Physics
Resistivity
Resistivity is a measure of a material's ability to resist the flow of electric current. It is a fundamental property of materials and is represented by the Greek letter rho (ρ). Resistivity depends on the material's composition and temperature, and it is used to calculate the resistance of a given material in electrical circuits.
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9 Key excerpts on "Resistivity"
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
In (b), the connection on each side is across the entire end face, which means that the end face is an equipotential surface. This connection results in lower resistance and higher cur- rent (closer streamlines). Unless otherwise stated, we will assume that any given potential difference is applied as in (b). Instead of considering the resistance of a particular object such as a resistor, we can take a more general view and consider the Resistivity of a material, such as copper, that is isotropic (the electrical properties are the same in all directions) and homogeneous (uniform composition). In words, the Resistivity is a measure of how well a material resists having an electric current when an electric field is set up in it to drive that current. A material with a high Resistivity is an insulator and even a strong electric field cannot drive a current through it. A material with a low Resistivity is a conductor and even a moderate electric field can drive a current through it. Pdf_Folio:578 578 Fundamentals of physics To write an expression for Resistivity for a material, we generalise our defining equation for the resistance of a device, R = V i , by making three replacements. 1. The potential V applied across the device becomes E, the field magnitude set up inside the material. 2. The current i through the device becomes J, the current density inside the material. 3. The resistance R of the device becomes , the Resistivity of the material. We then have = E J . (26.14) For the unit of , we write unit () = unit (E) unit (J) = V∕m A∕m 2 = V A m.
- John G. Webster(Author)
- 2003(Publication Date)
- CRC Press(Publisher)
A more correct understanding of the electrical Resistivity of materials requires a thorough understanding of quantum mechanics [2]. On a microscopic level, electricity is simply the movement of electrons through a material. The smaller white circle in Figure 7.1 represents one electron flowing through the material. For ease of explanation, only one electron is shown. There are usually many electrons flowing through the material simultaneously. The electron tends to move from the left side of the material to the right side because an external force (represented by the large minus and plus signs) acts on it. This external force could be due to the voltage produced by an electrical power plant, or a battery connected to the material. As the electron moves through the material, it collides with the “stationary” atoms of the material, represented by the larger black circles. These collisions tend to slow down the electron. This is analogous to a pinball machine. The electron is like the metal ball rolling from the top to the bottom of a pinball machine, pulled by the force of gravity. The metal ball occasionally hits the pins and slows down. Just like in different pinball machines, the number of collisions the electron has can be very different in different materials. A material that produces lots of collisions is a high-Resistivity material. A material that produces few collisions is a low-Resistivity material. The Resistivity of a material can vary greatly at different temperatures. The Resistivity of metals usually increases as temperature increases, while the Resistivity of semiconductors usually decreases as tempera-ture increases. The Resistivity of a material can also depend on the applied magnetic field. The discussion thus far has assumed that the material being measured is homogeneous and isotropic. Homogeneous means the material properties are the same everywhere in the sample. Isotropic means the material properties are the same in all directions.
- J.S. Sumner(Author)
- 2012(Publication Date)
- Elsevier Science(Publisher)
Resistivity is a measure of the opposition to flow of charge in a material, whereas electrical conductivity is the flow mobility of charge car-riers. Conductivity σ is derived from the relationship σ = ηβμ, where η is the density of charge carriers, e is their charge, and μ is their mobility measured by velocity in meters per second per unit electric field. The charge carriers may be ions, electrons, or holes (the absence of a charge). Although the concept of conductivity is perhaps physically more funda-mental than that of Resistivity, for the sake of consistency, in this book Resistivity will usually be referred to rather than conductivity because of the prior usage in the study of Resistivity as a geophysical exploration method. Low-frequency IP measurements are more often related to Ohm's law and notions of Resistivity. The more complex higher frequency electrical phenom-ena usually introduce the concepts of conductivity. Other factors remain-ing constant, apparent Resistivity is proportional to potential difference and Resistivity is directly related to voltage values measured in the field. 21 The physical units or dimensions of Resistivity in the mks system are ohm-meters (Ωιη), which is resistance times length. Equations that define the Resistivity of materials by measurement, such as are developed in this chapter, can be rearranged as ρ = (V/I)K, where Κ is known as a geometric factor or form factor with units of length. The geometric factor Κ is con-stant for a given array and spacing, varying with the electrode interval. Some groups doing Resistivity and IP surveying have preferred to leave the 2π term from eq. 17 on the same side of the Resistivity equation with p, thus creating a ρ/2π unit of Resistivity, the definition for which is 2π or 6.283 times the unit Resistivity of ρ. Table II gives the relationship of the various units that have been used for Resistivity measurements.
eBook - PDF- Adel El Shahat(Author)
- 2017(Publication Date)
- IntechOpen(Publisher)
Keywords: Resistivity sensors, Resistivity measurement techniques, impedance, fringing, cell constant 1. Introduction Electrical Resistivity is defined as the ability of the material to resist the flow of electricity. Resistivity is calculated using Ohm ’ s law when dealing with the material is homogeneous and isotropic. To provide a more accurate version of Resistivity that can be applied for every material, the more general form of Ohm ’ s law is used [1]: E ¼ ρ J (1) In this equation, E is a vector that represents the electric field generated in the material (V/m), J is also a vector that represents the current density within the material (A/m � 2 ), and ρ is a tensor which is basically the proportionality coefficient ( Ω m). © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Eq. (1) is Ohm ’ s law in a more general context where E and J are vectors, and ρ is a tensor. This indicates that the current does not necessarily flow in the direction of the applied electric field. If it is assumed that the sample is homogeneous, meaning that it has the same properties everywhere, and that the material is isotropic, meaning that the material has the same proper-ties in all directions, then ρ becomes a scalar. This is not always a valid assumption though. In this chapter, isotropic and homogeneous materials are assumed, so ρ is considered to be a scalar.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
A disk-shaped magnet is levitated above a superconducting material that has been cooled by liquid nitrogen. The goldfish is along for the ride. Courtesy of Shoji Tonaka/International Super- conductivity Technology Center, Tokyo, Japan 809 QUESTIONS Resistance of a Conductor The resistance R of a con- ductor is defined as R = V __ i (definition of R), (26.3.1) where V is the potential difference across the conductor and i is the current. The SI unit of resistance is the ohm (Ω): 1 Ω = 1 V/A. Similar equations define the Resistivity and conductivity σ of a material: ρ = 1 __ σ = E __ J (definitions of and σ), (26.3.5, 26.3.3) where E is the magnitude of the applied electric field. The SI unit of Resistivity is the ohm-meter (Ω · m). Equation 26.3.3 cor- responds to the vector equation E → = ρ J → . (26.3.4) The resistance R of a conducting wire of length L and uni- form cross section is R = ρ L __ A , (26.3.9) where A is the cross-sectional area. Change of ρ with Temperature The Resistivity for most materials changes with temperature. For many materials, including metals, the relation between and temperature T is approximated by the equation – 0 = 0 α(T – T 0 ). (26.3.10) Here T 0 is a reference temperature, 0 is the Resistivity at T 0 , and α is the temperature coefficient of Resistivity for the material. Ohm’s Law A given device (conductor, resistor, or any other electrical device) obeys Ohm’s law if its resistance R, defined by Eq. 26.3.1 as V/i, is independent of the applied potential dif- ference V. A given material obeys Ohm’s law if its Resistivity, defined by Eq. 26.3.3, is independent of the magnitude and direction of the applied electric field E → . Resistivity of a Metal By assuming that the conduction electrons in a metal are free to move like the molecules of a gas, it is possible to derive an expression for the Resistivity of a metal: ρ = m _____ e 2 nτ .
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
A given material obeys Ohm’s law if its Resistivity, defined by Eq. 26.3.3, is independent of the magnitude and direction of the applied electric field E → . Resistivity of a Metal By assuming that the conduction elec- trons in a metal are free to move like the molecules of a gas, it is possible to derive an expression for the Resistivity of a metal: ρ = m _____ e 2 nτ . (26.4.5) Here n is the number of free electrons per unit volume and τ is the mean time between the collisions of an electron with the atoms of the metal. We can explain why metals obey Ohm’s law by pointing out that τ is essentially independent of the magni- tude E of any electric field applied to a metal. Power The power P, or rate of energy transfer, in an electrical device across which a potential difference V is maintained is P = iV (rate of electrical energy transfer). (26.5.2) Resistive Dissipation If the device is a resistor, we can write Eq. 26.5.2 as P = i 2 R = V 2 ___ R (resistive dissipation). (26.5.3, 26.5.4) In a resistor, electric potential energy is converted to internal thermal energy via collisions between charge carriers and atoms. Semiconductors Semiconductors are materials that have few conduction electrons but can become conductors when they are doped with other atoms that contribute charge carriers. Superconductors Superconductors are materials that lose all electrical resistance at low temperatures. Some materials are superconducting at surprisingly high temperatures. 1 Figure 26.1 shows cross sections through three long conduc- tors of the same length and material, with square cross sections of edge lengths as shown. Conductor B fits snugly within con- ductor A, and conductor C fits snugly within conductor B. Rank the following according to their end-to-end resistances, greatest first: the individual conductors and the combinations of A + B (B inside A), B + C (C inside B), and A + B + C (B inside A inside C).
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
Using this information and recalling that the electrical field is proportional to the Resistivity and the current density, we can see that the voltage is proportional to the current: E = ρJ V L = ρ I A V = ⎛ ⎝ ρ L A ⎞ ⎠ I . Resistance The ratio of the voltage to the current is defined as the resistance R: (9.8) R ≡ V I . The resistance of a cylindrical segment of a conductor is equal to the Resistivity of the material times the length divided by the area: (9.9) R ≡ V I = ρ L A . The unit of resistance is the ohm, Ω . For a given voltage, the higher the resistance, the lower the current. Resistors A common component in electronic circuits is the resistor. The resistor can be used to reduce current flow or provide a voltage drop. Figure 9.14 shows the symbols used for a resistor in schematic diagrams of a circuit. Two commonly used standards for circuit diagrams are provided by the American National Standard Institute (ANSI, pronounced “AN-see”) and the International Electrotechnical Commission (IEC). Both systems are commonly used. We use the ANSI standard in this text for its visual recognition, but we note that for larger, more complex circuits, the IEC standard may have a cleaner presentation, making it easier to read. Figure 9.14 Symbols for a resistor used in circuit diagrams. (a) The ANSI symbol; (b) the IEC symbol. Chapter 9 | Current and Resistance 401 Material and shape dependence of resistance A resistor can be modeled as a cylinder with a cross-sectional area A and a length L, made of a material with a Resistivity ρ (Figure 9.15). The resistance of the resistor is R = ρ L A . Figure 9.15 A model of a resistor as a uniform cylinder of length L and cross- sectional area A. Its resistance to the flow of current is analogous to the resistance posed by a pipe to fluid flow. The longer the cylinder, the greater its resistance. The larger its cross-sectional area A, the smaller its resistance. The most common material used to make a resistor is carbon.
eBook - PDFApplied Geophysics for Geologists and Engineers
The Elements of Geophysical Prospecting
- D. H. Griffiths, R. F. King(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
In dealing with such problems the starting point is Ohm's Law V j =R (4.2) where / = current in a conducting body, V = potential difference between two surfaces of constant potential, R = constant called the resistance between the surfaces. We must also introduce at this point the definition of Resistivity. If a conductor carries a current with parallel lines of flow over a cross-sectional area A, then its Resistivity p is defined by RA p = r < 4 -3 > where R is the resistance measured between two equipotential surfaces separated by a distance L (see Fig. 4.1). It follows from this equation and the previous one that the total current over the area A is I --- — R pL Fig. 4.1 The definition of Resistivity. 74 Applied Geophysics for Geologists and Engineers and that the ' Current density' ' j is given by / V J = -= — (4.4) A pL If the lines of current flow are not parallel, so that the current density varies over the conductor, this same argument can be applied to an infinitesimal element of the conductor bounded by equipotential surfaces which may be curved. The ratio V/L becomes in the limit the potential gradient dV/dL, and the expression of Ohm's Law is the equation ._ _±d_V_ p dL The negative sign has been introduced here to express the fact that potential increases in the opposite direction to the current flow. The component of the current density in a direction r is 1 dV Jr=--'— (4.5) p ôr in which the potential gradient in the direction r is used thus being always less than that in the direction of the current flow. Note the important fact that in a homogeneous medium an increase in current density, seen as a crowding or convergence of current lines, means an increase in the magnitude of the potential gradient. Conversely a divergence means a decrease in gradient.
eBook - PDF- Nikolai Bagdassarov(Author)
- 2021(Publication Date)
- Cambridge University Press(Publisher)
8 Electric Resistivity Electric properties of rocks, especially clays and ores, as well as fluid-bearing rocks have a major influence on the electrical conductivity underground. With geoelectric and magneto-telluric methods, geoscientists may determine localities of electrical conductivity anomaly in the Earth. Compared with the potential and spectral methods, these methods have the advantage because they permit not only mapping but also probing, and thus, a three-dimensional exploration is possible due to the vertical resolution of electrically contrasting geological units. The electrical parameters of rocks in the first place are the specific electrical resistance ρ, presented in this chapter, and the dielectric constant ε, presented in Chapter 9. These two important material properties occur in all electrical and magnetic processes of geophysical interest. 8.1 Physical Principles and Units of Measurement Electrical conductivity σ and dielectric constant ε determine the current density J s → = ~ J A in a medium caused by an electric field (V m −1 ) ~ E ¼ gradðUÞ, where U is the voltage potential and ~ J is the total electric current flowing through the cross-sectional area A. The displacement field is called ~ D ¼ ε ~ E, where by ε* one understands a complex number, which in the general case depends on the frequency ω of the time-varying electric field ~ E e e iωt . Ohm’ s law for a continuous medium is formulated as follows: ~ j s ¼ σ ~ E , so the proportionality coefficient between the current density ~ j s and the strength of the electric field ~ E is called the electric conductivity σ, and the reciprocal parameter ρ = 1/σ is the specific resistance. In a static electric field ~ E (corresponding to a constant gradient of electric potential U), a charged particle q experiences a force q ~ E. If the sum of all forces equals 0, then this charge q moves at a constant velocity ~ v ¼ μ ~ E, where the coefficient μ is the mobility.
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