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2006ENS203_2006_Midterm_Sol

# 2006ENS203_2006_Midterm_Sol - Question 1(20 Points Consider...

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Unformatted text preview: Question 1 (20 Points) Consider the circuit given in the following figure: In the above circuit, V1 = 10V, V2 = 9V, V3 =1V, R1 = 50, R2 = 100, R3 = 50, R4 = 50 a) Write mesh currents in the circuit above and solve for mesh currents. b) Determine the voltages across the resistors Vm, VR2, VR3, VR4. V1 ___ Q‘i,‘ +Vz+ R1(:i_—IL) \JZ‘t‘ R1 (I\FT2> 7'- 23,11 +\/3 ’i" '12, 10:5.11—r9 +io(1.~11) —> Fag-{\$1.40}; E 9+ro(L—1J:5‘[email protected] (Sch/W ’H’m Quah‘wu: 2:goI,._2°IL [O 20]: 8:- 3 = i ‘01! +7.01; _> Tim/L VR135ﬂ\$2.SV g:—§+7DIL Vim: ion x (OS-0.65»; -15 v 11‘— 0'“ A i We —_ 5n 1 (0.53%: 12'; v Vfu‘t : Sin— 3‘ 0.63); : \/ Question 2 (20 Points) 3V] "ZVX =30 +Vx W2 ‘3er-‘0 > 3V1 \$011414) =30 4N2 4024/1) =40 Lu :3; 2 equa+u‘ons 02 van knowns... Question 3 (20 Points) Consider the circuit given in the following figure: 81 +VC - \ 10V In the circuit above C = 1uF, R = 1KQ. The capacitor is initially discharged and both switches are open prior to t=0. At time t=0, the switch S1 is closed while switch 82 remains open. quaq‘lor U9 Cam noi‘ 051(1an 3) Determine the following: mffmignwgd +) O l. Vc(0-) and vc(o+) —/”’ ‘(O = ‘ (0 — ll. VR(O') and VR(O+)/—‘> VR(O_)=O EMA” VR(0+)= iOV m. |c(0-) and IC(0+) a I<(o')=0 Lie“ 2 %ziomA we» Ia<o+> —> lam—ho , :1 (0”):1omA b) Redraw the circuit after t>0 and solve the differential equation for Vc(t>0) and VR(t>0)i c What is the time constant of the circuit? ) d) At t=23ec switch S1 is opened and switch 82 is closed. Find VR(t>2). ) 9 Sketch )\/R(t) for all t. V<(+ - ~ L) + He + C) MC a 70 i V C + e: - .1 F: t ° R VaH-J ” 1M" ‘ ’3: ’imiec Van); A +Be MW “RC Vc(0)=O 5° (A+B=O "D Bz—A M A )OCLOMM A:10\/ \ r -'é/RC Vc(+): io—loe ~‘L/RC “41(4): 10v h Vcw : 10 6 WM [0" CD 4; Now a} 4:2 Sec 51.34614 51 75 919% and 52 :5 Clcxccl--, Chou” F5 ot+ 3+earjj J‘fa‘tg SIMLQ "c u‘; i msec anal 2 Lu 3‘; alwayf MﬂMT-ﬁ‘j (“JV-Ha raped +° 'H’L‘ ,L‘w cons+q4+'_ Question 4 (20 Points) Consider the circuit given above: a) What is Vom at very high frequencies, ie., as u) a no ? (Explain why in one sentence.) b) What is Vout at very low frequencies, ie, as m —> 0 ’? (Explain why in one sentence) ' V0”! 0) Solve forthetransferfunctionH(ca)= V . i d) Draw the magnitude and the phase BODE plots indicating the important point such as break frequencies, amplitudes in dB and slopes, etc. in terms of R and C. (1’) high cachﬂlo; is Sker‘l... 31—)0V 2'4? 1‘“ V‘H/f = VI—V1 am fV|->\JM ’Vl—ao —D V°U+T~ Vin 1 C) New W m v1: Lava 1— + R — 143‘“ 3%, L} {ow -—) V2: R 1 Vi“ : Jugc Ul‘Vl R+':‘ 10““ (\9 Quesnou 4 ad. Question 5 (20 points) Consider the circuit given in the following figure: R1 1311(7) : 5cm<1or + 30”) C =10mF, L = 0.25H, and R1: R2 = R3 =1OQ, in circuit above: Find Norton equivalent of the circuit to the left of the inductor and the capacitor first. Then, a) Find the output voltage Vout(t). b) Find the inductor current. 0) Find the capacitor current. [Write the voltages and currents exactly in time domain notation, like Acos(wt + 0) ] (ML d) What is the resonance frequency, we of the circuit? loSL U V M --‘) :1 l Vin (057. 551 ml 5 g ‘L Vouf : 2 14306 / cm! 1_ 3 +1 + 1 #7 3J4}; _1 2:7- I—5 .J'Io J10 (j) (y) H) ...
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