PRE-LAB Report - Due prior to lab (If you need more pages to answer the questions below, staple them together.) Full Name: Lab Section: Khizar Ismail 11 1) 2pts What are the objectives of the lab? Learning Full Title of Experiment: Resistance Measurement Wheatstone to use multimeter and a bridge to measure resistance. Using Resistance measurements for determining material resistivities. 2) 4pts Briefly describe the procedure of the laboratory and the equipment/software that will be used. -Wheatstone Bridge → for measuring unknown resistor R. - Digital Multimeter, unknown resistor fot Wire Spools. The resistance Ra is a decade resistame box adjustable blu and 9999. 1 3) 4pts Briefly describe the theory, including all relevant equations and calculations. R₁ Ra > Rx = Ra R₂ Ra R = P A R2. P (T) = P20 = (1+α (120 R₁ Resistance Measurement Page 2 H R₂ = R₁+ EXPERIMENT 5 Resistance Measurement (inte CORE m5 inside" PILO I. OBJECTIVES 1. To learn how to use a multimeter and a Wheatstone bridge to measure resistances. 2. To use resistance measurements to determine material resistivities. II. EQUIPMENT Wheatstone bridge - used to accurately measure an unknown resistor R, based on known values for the other resistors forming the bridge, i.e. R1, R2, and Ra (see box below). For the bridge used in the lab: - the resistances R1 and R2 can take the values 1, 10, or 100 based on the positioning of two shorting-out plugs on each corresponding arm. Thus, the multiplier factor for this bridge, i.e. R2/R1, can take values from 100 to 1/100. For the example shown in the figure the multiplier is R/R = 10/100 = 1/10. the resistance Ra is a decade resistance box adjustable between 1Ω and 9,999 Ω in 1 increments. Digital multimeter, unknown resistor, wire spools. The Wheatstone Bridge D R₁ 100 10 0000 Ra 1 Metal plugs used for Rshorting-out resistors 10 100 Rx C Figure 1. The Wheatstone bridge used in The Wheatstone bridge, invented by S.H. Christie in 1833, and popularized by C. Wheatstone, is an electronic instrument used when high accuracy resistance measurements are needed. The bridge consists of a network of four resistors, where three are known and adjustable R1, R2 and Ra, while the forth one Rx is the one to be determined. The two resistor branches are bridged by a voltmeter as shown in the figure on the right. If the three known resistances are adjusted so that the voltmeter reads zero, then points B and C will be at the same potential: VB = VC. D the lab. B Rx Ra C ニド This implies that the potential differences between the corners of the bridge satisfy the following: (VDB = VDC (1) In this case, assuming an ideal voltmeter (i.e. very high internal resistance): A VBA = VCA VDB = iR1 = VBA = iR2 VDC 'RafiR₁ = 'Ra liR₂ = i'Rx (2) (3) If equation (2) is divided by equation (3): Ra R2 Rx VCA = i'Rx The last equation can be rewritten as: R2 Rx = Ra R1 (4) Equation (4) provides an accurate way for calculating/measuring the unknown resistor Rx, if the values for Ra and the multiplier ratio R₂/R, required for bridge balancing are known. Resistance Measurement Page 3 ts, aspiring to zation. Possessing ive shifts through collabor ull capabilities. A sharp-mindeu, mize operations, automate processes, - 2022 d by touching them with pended sphere. Set tore ings. rks divi arr C Resistance and Resistivity The resistance of an object to the passage of an electrical current depends on what the object is made off and what is its shape. For a wire shaped object the resistance R is given by: R: (5) where L is the length of the wire, A is the cross-sectional area of the wire and p is the material resistivity. Gold Aluminum Material Resistivity at 20°C Temperature Coefficient e[m] a [K- Silver 1.59×10-8 0.0038 Copper 1.68×10-8 0.0039 2.44×10-8 0.0034 Conductors 2.82×10-8 0.0039 Nickel Silver 21-38×10-8 5x10-7-10-10-3 0.0004 6.40×102 10x1010-1014 10×1022-1024 -0.075 Semiconductors Insulators GaAs Silicon Glass Teflon The table gives examples for the resistivity of different materials. Since the resistivity is dependent on temperature the table list the resistivity values at 20°C (room temperature) P20°c and the also the temperature coefficient a. For conductors the temperature dependence of the resistivity at temperatures close to room temperature can be approximated by: P(T) = P20°c(1+ a(T-20°C)) (6) As seen in the table the resistivities values span orders of magnitude. Thus they provide an easy criteria for classifying materials in terms of their electrical properties. III.PROCEDURE & DATA ANALYSIS CAUTION: At no time should the resistance box R, have all of its dials set to zero. This may result in excessive current through the box which will cause damage to it. A. Resistance Measurement Using 1. Resistance measurement using color codes: Use the color codes specified in "Appendix Resistor Color Codes" to estimate the value of the standard resistor given to you. Make sure you also record the range of acceptable values based on the tolerance color bar. R=6.8 10% 2. Resistance measurement using the digital multimeter (DMM): put the DMM in ohmmeter mode and connect the two resistor leads to the meter. Set the range to get the maximum number of digits displayed. If the display on the meter flashes, this means that you must go up in range. R=7.06 Lohms) R1=100 R21 RA-200 ohme 3. Resistance measurement using the Wheatstone bridge: a. Place your resistor in the section labeled Rx. b. Set the power supply voltage to about 1 Volt. c. Set the decade resistance box to 999 Ohms. d. Set both ratio arms (i.e. R, and R2) to 10. e. Adjust the ratio R2/R, and the decade resistance box until the voltmeter installed across the bridge reads zero. Continue adjusting until you can estimate the unknown resistance Rx with the greatest number of significant digits. Operationally, this means that the most significant decade of the resistance box Ra should have a non-zero resistance reading. For example, if the resistor is 1.23 Ohms, then the resistance box should read 123 Ohms and the ratio R₂/R ance Measurement would be 1/100. Coefficient (K-1 Temperature 38 Conductors ductors مها = 700 1 R PILO R-7 2 f. Calculate R, using equation (4). 100 Question 1: Are the values measured in Step 2 (DMM measurement) and Step 3 (Wheatstone bridge measurement) consistent with the value specified by the manufacturer through the color code? -The valves are pretty close. It is the ± 10% tolerance valve. Question 2: Rank the three methods (best to worst) based on: accuracy: Wheatstone Bridge. DMM color - easiness to use: 1) color code 2) DMM 3) Wheatstone Bridge B. Resistivity Measurement = 452 R approximately very near Close Dear to RA-432 You will now measure the resistance of two wire spools made of Copper and Nickel Silver. Since the wire length and diameter are known, you can use equation (5) to calculate the resistivity of the two materials. Because the resistances of the two spools are very small, we will use the Wheatstone Bridge. R-4324. First, measure the resistance of the Cu and Ni-Ag spools of wire using the Wheatstone Bridge as explained in Step 3 above. Make sure that you obtain values of resistance with the maximum I = 24 number of significant digits. 100 8-2452 R = Rspool of Cu-432- Rspool of nickel-silver = 2.45 5. Record the number of your spools of wire and their lengths. = Lspool of Cu 20m Lspool of nickel-silver= 04 6. The two spools of wire are specified as #28 and #30 respectively based on the American Wire Gauges standard (easily searchable on the internet). Use this information to determine the cross sectional area of the wires. Please not that most websites will list the wire diameter in inches, so you will have to convert it in SI units (i.e.meters): DCu wire = AreaCu wire 32x LO 8.04x 108m2 DNickel-silver wire = AreaNickel-silver wire 7. Use equation (5) to calculate the resistivity of the two materials: Resistance Measurement. Pcu = 1-73 x 10-8 -2/m 4.32×10 omm/m PNickel-silver Ra = 25-4×16-5 -5.06×108 m m² 3.099×10 hom Jan 30 14 1 Hamillo bas A = 2.45x 5.0x 3p 0.4 Page 5 R+ Cof Question 3: Briefly discussed what could the sources of error in the above resistivity measurement: calculation of the area, unit conversion from cm->m. & calculation of Rox car also cause errors. Human error and calculation ferror. 8. Record the temperature in the room: T = 24°C 9. Based on equation (6)(see "Resistance and resistivity" box from page 2) and the temperature coefficient a listed in the table, calculate the resistivities for copper and nickel-silver at 20°C: PCu 20C = 1.70933×108 Valve was Ohmm PNickel-silver 20C= 836810 Omypp 30.04x108 0mm.m Question 4: Is the value you have obtained for the nickel-silver alloy consistent with the accepted range? consistent as it is not in the rang due to compounding given accepted PICU CA +α (T-200 ― exfor Tolerance APPENDIX USING RESISTANCE COLOR CODES Typical resistors have a group of three color bands close to each other, coding the resistance value of the resistor, and a separate single band, coding the manufacturing tolerance. In the group of three color bands, the first two from the left side are to be read as numbers, while the third one as the multiplier. For the example shown in the figure the reading is: brown ("1"), violet ("7"), orange ("x 103"), Silver ("±5%"). Thus the value of the resistor is 17000 2±5%, i.e. 17 ks2 ± 850 2. 1st digit 2nd digit Multiplier Color Corresponding Number Corresponding Multiplier Corresponding Tolerance Black 0 X 1 Brown 1 x 10 ±1% Red 2 x 102 ±2% Orange 3 x 103 Yellow x 104 ±5% Green 5 x 105 ±0.5% Blue 6 X 106 ±0.25% Violet 7 X 107 ±0.1% Gray 8 x 108 ±0.05% White x 109 Gold x 10-1 Silver X 10-2 ±5% ±10% None Resistance Measurement ±20% age Conclusion: we learned to use the wheatstone bridge and multimeter accurately and whose ago for resistance and also learned to myavby using resistare mcarnement Consistent valves get accurate resistivities value/n ***PHY 244 STUDENTS ONLY*** WAC Essay#2 – PHY 244 Provide a brief description of Experiment #5 Resistance Measurement. In your essay you can also discuss the broader implications of the analysis from this lab. - Your essay should be written in size 11 "Times New Roman" font, double-spaced with 1 inch left and right margins. Place your name, the date, course name, professor, and TA in the top right corner of the essay. Your essay must meet the 500-word minimum, headings not included. - Your essay will be checked for plagiarism. If this is detected the penalties specified in the Student Conduct Code will be applied. - Please submit an electronic copy of your essay on Blackboard by the specified deadline. - Grading rubric for your essay: Essay Possible Your Points Score 1. Describe the goals of the experiment. 5 2. Concepts behind the experiment. 15 3. History & importance of the phenomena illustrated, or physical quantity measured. 20 4. Organization & Structure 20 5. Clarity of Expression 20 6. References - Minimum of three, MLA format. 10 7. Punctuality 10 Essay Score 100 IF ESSAY IS NOT ACCEPTED: REVISE AND BE SURE TO INCLUDE THE ORIGINAL ESSAY AND SCORING RUBRIC WITH THE REVISION. REVISION DUE: In order to pass the WAC requirements, your essay score must be 70% or greater. 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