Name: Instructor:ID #: Class Time:EE 201/201C Final Exam December 11, 1996General Instructions:• The exam is closed book, closed notes, no calculator.• Do not open the exam until you are told to begin.• Put your name, student identification number, and instructor name in the blanksabove. Fill in your name, student identification number, and section number in theappropriate places on the computer scan forms.Time Instructor Section Number7:30 am Krogmeier (EE201C) 00018:30 am Nyenhuis (EE201) 000211:30 am Doerschuk (EE201) 00032:30 pm Krogmeier (EE201C) 0004• The exam consists of 14 multiple choice questions (10 points each) and 4 workoutproblems (15 points each).• Please keep your computer scan sheets covered while you are working on the exam.• An official crib sheet will be handed out separately.1Name:Problem 1. Consider the circuit shown. The switch has been closed for a long time beforeit is opened at time t = 0. What is the current iC(0+) into the capacitor at time t =0+(inAmperes)?(1) 1 (2) 2 (3) 0(4) 0.5 (5) -2 (6) -0.5(7) 7t =0+--15 V20 Ω10 Ω1 FiCProblem 2. Consider the circuit shown below. The switch has been closed for a long timebefore it is opened at time t = 0. What is the voltage vL(0+) across the inductor just afterthe switch is opened (in Volts)?(1) -20 (2) -10 (3) 0(4) 10 (5) 5 (6) 15(7) 20+--t =0+--10 V10 Ω1 HLv10 Ω2Name:Problem 3. Consider the sinusoidal steady state circuit shown below. Choose R and Csuch that maximum average power is absorbed in the resistor RL. Hint: do not try to applythe maximum power transfer theorem here.(1) R =0Ω,C =0.01 F (2) R =5Ω,C =0.01 F (3) R = 100 Ω, C =0.1F(4) R =10Ω,C =0.01 F (5) R =10Ω,C =1.01 F (6) R =6Ω,C =0.001 F(7) R =0Ω,C =0.05 F+--100 cos(1000t) VRC10 H-4LR = 10 ΩProblem 4. Consider the circuit shown below which appears in the equivalent circuit fora common collector transistor amplifier. What is an expression for the Thevenin equivalentresistance seen between the two terminals shown?(1) rπ+(β0+1)RE(2) rπ+ RE/(β0+1) (3) rπ(4) rπ+ RE(5) β0rπ+ RE(6) RE(7)rπRErπ+(β0+1)RErπibREβ0ibRT3Name:Problem 5. For the following circuit, choose the correct set of nodal equations. Answers:(1)−i(t)+va(t)−vb(t)R1=0vb(t)−va(t)R1+vb(t)−v(t)R2+ Cdvb(t)dt=0(2)i(t)+va(t)−vb(t)R1=0vb(t)−va(t)R1+vb(t)−v(t)R2+ Cdvb(t)dt=0(3)−i(t)+va(t)−vb(t)R1=0vb(t)−va(t)R1+vb(t)−v(t)R2− Cdvb(t)dt=0(4)−i(t)+va(t)−vb(t)R1=0vb(t)−va(t)R1+vb(t)−vc(t)R2+ Cdvb(t)dt=0vc(t)−vb(t)R2+ v(t)=0(5)i(t)+va(t)−vb(t)R1=0vb(t)−va(t)R1+vb(t)−vc(t)R2+ Cdvb(t)dt=0vc(t)−vb(t)R2+ v(t)=0(6)ni(t)+vb(t)−v(t)R2+ Cdvb(t)dt=0(7)ni(t)+vb(t)−v(t)R2− Cdvb(t)dt=0+--Cv(t)i(t)R1vavbvcR24Name:Problem 6. Compute the Thevenin equivalent of the circuit drawn below at the a-b termi-nals. Answers:(1) Voc=4V,Rth=2Ω (2) Voc=2V,Rth= −1Ω (3) Voc=0V,Rth=4Ω(4) Voc=4V,Rth= −4Ω (5) Voc=2V,Rth=1Ω (6) Voc=6V,Rth=4Ω(7) Voc=1V,Rth=1Ω+--8 V2 Ωab1 Ω2 Ω2 ΩProblem 7. Compute the Thevenin equivalent of the circuit drawn below at the a-b termi-nals. Answers:(1) Voc=4V,Rth=2Ω (2) Voc=2V,Rth= −1Ω (3) Voc=0V,Rth=4Ω(4) Voc=4V,Rth= −4Ω (5) Voc=2V,Rth=1Ω (6) Voc=6V,Rth=4Ω(7) Voc=1V,Rth=1Ω+--2 A2 ΩabVx2Vx2 Ω5Name:Problem 8. The steady state solution for the capacitor voltage is of the formvC(t) = 3 cos(ωt + θ)V.Find θ (in degrees).(1) 45◦(2) −45◦(3) −90◦(4) 90◦(5) 30◦(6) −30◦(7) 60◦RC+- 5 cos(ωt) Av (t)CProblem 9. For the RLC circuit and current source waveform shown below, find thecapacitor current iCat t =0+(in Amperes).(1) −2 (2) 2 (3) −4 (4) 4(5) −5 (6) 3.5 (7) −3.54 A0 A0ti (t)s+--50 Ω1 F1 H5 ViC50 Ωi (t) s6Name:Problem 10. The capacitor voltage in the RLC circuit shown below is of the formvC(t)=(A + Bt)e−σtfor t>0.Find the value of R (in Ohms).(1) 1 (2) 2 (3) 3 (4) 4(5) 5 (6) 6 (7) 710 A1/4 Ω1 mF16 mHt = 0vC+-RProblem 11. Determine the effective (rms) value (in V rms) of the voltage waveform:v(t) = 5(1 + cos ωt)V.(1) 5p3/2 (2) 5√2/2 (3) 5√2 (4) 5+5√2(5) 5 (6) 6 (7) 107Name:Problem 12. Compute Vofor the circuit drawn below. Answers:(1) V0= −RfRsVs(2) V0=+RfRsVs(3) V0= −Rf+RoRsVs(4) V0=+Rf+RoRsVs(5) V0= −RfRo(Rf+Ro)RsVs(6) V0=+RfRo(Rf+Ro)RsVs(7) V0= −RL(RL+Rf)RsVs+--+--+--idealRsRfRoRLVsVoProblem 13. Compute Vafor the circuit drawn below. Answers (in Volts):(1) 1 (2) 2 (3) 3 (4) 0(5) -3 (6) -2 (7) -1+--+--+--+--3 Ω3 VVa2 Ω4 Ω2 Ω1 Ω2 V1 V8Name:Problem 14. Compute I for the circuit drawn below. Answers (in Amperes):(1) 1 (2) 2 (3) 3 (4) 0(5) -3 (6) -2 (7) -12 A1 A3 A4 A8 Ω14 Ω3 Ω2 Ω12 Ω1 Ω4 Ω10 ΩI9Name:Workout Problems. There are four workout problems contained in the following pages.Each is worth 15 points. In order to receive credit for these problems, your workmust be shown and your final answers must be in the boxes provided.Workout Problem 1. (15 points)In the circuit shown below assume an ideal OP AMP. Find the correct expression for thevoltage v0(t)fort ≥ 0. Assume that the capacitor voltage is zero at t =0−.+--+--+--idealR1R2R3Cv (t)ot = 01 Vv0(t)=10Name:Workout Problem 2. (15 points)The source in the circuit below is operating at 10 Vrms with radian frequency 40 radi-ans/second. The load in the box is 3000 W at a power factor of 0.6 lagging (i.e., the angleof the load current is smaller than the angle of the load voltage). See the figure. Find:(a) the reactive power absorbed by the load in the box (in VAR).(b) the value of the capacitor C (in F) to adjust the power factor of the combined load tounity (i.e., PF = 1).10 V rms40 rad/secLoad3000 W0.6 powerfactor lagging+--CQload=C =11Name:Workout Problem 3. (15 points)Consider the circuit in the figure with two capacitors. Just before the switch is closed,the capacitor voltages are v1(0−) = 6 V and v2(0−) = 12 V. What is the capacitor voltagev1at time t = ∞? Hint: apply conservation of electric charge.+--t =02 F 1 F20 Ω+--v1v2v1(∞)=12Name:Workout Problem 4. (15 points)The circuit shown below operates in the sinusoidal steady state at frequency ω = 1000radians per second.(a) Compute the input impedance Zin= Rin+ jXin.Rin=Xin=(b) If you could choose any positive values for R, L,andC in the circuit below, is itpossible to achieve Rin< 0? Give a reason (think average power).Yes/No, Reason:2 mH0.5 mF4
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