Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2004 Quiz 3 28 April 2004 Name Instructor Time Kassakian 10 Kassakian 11 Wilson 12 Berggren 1 Berggren 2 Please put your name in the space provided above and circle the name of your recitation instructor together with the time of your recitation Do your work for each question within the boundaries of the question When nished write your answer to each question in the corresponding answer box that follows the question This is a closed book quiz but calculators are allowed Graded quizzes will be returned in tutorial on Monday May 3 and also in Recitation on Wednesday May 5 If you do not attend tutorial and or recitation on those days then it is your responsibility to get your quiz from your recitation instructor You will have until Monday May 17 to request a quiz grading review regardless of whether or not you attend tutorial on Monday May 3 and take back your quiz If you wish to have your quiz grade reviewed you must return your quiz to your recitation instructor within the two week period together with a written explanation of why you think a grading mistake was made This is the only way in which a quiz grade will be reviewed Good luck Problem 1 Problem 2 Problem 3 Total Grade Problem 1 20 This problem focuses on the circuit shown below which contains a constant current source two switches a capacitor and an inductor Prior to t 0 the two switches are closed and the capacitor and inductor are both at rest vC iL C I 1A S1 S2 L 5 At t 0 switch S1 opens Determine the capacitor voltage vC and the inductor current iL at t T vC T iL T 1B 5 At t T switch S2 opens and then switch S1 closes immediately thereafter Determine the time at which the capacitor voltage vC next goes to zero t 1C 5 Determine the inductor current iL when the capacitor voltage vC goes to zero as described in Part B iL 1D 5 When the capacitor voltage vC goes to zero as described in Part B switch S2 closes and then switch S1 opens immediately thereafter After a further period of duration T switch S2 opens and then switch S1 closes immediately thereafter Determine the inductor current iL when the capacitor voltage vC next goes to zero iL Problem 2 35 The circuit shown below contains a capacitor an inductor and a MOSFET Its purpose is to deliver a pulse of current to the inductor Model the MOSFET as a switch having on state resistance RON Prior to t 0 vC V iL 0 and the MOSFET is held o by vIN For t 0 the MOSFET is turned on by vIN iL vC L C 2A vIN 15 Derive an expression for the inductor current iL for t 0 In doing so assume 2 that C satis es C 4L RON iL t 0 2B 10 It is desired that the inductor current iL be a single pulse of minimal time duration with no reversal in sign Determine the value of C that achieves this objective 2 C need not satisfy C 4L RON C 2C 10 Determine the peak or maximum positive value of the inductor current iL given the design of Part B Peak iL Problem 3 45 This problem focuses on the network shown below It contains a current source a capacitor an inductor and two identical resistors It also has a single port Except for the last part of this problem the network operates in the sinusoidal steady state with the sourced current taking the form iS t I cos t For the last part of this problem the network is at rest until the sourced current takes a step of the form iS t Iu 1 t R iS 3A L C R vO 10 The output voltage vO at the port takes the form vO t V cos t in sinusoidal steady state Determine V and V 3B 10 The sinusoidal steady state Thevenin equivalent of the network as viewed from its port is shown below Determine the parameters VTH TH and Z TH that de ne the equivalent Note that Z TH is the complex Thevenin equivalent impedance ZTH VTH cos t TH VTH TH Z TH The gures shown below present a numerical evaluation of the magnitude V and the phase of vO as functions of frequency for the speci c case of I 100 mA Use this numerical evaluation to answer Parts C and D of this problem 1 vO Magnitude V 10 0 10 1 10 2 10 2 10 3 10 4 Frequency rad s 10 5 10 vO Phase Degrees 100 50 0 50 100 2 10 3 10 4 Frequency rad s 10 5 10 3C 15 Determine the numerical values of R L and C Remember to include units R L C 10 Assuming the network is at initially rest which of the following gures corresponds to vO for t 0 given that iS t 100 mA u 1 t 0 5 0 5 Figure B vO V vO V Figure A 0 0 5 0 1 2 Time ms 3 0 0 5 4 0 5 0 1 2 Time ms vO V vO V 0 1 2 Time ms 3 0 0 5 4 0 5 0 1 2 Time ms 3 4 0 5 Figure F vO V Figure E 0 0 5 4 Figure D 0 0 5 3 0 5 Figure C vO V 3D 0 1 2 Time ms Circle One A 3 4 B 0 0 5 C 0 1 D 2 Time ms E 3 4 F
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