11 32*“ 3C 13 ,_T ‘ ‘SQJ DELK \JT +12, +jZJ—L ~]I\ =~ / ’ ‘ r '3; V ,—\/ Myl ~ J_I \JT )1 "1‘, \"r3,},{:( ,,,,,,,,,, LE P 3‘ 5’5 U’an/r L —j 1+3“; 4:2 “VTX :2 - ’(HQE’HWT 5) I 2. : \m x , H—ml M 4+ fin fl. ._... ., ”Maw..." _ . '— 24h+ EL. 05 +3- \»g + (2.;jS 3,03 4152’3‘ 3L 1: 3-2 [63.10 9M“ ; \I._\Q. 25$” 24 13 \M .L -Z C3 g|_;:2-§$_+j "\ €13: Co") (g’v‘QLB :— Co$ G; :2 C03 (+0” fi§>> A m ww some mi a wewr A: chz-ru W m c/& (36% (L We \0: W30‘ (1H) : 9.9 4X0 ++fem Jqfidtld't) . a) 9“ “5‘3 “W m 4 1+:— 35 m) as a bamdeel papal» will ' ? " "L + u+ [L0H f3 (1. i) U0) 6". Q bounded 01/ P - [Q(0)é#(l+ii)+cllo):4‘ * 3'4, and + + ‘4 .. __,- ‘Yr +e,’+ ' 2:6 - Woke ‘1“ (ow—g 6' are, bounded, ‘ * / + C +-‘t nun '/ 342 f z 5% ”‘3’ ‘5‘ ‘2 0M: - -L-‘z “way/2 ‘2’“ 0 Jr , 4 ,. t;— ,1 :6 drc . -ii.‘ 4-153: -3 o z 2 4 .4 4 4 Jaw: 4;}th +2f'Ld'L ‘4' _4_242+41-(+1++)e:+du‘)v .. a ' 44424341“ «3195* UH) 9 ...
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