ECE 201 Spring 2010 Exam 3 Wednesday April 14 2010 Division 0101 Prof Capano 9 30am Division 0201 Prof Tan 10 30 am Division 0301 Prof Jung 7 30 am Division 0401 Prof Capano 11 30am Instructions 1 DO NOT START UNTIL TOLD TO DO SO 2 Write your Name division professor and student ID PUID on your scantron sheet 3 This is a CLOSED BOOKS and CLOSED NOTES exam 4 There is only one correct answer to each question 5 Calculators are allowed 6 If extra paper is needed use back of test pages 7 Cheating will not be tolerated Cheating in this exam will result in an F in the course 8 If you cannot solve a question be sure to look at the other ones and come back to it if time permits 9 As described in the course syllabus we must certify that every student who receives a passing grade in this course has satisfied each of the course outcomes On this exam you have the opportunity to satisfy outcomes iii iv v and ix See the course syllabus for a complete description of each outcome On the chart below we list the criteria we use for determining whether you have satisfied these course outcomes If you fail to satisfy any of the course outcomes don t panic There will be more opportunities for you to do so Course Outcome iii iv v ix Exam Questions 9 1 6 11 14 7 10 Total Points Possible 7 42 28 28 Minimum Points required to satisfy course outcome 7 21 14 14 10 You will find formulas on the final page of this exam You can tear the page out if you want to Page 1 1 At t 0 sec the inductor current is iL 0 5A and the capacitor voltage is vc 0 0V Find vc t for t 0 s in V vc t 25sin 106 t vc t 12 5cos 103 t 4 vc t 12 5cos 103 t 12 5sin 103 t 6 vc t 12 5sin 103 t 1 vc t 25cos 106 t 25sin 106 t 3 5 2 vc t 25cos 106 t 7 vc t 0 2 Find the resistance R which causes the roots of the characteristic equation s2 bs c 0 to be identical for circuits a and b below 1 1 2 2 3 3 5 5 6 6 7 7 Page 2 4 4 3 In the circuit below calculate diL 0 dt in A s assuming iL 0 0 A and vc 0 50 V 1 10 000 2 20 000 3 36 5 5 000 6 60 7 8 000 4 The inductor current response for the circuit below is i L t Find the initial condition vc 0 in V 1 24 2 12 3 0 5 24 6 36 7 48 Page 3 4 40 20 160t e 20t 4 12 for t 0 sec 5 In the circuit shown below vc 0 1V and iL 0 0A Which curve represents vc t Hint You don t need to find the exact equation for vc t 1 0 0 2 0 5 vC t 0 4 vC t 0 6 0 0 5 1 0 8 0 0 05 0 1 0 15 1 0 2 0 05 0 1 t 1 2 0 0 15 0 2 0 15 0 2 1 0 2 0 5 0 4 vC t 0 6 vC t 0 0 5 0 8 1 0 t 0 0 05 0 1 0 15 1 0 2 0 0 05 0 1 t t 3 4 1 1 0 8 0 8 0 6 0 6 vC t vC t 0 4 0 4 0 2 0 2 0 0 0 05 0 1 0 15 0 0 2 0 0 05 0 1 t t 5 6 Page 4 0 15 0 2 6 Find R in in the circuit below so that the response vc t is critically damped for t 0 sec 1 0 125 2 0 25 3 0 5 5 2 6 2 5 7 5 4 1 7 In the ideal Op Amp circuit below when vs1 10mV and vs2 5mV vout 15V If vs1 40mV and vs2 7mV find vout in V 1 40 2 26 3 33 5 15 6 35 7 47 Page 5 4 0 8 In the circuit below find vout 1 1 V 2 2V 3 4V 5 1V 6 2V 7 4V 4 8V 9 Determine the Thevenin equivalent resistance RTH and the short circuit current isc for the ideal Op Amp circuit below 1 2 4A 2 2 2A 3 6 4A 5 0 0A 6 6 2A 7 4 2A Page 6 4 4 6A 10 Find the output voltage vout t in V for t 0 sec for the ideal Op Amp circuit below assuming that vc 0 2V 1 12 e 2t 2 6 2 e 2t 3 6 e 2t 5 10 e 2t 6 6 2 e 2t 7 8 e 2t 4 4 e 2t 11 Calculate the equivalent impedance Zeq in for the circuit below 1 2 53 13 2 2 53 13 3 2 36 7 5 1 40 6 1 40 7 1 45 Page 7 4 2 36 7 12 The circuit shown below is in steady state When vin t 10 cos t vout t 5 cos t Find in rad sec 1 1 2 10 3 100 5 10 000 6 100 000 7 1 000 000 4 1 000 13 The circuit shown below is in steady state Find vL t 1 L t 2 cos 100t 90 L t 2 cos 100t 90 2 3 L t 2 cos 100t 135 2 cos 100t 135 4 L t 5 L t 2 cos 100t 170 2 cos 100t 170 6 L t 7 L t 2 cos 200t 170 Page 8 14 The circuit below is in sinusoidal steady state The phasor voltage and current at 1 rad sec are as shown graphically Find the values of R and C 1 0 1 0 17 F 2 0 1 5 77 F 3 0 2 0 08 F 5 2 5 0 43 F 6 2 5 4 33 F 7 5 4 33 F Page 9 4 0 2 2 89 F Potentially Useful Formulas x t x x t o x e t t o L R RC x t x A cos d t Bsin d t e t x t x A Bt e t x t x Aes1t Bes2 t b b 2 4c 1 for s 2 bs c 0 where c LC 2 s1 s 2 R 2L series b 1 2 parallel 2RC o 1 LC s1 2 2 o2 d 4c b 2 2 o2 2 Page 10
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