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: 1Name:__________________________________________ Problem 1 - (10 points) For the Wheatstone bridge circuit shown below determine the Thevenin equivalent circuit seen by resistor RL. R1R3R2R4RLIs 22.071/6.071 Spring 2006 Quiz#1 Page: 2Name:__________________________________________ Problem 2 - (15 points) Using nodal analysis, derive and put in matrix form the equations for the node voltages of the following circuit. VsR1R2R3R4R5v1v2v3 22.071/6.071 Spring 2006 Quiz#1 Page: 3Name:__________________________________________ 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). FourierTransformAdderS1(t)S2(t)S3(t)X(t) Y(f) 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: 4Name:__________________________________________ Problem 4 - (10 points) A certain unknown circuit has the i-v characteristic shown below. Unknowncircuit+-vi vi0-39((Amps.)Volts) 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: 5Name:__________________________________________ 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. 9 V 3 V+_+_RL5 Ω V1 V1 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=5Ω 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: 6Name:__________________________________________ 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. ABunkown linearcircuit 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. RiA 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. ABunkown linearcircuitRiA 22.071/6.071 Spring 2006 Quiz#1 Page: 7Name:__________________________________________ 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. ABunkown linearcircuitRiA10 Ω vm+- 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: 8Name:__________________________________________ 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. V112 V R130 Ω R260 Ω R4100 Ω R380 Ω I110 A abRhheater 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: 9Name:__________________________________________ Blank page: For computation 22.071/6.071 Spring 2006 Quiz#1 Page: 10Name:__________________________________________ Blank page: For computation 22.071/6.071 Spring 2006 Quiz#1 Page: 11Name:__________________________________________ Problem Points 1 2 3 4 5 6 7 Total 22.071/6.071 Spring 2006 Quiz#1 Page: