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Unformatted text preview: EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 1 (20 points) Resistance and resistivity A friend of yours bought new 4‐Ω speakers for his audio system and asked you to determine how far from the output amplifier he could put them using No. 20 AWG aluminum wire. As a knowledgeable EECS 314 student, you solve the problem assuming that the wire resistance should be kept below 5% of the speaker resistance so that at least 95% of the output power reaches the speaker. Part 1 (5 points) Draw the equivalent circuit diagram of the setup (in each channel): show the output amplifier as a voltage source VS; the speaker as a load resistor RLOAD; and the connecting wires as additional resistances RWIRE. Your circuit diagram: Part 2 (15 points) Calculate the maximal distance between each speaker and the amplifier, in meters. L Provide two answers: (1) based on your calculations using the equation R = ! " A and (2) based on the resistance per km data listed in the Table (see the Table on the next page); and discuss whether these answers agree. Note that the table shows resistance per km for copper, not aluminum. Show your work on the other side. Write your answers below: Maximal distance, meters Based on calculations Based on the Table date © 2011 Alexander Ganago Last printed 1/20/11 6:01 PM Page 1 of 2 File: 2011 W 314 HW 3 p1.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Table AWG gauge 0000 0 20 24 30 36 Conductor diameter, inches 0.46 0.3249 0.032 0.0201 0.01 0.005 Conductor Ohms per diameter, mm km (copper) 11.684 0.16072 8.25246 0.322424 0.8128 33.292 0.51054 84.1976 0.254 338.496 0.127 1360 Maximum amps (copper) for power transmission (conservative rule) 302 150 1.5 0.577 0.142 0.035 Problem 1 Workspace © 2011 Alexander Ganago Last printed 1/20/11 6:01 PM Page 2 of 2 File: 2011 W 314 HW 3 p1.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 2 (30 points) Potentiometer used as a part of a liquid level sensor The diagram below shows a linear potentiometer used is used to measure the amount of liquid in a cylindrical tank. This is similar to how your fuel gage measures how much gas you have in the tank of your car. Assume the following parameters: the cross‐section area of the tank equals S = 720 cm2; the length of the linear potentiometer (from A to B) equals L = 24 cm; the middle position of the potentiometer’s tap corresponds to the liquid level equal to H = 15 cm; the total resistance of the potentiometer is RP = 120 kΩ; the source voltage is VS = 14 V. Part 1 (10 points) Evidently, the circuit’s readings are accurate only if the volume of liquid in the tank P remains within certain limits: if the float moves too low, the output voltage equals zero regardless of the amount of liquid; if the float moves too high, the output voltage saturates at VS regardless of the amount of liquid. Obtain and record the algebraic expressions for PMIN and PMAX in terms of S, L, and H. Neglect the volume of the float. PMIN = _________________________ PMAX = _________________________ Calculate and record below the minimal and maximal volumes of liquid in the tank PMIN and PMAX in liters (1 liter = 1,000 cm3) that can be accurately measured with this circuit. PMIN = _________________________ © 2011 Alexander Ganago Last printed 1/20/11 6:19 PM PMAX = _________________________ Page 1 of 2 File: 2011 W 314 HW 3 p2.doc Show your work on additional pages. EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 2, continued Part 2 (10 points) The output voltage can be expressed as VOUT = K ⋅ VS. When the volume of liquid in the tank varies between PMIN and PMAX , the coefficient K varies between 0 and 1. Derive and record the algebraic expression for K in terms of S, L, H, RP, and VS. K = Use the given numerical values to calculate the volume of liquid in the tank (in liters) P¾ that corresponds to VOUT = ¾ VS. P¾ = _________________________ Part 3 (10 points) Assume that the error of the voltage readout is ΔVOUT = 10 mV. Calculate the error of the readout in liters ΔP. ΔP = __________________________ Consider the list of measures for reducing the error ΔP (each measure assumes that only one parameter is altered, while all the rest remain as listed above). Circle the good ones. Increase RP Increase L Increase VS Increase H Increase S Decrease RP Decrease L Decrease VS Decrease H Decrease S © 2011 Alexander Ganago Last printed 1/20/11 6:19 PM Page 2 of 2 File: 2011 W 314 HW 3 p2.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 3 (40 points) Resistive temperature sensors in voltage dividers In this and the following problem, refer to the files “US sensor catalog p.40” and “Vishay Beyschlag catalog” on CTools. Part 1 (15 points) Consider circuit 1 with VS = 12 V, R1 = 1,500 Ω, and RSENSOR = 1,000 Ω at 0˚C – a temperature‐dependent resistor made by Vishay Beyschlag. Make a computer‐ generated plot of the output voltage VOUT, 1 as function of temperature from –40 ˚C to +140 ˚C. For simplicity assume that RSENSOR (T ) = RSENSOR (T = 0 ) ! (1 + 0.004 ! T ) , where T is temperature in ˚C, and RSENSOR (T = 0 ) = 1,000 Ω. Given that the error of voltage measurements equals 10 mV, estimate the error of temperature measurement in ˚C at –40 ˚C and at +140 ˚C. Your answers: Error at –40 ˚C equals _________________ ˚C; Error at +140 ˚C equals ________ ˚C. Show your work below and/or on additional page. Page 1 of 2 File: 2011 W 314 HW 3 p3.doc © 2011 Alexander Ganago Last printed 1/20/11 10:16 PM EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 3 Part 2 (15 points) Consider circuit 2 (see page 1) with VS = 12 V, R1 = 1,500 Ω, and RSENSOR = 1,000 Ω at 25˚C – a thermistor made by US Sensor. Make a computer‐generated plot of the output voltage VOUT, 1 as function of temperature from –40 ˚C to +140 ˚C. Use the data from the table (a point every 10 ˚C is enough). Given that the error of voltage measurements equals 10 mV, estimate the error of temperature measurement in ˚C at –40 ˚C and at +140 ˚C. Your answers: Error at –40 ˚C equals _________________ ˚C; Error at +140 ˚C equals ________ ˚C. Show your work below and/or on additional page. Part 3 (10 points) Briefly compare the temperature measurements with the two sensors (use your results obtained in Parts 1 and 2). Answer the following questions: Which sensor provides smaller errors in temperature measurements? Does any of these sensors provide nearly the same error over the entire temperature range? Which sensor would you prefer in your project, and why? © 2011 Alexander Ganago Last printed 1/20/11 10:16 PM Page 2 of 2 File: 2011 W 314 HW 3 p3.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 4 (40 points) Resistive temperature sensors in voltage dividers In this problem, refer to the files “US sensor catalog p.40” and “Vishay Beyschlag catalog” on CTools. Take advantage of your results in Problem 3 of this set. Part 1 (15 points) Consider circuit 3 with VS1 = 12 V, R2 = 1000 Ω, RSET = 1,500 Ω, RA = 1,200 Ω, and RT = 1,000 Ω at 0˚C – a temperature‐ dependent resistor made by Vishay Beyschlag. Make a computer‐generated plot of the output voltage VOUT, 1 as function of temperature from –40 ˚C to +140 ˚C. For simplicity assume that RSENSOR (T ) = RSENSOR (T = 0 ) ! (1 + 0.004 ! T ) , where T is temperature in ˚C, and RSENSOR (T = 0 ) = 1,000 Ω. Given that the error of voltage measurements equals 10 mV, estimate the error of temperature measurement in ˚C at –40 ˚C and at +140 ˚C. Your answers: Error at –40 ˚C equals _________________ ˚C; Error at +140 ˚C equals ________ ˚C. Show your work below and/or on additional page. © 2011 Alexander Ganago Last printed 1/20/11 10:15 PM Page 1 of 2 File: 2011 W 314 HW 3 p4.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 3 Part 2 (15 points) Consider circuit 4 with VS = 12 V, R2 = 1,000 Ω, RSET = 1,500 Ω, RA = 1,200 Ω, and RT = 1,000 Ω at 25˚C – a thermistor made by US Sensor. Make a computer‐generated plot of the output voltage VOUT, 1 as function of temperature from –40 ˚C to +140 ˚C. Use the data from the table (a point every 10 ˚C is enough). Given that the error of voltage measurements equals 10 mV, estimate the error of temperature measurement in ˚C at –40 ˚C and at +140 ˚C. Your answers: Error at –40 ˚C equals _________________ ˚C; Error at +140 ˚C equals ________ ˚C. Show your work below and/or on additional page. Part 3 (10 points) Briefly compare the temperature measurements with the two sensors (use your results obtained in Parts 1 and 2). Answer the following questions: Which sensor circuit provides smaller errors in temperature measurements? Does any of these sensor circuits provide nearly the same error over the entire temperature range? Which sensor circuit would you prefer in your project, and why? © 2011 Alexander Ganago Last printed 1/20/11 10:15 PM Page 2 of 2 File: 2011 W 314 HW 3 p4.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 5 (50 points) Measurements of voltage and current Part 1 (10 points) In order to measure the voltage across a resistor, we connect the voltmeter in parallel with this resistor as shown on the diagram for a circuit of 2 identical resistors, with a voltmeter connected to measure the voltage across one of them. Calculate voltage VX measured by the voltmeter in terms of the source voltage VS and resistances R and RV V Also, calculate the ratio of the measured voltage to the original voltage X V
in terms of resistances R and RV = VX 1 VS 2 V Write your result: X V = Show your work. Use additional pages as needed. Part 2 (10 points) Assume that the voltage in the circuit above is measured with a good voltmeter, which has RV = 500 MΩ, and a so‐so voltmeter, which has RV = 5 MΩ. Calculate the error of measurement, or percentage difference: % Difference = R = 10 Ω, 10 kΩ, 10 MΩ. Keep the sign. Write your results in the table. Good voltmeter 10 Ω 10 kΩ 10 MΩ VX ! V " 100% for 3 values of the resistances in the circuit: V
So‐so voltmeter 10 Ω 10 kΩ R Error of voltage measurement 10 MΩ © 2011 Alexander Ganago Last printed 1/21/11 12:09 PM Page 1 of 3 File: 2011 W 314 HW 3 p5.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Problem 5 Part 3 (10 points) In order to measure the current through a resistor, we connect the ammeter in series with this resistor as shown on the diagram for a circuit of 2 identical resistors. Calculate current IX measured by the ammeter in terms of the source current IS and resistances R and RA Also, calculate the ratio of the measured current to the Winter 2011 Homework set 3 I original current X I = IX in terms of resistances R and RA 1 IS 2 Write your result: IX = I Show your work. Use additional pages as needed. Part 4 (10 points) Assume that the current in the circuit above is measured with a good ammeter, which has RA = 0.1 Ω, and a so‐so ammeter, which has RA = 0.5 Ω. Calculate the error of measurement, or percentage difference: % Difference = = 1 Ω, 1 kΩ, 1 MΩ. Keep the sign. Write your results in the table. IX ! I " 100% for 3 values of the resistances in the circuit: R I
Good ammeter 1 Ω 1 kΩ 1 MΩ 1 Ω So‐so ammeter 1 kΩ 1 MΩ R Error of current measurement © 2011 Alexander Ganago Last printed 1/21/11 12:09 PM Page 2 of 3 File: 2011 W 314 HW 3 p5.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 5 Part 5 (10 points) In the following text circle the correct adjectives: With the given instruments, measurements of currents are more accurate in circuits with small/large resistances R, while measurements of voltages are more accurate in circuits with small/large R. With the given resistances in the circuit, measurements of voltages are more accurate with voltmeters that have small/large internal resistances RV, while measurements of currents are more accurate in circuits with ammeters that have small/large internal resistances RA. Justify your answers using your results in Parts 1 – 4 of this problem. © 2011 Alexander Ganago Last printed 1/21/11 12:09 PM Page 3 of 3 File: 2011 W 314 HW 3 p5.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 6 (40 points) Digital Multimeters (DMMs): Functionality and Accuracy, or Why Would Anyone Pay Double Price? In this problem, you will compare two models of hand‐held DMMs by a well‐known manufacturer. The information provided in the manufacturer’s documents and the conclusions you draw upon comparison serve purely educational purposes: they do not constitute any advertisement, promotion, or recommendation for purchase and specific applications. Refer to the files “Fluke 113 manual” and “Fluke 175 manual” [note that 3 models are covered by this manufacturer’s file] on CTools for comparison between model 113 (current price of this DMM ~ $120) and model 179 (current price ~ $260). Part 1 (20 points) Compare the functionality and specifications of the two models: fill the table below: Allows DC voltage (DCV) measurements: Yes/No Impedance (input resistance) for DCV measurements Minimal range of DCV measurements (low voltages) Resolution of DCV measurements (at low voltages) The highest DCV that can be measured with this DMM Allows AC voltage (ACV) measurements: Yes/No Impedance (input resistance) for ACV measurements Minimal range of ACV measurements (low voltages) The highest ACV that can be measured with this DMM Allows frequency measurements of ACV: Yes/No Frequency range for ACV measurements © 2011 Alexander Ganago Last printed 1/21/11 12:18 PM Page 1 of 3 Model 113 Model 179 File: 2011 W 314 HW 3 p6.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 6 Part 1, continued Allows DC current measurements (Yes/No) Model 113 Model 179 Minimal range of DC current measurements (low currents) Resolution of DC current measurements (at low currents) The highest DC current to be measured with this DMM Allows AC current measurements (Yes/No) Minimal range of AC current measurements (low currents) Resolution of AC current measurements (at low currents) The highest AC current to be measured with this DMM Allows frequency measurements of AC current: Yes/No Frequency range for AC current measurements Allows resistance R measurements: Yes/No The range of R measurements (lowest to highest) Resolution of R measurements (lowest resistances) Resolution of R measurements (highest resistances) Accuracy of R measurements (lowest resistances) Accuracy of R measurements (highest resistances) Allows capacitance measurements: Yes/No Allows continuity measurements: Yes/No Allows diode test measurements: Yes/No © 2011 Alexander Ganago Last printed 1/21/11 12:18 PM Page 2 of 3 File: 2011 W 314 HW 3 p6.doc EECS 314 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructoris not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Winter 2011 Homework set 3 Problem 6 Part 2 (10 points) Consider the following applications and write your conclusions on which DMM models are adequate: fill the table below: in columns 2 and 3 write YES or NO. Measurements of DC and AC (60 Hz) voltages from 2 V to 240 V Measurements of DC and AC (60 Hz) voltages from 2 V to 980 V Measurements of DC and AC (60 Hz) voltages from 2 V to 240 V and currents from 0.2 A to 5 A Measurements of DC and AC (60 Hz) voltages from 2 V to 240 V and currents from 2 A to 25 A Measurements of resistances from 100 Ω to 20 kΩ Measurements of resistances from 100 Ω to 200 kΩ Model 113 Model 179 Part 3 (10 points) In the list below, circle valid justifications for purchase of the more expensive DMM; if needed, refer to Part 1 and the manufacturer’s specs. • More types of measurements are available • Broader range of parameters (V, I, R) can be measured • Better resolution at low values of parameters (V, I, R) • Better resolution at high values of parameters (V, I, R) • Fancier body style of the instrument • Higher accuracy of measurements • Broader range of frequencies • Easier operation (fewer terminals for connections to the circuit) • The more advanced model is significantly lighter than the simple one • Only the more expensive model allows temperature measurements • Only the more expensive model allows diode tests. © 2011 Alexander Ganago Last printed 1/21/11 12:18 PM Page 3 of 3 File: 2011 W 314 HW 3 p6.doc ...
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This note was uploaded on 03/20/2011 for the course EECS 314 taught by Professor Ganago during the Spring '07 term at University of Michigan.
 Spring '07
 Ganago

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