Name Massachusetts Institute of Technology Department of Nuclear Science and Engineering Department of Electrical Engineering and Computer Science 22 071 6 071 Introduction to Electronics Signals and Measurement Spring 2006 Quiz 1 Please write your name on each page of the exam in the space provided Please verify that there are 12 pages in your exam To the extent possible do your work for each question within the boundaries of the question or on the back side of the page preceding the question Extra pages are also provided for computation Note that the total number of points is 100 Closed book No Calculators 22 071 6 071 Spring 2006 Quiz 1 Page 1 Name Problem 1 10 points For the Wheatstone bridge circuit shown below determine the Thevenin equivalent circuit seen by resistor RL R3 R1 RL Is R2 22 071 6 071 Spring 2006 Quiz 1 R4 Page 2 Name Problem 2 15 points Using nodal analysis derive and put in matrix form the equations for the node voltages of the following circuit R5 R2 v2 v1 R1 22 071 6 071 Spring 2006 Quiz 1 R3 R4 v3 Vs Page 3 Name Problem 3 10 points Signals S1 t S2 t and S3 t are operated upon by the adder resulting in the output signal X t In turn the Fourier transform of signal X t is determined resulting in the signal Y f S1 t S2 t Adder X t Fourier Transform Y f S3 t The Fourier Transform Y f of the signal X t is given on the following plot The vertical axis represents the RMS amplitude of the signal and the horizontal axis is the frequency f in Hz The system is linear and so each peak shown on the Y f versus f plot is associated with only one signal A From the information given above reconstruct the general form of signals S1 t S2 t and S3 t B What is the minimum sampling frequency of signal X t in order to avoid aliasing 22 071 6 071 Spring 2006 Quiz 1 Page 4 Name Problem 4 10 points A certain unknown circuit has the i v characteristic shown below i Unknown circuit v Amps i 0 9 v Volts 3 From the information given in the i v plot determine the Thevenin and the Norton equivalent circuits of the unknown circuit 22 071 6 071 Spring 2006 Quiz 1 Page 5 Name Problem 5 15 points The following circuit was built by a person named Egatlov who did not take 6 071 V1 and V2 are batteries with the voltage and polarity as indicated in the circuit V1 9V V1 3V RL 5 A What is wrong with Egatlov s circuit B Egatlov notices that the batteries were getting warm and that they did not really last that long Your task is to explain to Egatlov why this happens By assuming that each battery has an internal resistance Ri 5 draw the circuit to include the internal resistance of the batteries C Calculate the power dissipated in each battery D Calculate the power dissipated in RL 22 071 6 071 Spring 2006 Quiz 1 Page 6 Name Problem 6 20 points The box shown below represents an unknown linear resistive network for which we would like to obtain the Thevenin equivalent circuit A unkown linear circuit B In order to obtain the Thevenin equivalent circuit we will use a voltmeter to measure the voltage across terminals A B and an ammeter in order to measure the current across A B The voltmeter is an ideal device with infinite input resistance The ammeter is characterized by an internal resistance Ri as shown in the following model A Ri Using the voltmeter you measure a voltage of 20 Volts across A B With the ammeter you perform the following two measurements 1 Connect the ammeter as indicated to measure a current of 2 0 A A A unkown linear circuit Ri B 22 071 6 071 Spring 2006 Quiz 1 Page 7 Name 2 Now by using the following arrangement you measure a current of 1 0 A and a voltage vm 2 0 Volts across the ammeter as indicated A 10 unkown linear circuit A vm Ri B A From the above measurements determine the Thevenin equivalent circuit of the unknown device B Draw the general i v characteristic curve of the unknown device 22 071 6 071 Spring 2006 Quiz 1 Page 8 Name Problem 7 20 points It is desired that the power delivered to the heater by the balance of the circuit as indicated is a maximum a R1 R3 heater 30 V1 12 V 80 R2 60 I1 10 A R4 100 Rh b A Determine Rh for maximum power transfer B What is the maximum power dissipated by the heater C Which source V1 or I1 delivers most of the power to the heater 22 071 6 071 Spring 2006 Quiz 1 Page 9 Name Blank page For computation 22 071 6 071 Spring 2006 Quiz 1 Page 10 Name Blank page For computation 22 071 6 071 Spring 2006 Quiz 1 Page 11 Name Problem Points 1 2 3 4 5 6 7 Total 22 071 6 071 Spring 2006 Quiz 1 Page 12
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