DOCSLIB.ORG

Developing Tissue Phantom Materials with Required Electric Conductivities

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Developing Tissue Phantom Materials with Required Electric Conductivities TALLINN UNIVERSITY OF TECHNOLOGY Faculty of Information Technology Thomas Johann Seebeck Department of Electronics Hip Kõiv 132707 IVEM Developing tissue phantom materials with required electric conductivities Master thesis Supervisor: Senior research scientist Rauno Gordon Tallinn 2015 Author’s declaration I declare that I carried out this master thesis independently, and only with the cited sources, literature and other professional sources. I certify that this research thesis or any part of it has not been previously submitted for a degree or any other qualification at the Tallinn University of Technology or any other institution. Date: 04.06.2015 Author: Hip Kõiv ………………………. /signature/ 2 Thesis Assignment Name of topic: Developing tissue phantom materials with required electric conductivities Kudedele sarnaste elektrijuhtivustega materjalide disainimine ja valmistamine Origin of topic: Tallinn University of Technology, Thomas Johann Seebeck Department of Electronics Thesis goals: Give an overview of bioimpedance, phantoms used to mimic tissues, and van der Pauw resistivity measurement method. Develop a fixed recipe for gelatine phantoms with desired electric conductivities. Manipulate the conductivities of the phantoms with sodium chloride and accurately measure and calculate resistivity with van der Pauw method. Expected results: Design tissue phantom material and manipulate its conductivities easily with NaCl. Use van der Pauw method and prove its reliability measuring resistivity of developed phantoms. To gain knowledge of bioimpedance, tissue phantoms and van der Pauw method. Solved problems: It is proposed how to prepare low-cost and simple tissue similar gelatine phantoms and how to measure their resistivity with van der Pauw method. Date: ……………………………… Student: …………………………… ………..…………………….. /given name(s) and surname/ /signature/ Supervisor: ...…………………………. …..………………………….. /given name(s) and surname/ /signature/ 3 Hip Kõiv Developing tissue phantom materials with required electric conductivities Master thesis Abstract This thesis is the final work for fulfilment of the Master of Science degree at the Thomas Johann Seebeck Department of electronics in Tallinn University of Technology. The overall aim of this research is to develop inexpensive tissue similar phantoms with required electric conductivities and find a reliable measurement technique for said phantoms. The master project includes two main parts: review of the state of art and phantom construction and testing. First part introduces different phantoms used in biomedical fields and potentially suitable materials for mimicking tissues. It also reviews the main concepts of bioimpedance and van der Pauw method for determining conductivity. This section is mainly based on scientific publications analysed to give theoretical basis for assumptions made in the study. Second part includes development process of phantoms and their measurement results with implemented measurement technique. After analysing subject matter literature and considering possibilities, gelatine material is used to make homogeneous phantoms with tissue similar conductivities because other discussed materials were either too expensive or too problematic to prepare. Van der Pauw method is applied for conductivity measurements due the interest to investigate its accuracy and reliability measuring thick biological samples. Biological tissues have different electric conductivities, which means it should be also possible to manipulate with phantom conductivities. 4 Gelatine phantoms developed in current study are manipulated with NaCl to increase resistivity of samples and get desirable electric properties. NaCl dependence of conductivity is confirmed to be linear. Van der Pauw method for gelatine phantoms between 100 Hz to 1 MHz was proved to be applicable and gave satisfying results. In addition, graphite powder was added to the gelatine mixture to analyse its influence to electrical conductivity on low frequencies. Although, the results did not show reliable trend in conductivities measured, it is worth developing and researching further in future studies. Presented gelatine phantoms and van der Pauw measurement system used, proved to meet the goal of the thesis. Experiments showed relatively good agreement between theory and implementation part and phantoms with desired electric conductivities were prepared for development of bioimpedance technologies. The thesis is in English and contains 66 pages of text, 6 chapters, 30 figures and 6 tables. 5 Abbreviations vdP – van der Pauw CT – computed tomography EIT – electrical impedance tomography PVA – polyvinyl alcohol MRI – magnetic resonance imaging AC – alternating current BLM – bilayer lipid membrane 2D – two dimensional CNC – computer numerical control PCB – printed circuit board Wt/vol% - weight/volume percentage NaCl – sodium chloride 6 List of figures and tables Figure 1. Complex plane ................................................................................................................. 17 Figure 2. Suspension of spherical cells, each of radius a is showed (a). Electric circuit equivalent of the effective conductivity of the suspension. (b) [33] .................................................................. 18 Figure 3. Overview of how alternating current passes through the cells in biological tissues on different frequencies. ....................................................................................................................... 19 Figure 4. α-, β-, and γ-dispersions of permittivity (ε) and conductance (σ) showed in relation to frequency (f). [Bourne 1996, 24] ..................................................................................................... 20 Figure 5. Flat lamella of arbitrary shape, with four small contacts M, N, O and P on the periphery. [43] ................................................................................................................................................... 22 Figure 6. Schematic illustration of four contact configurations of Van der Pauw method [2]. ...... 24 Figure 7. Very thin sample geometry. Contacts are at the perimeter (a). The contacts are placed across the entire edge to produce uniform current distribution (b). D is the diameter and d is the thickness. [51] .................................................................................................................................. 26 Figure 8. Designed conductance cell for four-electrode measurement, where h is the height of the cell. Electrodes are named A, B, C, D and voltage and current is applied. [45] .............................. 28 Figure 9. Plexiglas enclosure with PCB-s inside it. ........................................................................ 29 Figure 10. Examples of planar coils with electrodes. On the left there is a side PCB with two electrodes for van der Pauw measurement and coil with 19 turns, diameter of 2 cm, and trace width of 0.1 mm. On the right there is a planar coil that goes on top of the gelatine cube with the same coil parameters. ................................................................................................................................ 30 Figure 11. Heating the gelatine mixture on water bath in the fume hood. ...................................... 33 Figure 12. When temperature rises resistance decreases and the relation to temperature is fairly linear. ............................................................................................................................................... 34 Figure 13. Wayne Kerr impedance analyser connected to gelatine sample with four electrodes. .. 36 Figure 14. Van der Pauw measurement method set up used in the research. Blue colour indicates one pair of measurement (1 and 3) and green colour other pair (2 and 4). ...................................... 37 Figure 15. 0.7 wt/vol% of salt is added is added to the gelatine mixture and four measurements are made. ................................................................................................................................................ 38 Figure 16. Syringe with gelatine mixture for resistivity measurement and for checking the correctness of our interpretation of van der Pauw method. .............................................................. 40 Figure 17. 3 samples with different salt concentrations were measured and conductivities were calculated with syringe and vdP method. Light blue, light red and light green lines represent conductivities found with syringe method and blue, red and green lines are conductivities calculated with vdP method. ............................................................................................................ 42 Figure 18. Conductivity of 18 different gelatine samples calculated. ............................................. 43 Figure 19. Conductivity dependence on NaCl. ............................................................................... 44 Figure 20. Graphite powder added to the gelatine phantom. .......................................................... 46 Figure 21. Sample 2 - 1 wt/vol% of NaCl and 44 g of graphite powder. Graphite flakes have settled in the bottom. ................................................................................................................................... 47 Figure 22. Sample 3 – 4 wt/vol% NaCl, 0 wt/vol% NaCl + graphite, 0 wt/vol% NaCl. ................ 48 Figure 23. 3 different samples with different layers constructed.
Load more

Recommended publications
  • Determination of Fabric Surface Resistance by Van Der Pauw Method in Case of Contacts Distant from the Sample Edge
    AUTEX Research Journal, Vol. 14, No 2, June 2014, DOI: 10.2478/v10304-012-0050-4 © AUTEX DETERMINATION OF FABRIC SURFACE RESISTANCE BY VAN DER PAUW METHOD IN CASE OF CONTACTS DISTANT FROM THE SAMPLE EDGE Magdalena Tokarska Department of Architecture of Textiles, Lodz University of Technology, 116 Zeromskiego St., 90-924 Lodz Poland E-mail: [email protected] Abstract: The van der Pauw method can be used to determine the electroconductive properties of textile materials. However, the sample surface resistance can be determined provided that the sample has characteristics typical for the van der Pauw structure. In the paper, a method of evaluating the sample structure is shown. The selected electroconductive woven fabrics are used as an example of van der Pauw structure. An analysis of impact of electrodes placement on the resistance measurements was conducted. Knowing how the resistance of the sample varies with the electrodes distance from the edge, the samples’ surface resistances were calculated in cases when the electrodes are placed at the sample edge. An uncertainty analysis of the samples’ surface resistances was conducted based on the Monte Carlo method. Keywords: Electroconductive properties, woven fabric, van der Pauw structure, van der Pauw method, surface resistance, electrodes placement, Monte Carlo method 1. Introduction of the sample. The effect of electrode placement on resistance measurement was investigated [8,10,14]. In the case of the The van der Pauw method was developed to determine the woven fabrics, the contacts should not be too close to the properties of thin semiconductors [1,2]. This method is currently boundaries of the sample because errors can be introduced used to evaluate the conductivity of thin layers deposited on [3,15].
    [Show full text]
  • Appendix a Hall Effect Measurements
    Lake Shore 7500/9500 Series Hall System Users Manual APPENDIX A HALL EFFECT MEASUREMENTS Contents: A.1 GENERAL..................................................................................................................................... A-2 A.2 HALL EFFECT MEASUREMENT THEORY................................................................................. A-2 A.3 SAMPLE GEOMETRIES & MEASUREMENTS SUPPORTED BY HALL SOFTWARE .............. A-5 A.3.1 System of Units ...................................................................................................................... A-5 A.3.2 Nomenclature......................................................................................................................... A-5 A.3.3 Van der Pauw Measurements................................................................................................ A-6 A.3.4 Hall Bar Measurements.......................................................................................................... A-8 A.3.4.1 Six-contact 1-2-2-1 Hall Bar............................................................................................... A-8 A.3.4.2 Six-contact 1-3-1-1 Hall Bar............................................................................................. A-10 A.3.4.3 Eight-contact 1-3-3-1 Hall Bar ......................................................................................... A-11 A.4 COMPARISON TO ASTM STANDARD ..................................................................................... A-13 A.5 SOURCES OF MEASUREMENT
    [Show full text]
  • Electrical Resistivity Measurement of Carbon Anodes Using the Van Der Pauw Method
    metals Article Electrical Resistivity Measurement of Carbon Anodes Using the Van der Pauw Method Geoffroy Rouget 1,2, Hicham Chaouki 2, Donald Picard 2, Donald Ziegler 3 and Houshang Alamdari 1,2,* 1 Department of Mining, Metallurgical and Materials Engineering, Laval University, Quebec, QC G1V0A6, Canada; [email protected] 2 NSERC/Alcoa Industrial Research Chair MACE and Aluminum Research Center, Laval University, Quebec, QC G1V0A6, Canada; [email protected] (H.C.); [email protected] (D.P.) 3 Alcoa Primary Metals, Alcoa Technical Centre, 859 White Cloud Road, New Kensington, PA 15068, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-418-656-7666 Received: 27 July 2017; Accepted: 8 September 2017; Published: 13 September 2017 Abstract: The electrical resistivity of carbon anodes is an important parameter in the overall efficiency of the aluminum smelting process. The aim of this work is to explore the Van der Pauw (VdP) method as an alternative technique to the standard method, which is commonly used in the aluminum industry, in order to characterize the electrical resistivity of carbon anodes and to assess the accuracy of the method. For this purpose, a cylindrical core is extracted from the top of the anodes. The electrical resistivity of the core samples is measured according to the ISO 11713 standard method. This method consists of applying a 1 A current along the revolution axis of the sample, and then measuring the voltage drop on its side, along the same direction. Theoretically, this technique appears to be satisfying, but cracks in the sample that are generated either during the anode production or while coring the sample may induce high variations in the measured signal.
    [Show full text]
  • Determination of the Riemann Modulus and Sheet Resistance of a Sample with a Hole by the Van Der Pauw Method
    January 8, 2015 Determination of the Riemann modulus and sheet resistance of a sample with a hole by the van der Pauw method K. Szyma ński, K. Łapi ński and J. L. Cie śli ński University of Białystok, Faculty of Physics, K. Ciołkowskiego Street 1L, 15-245 Białystok, Poland The van der Pauw method for two-dimensional samples of arbitrary shape with an isolated hole is considered. Correlations between extreme values of the resistances allow one to determine the specific resistivity of the sample and the dimensionless parameter related to the geometry of the isolated hole, known as the Riemann modulus. The parameter is invariant under conformal mappings. Experimental verification of the method is presented. I. Introduction Determination of direct relations between geometrical size or shape of the sample and electrical quantities is of particular importance as new measurement techniques may appear or the experimental accuracy can be increased. As an example, we indicate a particular class of capacitors in which cross-capacitance per unit length is independent of their cross- sectional dimension [1]. Development of this class of capacitors leads to a new realization of the unit of capacitance and the unit of resistance [2-4]. The second example is the famous van der Pauw method of measuring the resistivity of a two- dimensional, isotropic sample with four contacts located at its edge [5,6]. The power of the method lies in its ability to measure the resistances with four contacts located at arbitrarily located point on the edge of a uniform sample. The result of the measurement is sheet resistance, i.e., the ratio of specific resistivity and thickness.
    [Show full text]
  • Measuring and Reporting Electrical Conductivity in Metal–Organic Frameworks: Cd
    Measuring and Reporting Electrical Conductivity in Metal–Organic Frameworks: Cd The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Sun, Lei et al. “Measuring and Reporting Electrical Conductivity in Metal–Organic Frameworks: Cd2(TTFTB) as a Case Study.” Journal of the American Chemical Society 138, 44 (November 2016): 14772– 14782 © 2016 American Chemical Society As Published http://dx.doi.org/10.1021/jacs.6b09345 Publisher American Chemical Society (ACS) Version Author's final manuscript Citable link http://hdl.handle.net/1721.1/115124 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Measuring and Reporting Electrical Conductivity in Metal-Organic Frameworks: Cd2(TTFTB) as a Case Study Lei Sun, Sarah S. Park, Dennis Sheberla, and Mircea Dincă* Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States ABSTRACT: Electrically conductive metal-organic frameworks (MOFs) are emerging as a subclass of porous materials that can have a transformative effect on electronic and renewable energy devices. Systematic advances in these materials depend critically on the accurate and reproducible characterization of their electrical properties. This is made difficult by the numerous techniques avail- able for electrical measurements and the dependence of metrics on device architecture and numerous external variables. These chal- lenges, common to all types of electronic materials and devices, are especially acute for porous materials, whose high surface area make them even more susceptible to interactions with contaminants in the environment.
    [Show full text]
  • A Robust Method to Determine the Contact Resistance Using the Van Der Pauw Set Up. G. González-Díaz1,2 *, D. Pastor1,2, E
    A robust method to determine the contact resistance using the van der Pauw set up. G. González-Díaz1,2 *, D. Pastor1,2, E. García-Hemme1,2, D. Montero1,2, R. García- Hernansanz1,2, J. Olea1,2, A. del Prado1,2, E. San Andrés1,2 and I. Mártil1,2 1Dept. de Física Aplicada III (Electricidad y Electrónica), Univ. Complutense de Madrid, 28040 Madrid, Spain 2CEI Campus Moncloa, UCM-UPM, 28040 Madrid, Spain * Author for correspondence [email protected] Abstract The van der Pauw method to calculate the sheet resistance and the mobility of a semiconductor is a pervasive technique both in the microelectronics industry and in the condensed matter science field. There are hundreds of papers dealing with the influence of the contact size, non- uniformities and other second order effects. In this paper we will develop a simple methodology to evaluate the error produced by finite size contacts, detect the presence of contact resistance, calculate it for each contact, and determine the linear or rectifying behavior of the contact. We will also calculate the errors produced by the use of voltmeters with finite input resistance in relation with the sample sheet resistance. 1.- Introduction The four-point probe measuring technique is very well known from the beginning of the XX century when Wenner proposed it to measure the earth resistivity1. Later Valdes2 adapted it for semiconductor measurements. The collinear four-point probe has been of great importance for the microelectronic industry. The determination of implantation uniformity over the whole wafer is an example. The method undergoes an important change with the famous paper by van der Pauw3 where the author solved the problem of measurements on arbitrary samples by placing four infinitely small contacts on the sample border.
    [Show full text]
  • 1 Functionalizing Semiconductor-Crystalline Oxide Heterostructures for Future Application in Energy Harvesting, Sensing, And
    FUNCTIONALIZING SEMICONDUCTOR-CRYSTALLINE OXIDE HETEROSTRUCTURES FOR FUTURE APPLICATION IN ENERGY HARVESTING, SENSING, AND COMPUTING TECHNOLOGIES By Zheng Hui Lim Dissertation Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at The University of Texas at Arlington August 2019 Arlington, Texas Supervising Committee: Dr. Joseph H. Ngai, Supervising Professor Dr. Alex Weiss Dr. Qiming Zhang Dr. Choong-Un Kim Dr. Seong Jin Koh 1 Abstract Energy harvesting, sensing, and computing technologies utilizing conventional semiconductors have seen a plateau in their advancement for future applications. In order to address these issues, alternate materials are needed to improve present technologies. In my research, I proposed here that complex oxides can serve as potential candidate materials due to their properties. Single crystalline SrZrO3 thin film can be a potential candidate as dielectric material for Ge-based metal-oxide-semiconductor technologies. I present here a structural and electrical characterization of SrZrO3 thin film grown epitaxially on Ge (001) substrate with oxide molecular beam epitaxy. X-ray photoemission spectroscopy has shown that SrZrO3 thin film has a large conduction band and valence band offset with respect to Ge. Moreover, electrical characterization of the 4 nm thin film with capacitance-voltage and current-voltage have shown low leakage current densities and high dielectric constant. The tunable charge transfer and built-in electric field have laid down groundwork for developing functional heterojunction for energy harvesting purposes. Charge transfer and built-in electric field were reported across heterostructures of epitaxial SrNbxTi1-xO3-δ grown on Si (001). Transport measurement shows the formation of hole gas in Si.
    [Show full text]
  • Lecture 17: Resistivity and Hall Effect Measurements
    ECE-656: Fall 2011 Lecture 17: Resistivity and Hall effect Measurements Mark Lundstrom Purdue University West Lafayette, IN USA 10/5/11 1 measurement of conductivity / resistivity 1) Commonly-used to characterize electronic materials. 2) Results can be clouded by several effects – e.g. contacts, thermoelectric effects, etc. 3) Measurements in the absence of a magnetic field are often combined with those in the presence of a B-field. This lecture is a brief introduction to the measurement and characterization of near-equilibrium transport. 2 Lundstrom ECE-656 F11 resistivity / conductivity measurements diffusive transport assumed For uniform carrier concentrations: We generally measure resisitivity (or conductivity) because for diffusive samples, these parameters depend on material properties and not on the length of the resistor or its width or cross-sectional area. Lundstrom ECE-656 F11 3 Landauer conductance and conductivity “ideal” contacts For ballistic or quasi-ballistic transport, replace the mfp with cross-sectional the “apparent” mfp: area, A n-type semiconductor 4 (diffusive) Lundstrom ECE-656 F11 conductivity and mobility “ideal” contacts cross-sectional 1) Conductivity depends on EF. area, A 2) EF depends on carrier density. 3) So it is common to characterize n-type semiconductor the conductivity at a given carrier density. 4) Mobility is often the quantity that is quoted. So we need techniques to measure two quantities: 1) conductivity 2) carrier density 5 Lundstrom ECE-656 F11 2D: conductivity and sheet conductance 2D electrons n-type semiconductor ⎛ Wt ⎞ ⎛ W ⎞ G = σ = σ t n ⎜ L ⎟ n ⎜ L ⎟ ⎝ ⎠ ⎝ ⎠ Top view “sheet conductance” 6 Lundstrom ECE-656 F11 2D electrons vs.
    [Show full text]
  • The Microwave Hall Effect Measured Using a Waveguide Tee J. E. COPPOCK , J. R. ANDERSON , and W. B. JOHNSON Dept. of Physics, U
    The Microwave Hall Effect Measured Using a Waveguide Tee J. E. COPPOCK 1, J. R. ANDERSON 1, and W. B. JOHNSON 2 1Dept. of Physics, University of Maryland, College Park, MD, 20741 2Laboratory for Physical Sciences, College Park, MD, 20740 This paper describes a simple microwave apparatus to measure the Hall effect in semiconductor wafers. The advantage of this technique is that it does not require contacts on the sample or the use of a resonant cavity. Our method consists of placing the semiconductor wafer into a slot cut in an X-band (8 - 12 GHz) waveguide series tee, injecting microwave power into the two opposite arms of the tee, and measuring the microwave output at the third arm. A magnetic field applied perpendicular to the wafer gives a microwave Hall signal that is linear in the magnetic field and which reverses phase when the magnetic field is reversed. The microwave Hall signal is proportional to the semiconductor mobility, which we compare for calibration purposes with d. c. mobility measurements obtained using the van der Pauw method. We obtain the resistivity by measuring the microwave reflection coefficient of the sample. This paper presents data for silicon and germanium samples doped with boron or phosphorus. The measured mobilities ranged from 270 to 3000 cm 2 /(V-sec). 1 1. Introduction A. Motivation Direct current electrical techniques for measuring the mobility and carrier concentration in semiconductors require making contacts that are mechanically reliable and electrically non- rectifying. The van der Pauw method is a standard d. c. technique for measuring the mobility and carrier concentration in a semiconductor wafer as long as the size of each contact is small [1].
    [Show full text]
  • Transport Measurements
    Transport measurements Patrick R. LeClair May 26, 2010 Contents 1 Electrical Resistivity 3 1.1 Electric Current . 3 1.1.1 Getting Current to Flow . 4 1.2 Drift Velocity and Current . 4 1.3 Resistance and Ohm’s Law . 6 1.3.1 Drift Velocity and Collisions . 6 1.3.2 Mean Free Path and Mobility . 8 1.3.3 Current, Electric Field, and Voltage . 9 1.4 Transport in Semiconductors . 10 2 Measuring resistive devices 11 2.1 Sourcing Voltage . 11 2.2 Sourcing Current . 13 2.3 Measuring Voltage . 14 2.4 Measuring Current . 16 3 Four point probe techniques 17 3.1 Four-point Probe Measurements . 18 3.2 Bulk samples . 19 3.3 Thin Films . 20 3.4 Wires . 22 3.5 The van der Pauw Technique . 22 4 Solving the van der Pauw equations numerically 24 5 dI/dV and d2I/dV2 measurements 27 5.1 Mathematical preliminaries . 27 5.2 Ohmic and non-ohmic devices . 28 1 5.3 Circuitry . 29 5.3.1 Sourcing . 31 5.3.2 Measuring Voltage . 31 5.3.3 Measuring Current . 32 5.3.4 Miscellanea . 33 5.4 Software . 33 5.4.1 Basic principles . 33 5.5 Further practical considerations . 33 6 Tunnel Junctions & other non-linear elements 33 6.1 Simmons & Brinkman models . 33 6.2 dI/dV measurements . 33 6.3 d2I/dV2 measurements . 33 6.4 Parallel RC model . 33 6.4.1 Magnitude of the capacitive current . 33 6.4.2 Parallel RC model in more detail . 35 6.4.3 Impedance spectroscopy .
    [Show full text]
  • Resistivity, Magnetoresistance, Hall
    V, I, R measurements: how to generate and measure quantities and then how to get data (resistivity, magnetoresistance, Hall). 590B Makariy A. Tanatar November 10, 2008 SI units/History Resistivity Typical resistivity temperature dependence First reliable source of electricity Alternating plates of Zn and Cu separated by cardboard soaked in saltwater Electrical action is proportional to the number of plates Alessandro Giuseppe Antonio Anastasio Volta 1745-1827 Count (made by Napoleon 1810) 1881- Volt unit adopted internationally Months after 1819 Hans Christian Ørsted's discovery of magnetic action of electrical current 1820 Law of electromagnetism (Ampère's law) André-Marie Ampère magnetic force between two electric currents. 1775 - 1836 First measurement technique for electricity Needle galvanometer Can be measured via Magnetic action of electric current Heat Mass flow (electrolysis) Light generation Physiological action (Galvani, You can do anything with cats!) Ampere main SI unit: D'Arsonval galvanometer Definition based on force of interaction between parallel current Replaced recently Amount of deposited mass per unit time in electrolysis process Thompson (Kelvin) mirror galvanometer 1826 Ohm’s apparatus Current measurement: magnetic needle Voltage source: thermocouple (Seebeck 1821) Steam heater Ice cooler Georg Simon Ohm 1789 - 1854 Resistivity I=V/R Our common experience: resistance is the simplest quantity to measure Use Ohm’s law True, but only inside “comfort zone” Resistor Digital Multi Meters -DMM Apply known I (V) Measure
    [Show full text]
  • Physics Lab's Documentation!
    Physics Lab Release 1.3.1 Martin Brajer May 31, 2021 CONTENTS: 1 Features 3 2 Installation 5 3 Compliance 7 4 License 9 4.1 Physics Lab overview..........................................9 4.2 Get started................................................ 10 4.3 Library.................................................. 13 5 Indices and tables 29 Python Module Index 31 Index 33 i ii Physics Lab, Release 1.3.1 Physics Lab is a free and open-source python package. Helps with evaluation of common experiments. Source code can be found on Github. CONTENTS: 1 Physics Lab, Release 1.3.1 2 CONTENTS: CHAPTER ONE FEATURES • Van der Pauw & Hall method • Magnetization measurements • Batch measurement evaluation • Using pandas.DataFrame 3 Physics Lab, Release 1.3.1 4 Chapter 1. Features CHAPTER TWO INSTALLATION pip install physicslab For usage examples see Get started section. 5 Physics Lab, Release 1.3.1 6 Chapter 2. Installation CHAPTER THREE COMPLIANCE Versioning follows Semantic Versioning 2.0.0. Following PEP8 Style Guide coding conventions. Testing with unittest and pycodestyle. Using Python 3 (version >= 3.6). 7 Physics Lab, Release 1.3.1 8 Chapter 3. Compliance CHAPTER FOUR LICENSE Physics Lab is licensed under the MIT license. 4.1 Physics Lab overview Physics Lab is a free and open-source python package. Helps with evaluation of common experiments. Source code can be found on Github. 4.1.1 Features • Van der Pauw & Hall method • Magnetization measurements • Batch measurement evaluation • Using pandas.DataFrame 4.1.2 Installation pip install physicslab For usage examples see Get started section. 4.1.3 Compliance Versioning follows Semantic Versioning 2.0.0.
    [Show full text]