Physics
Resistance and Resistivity
Resistance is the measure of how much a material opposes the flow of electric current. It is determined by the material's resistivity, which is a property specific to each material. Resistivity is a measure of how strongly a material resists the flow of electric current and is dependent on the material's composition and temperature.
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8 Key excerpts on "Resistance and Resistivity"
- 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.
- John G. Webster(Author)
- 2003(Publication Date)
- CRC Press(Publisher)
7 -1 0-8493-1733-9/04/$0.00+$1.50 © 2004 by CRC Press LLC 7 Electrical Conductivity and Resistivity 7.1 Basic Concepts .................................................................... 7 -1 7.2 Simple Model and Theory ................................................. 7 -2 7.3 Experimental Techniques for Measuring Resistivity ....... 7 -4 Two-Point Technique • Four-Point Technique • Common Experimental Errors • Sheet Resistance Measurements • Instrumentation for Four-Point Resistivity Measurements • Instrumentation for High-Intensity Measurements • van der Pauw Technique Electrical resistivity is a key physical property of all materials. It is often necessary to accurately measure the resistivity of a given material. The electrical resistivity of different materials at room temperature can vary by over 20 orders of magnitude. No single technique or instrument can measure resistivities over this wide range. This chapter describes a number of different experimental techniques and instruments for measuring resistivities. The emphasis is on explaining how to make practical measurements and avoid common experimental errors. More theoretical and detailed discussions can be found in the sources listed at the end of this chapter. 7.1 Basic Concepts The electrical resistivity of a material is a number describing how much that material resists the flow of electricity. Resistivity is measured in units of ohm·meters ( W m). If electricity can flow easily through a material, that material has low resistivity. If electricity has great difficulty flowing through a material, that material has high resistivity. The electrical wires in overhead power lines and buildings are made of copper or aluminum. This is because copper and aluminum are materials with very low resistivities (about 20 n W m), allowing electric power to flow very easily.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
26.18 Apply the relationship between resistivity and conductivity σ. 26.19 Apply the relationship between an object’s resis- tance R, the resistivity of its material , its length L, and its cross-sectional area A. 26.20 Apply the equation that approximately gives a conductor’s resistivity as a function of temperature T. 26.21 Sketch a graph of resistivity versus temperature T for a metal. 653 26-3 Resistance and Resistivity Resistance and Resistivity If we apply the same potential difference between the ends of geometrically simi- lar rods of copper and of glass, very different currents result. The characteristic of the conductor that enters here is its electrical resistance. We determine the resistance between any two points of a conductor by applying a potential dif- ference V between those points and measuring the current i that results. The resistance R is then R = V i (definition of R). (26-8) The SI unit for resistance that follows from Eq. 26-8 is the volt per ampere. This com- bination occurs so often that we give it a special name, the ohm (symbol Ω); that is, 1 ohm = 1 Ω = 1 volt per ampere = 1 V/A. (26-9) A conductor whose function in a circuit is to provide a specified resistance is called a resistor (see Fig. 26-7). In a circuit diagram, we represent a resistor and a resistance with the symbol . If we write Eq. 26-8 as i = V R , we see that, for a given V, the greater the resistance, the smaller the current. The resistance of a conductor depends on the manner in which the poten- tial difference is applied to it. Figure 26-8, for example, shows a given potential difference applied in two different ways to the same conductor. As the current density streamlines suggest, the currents in the two cases — hence the measured resistances — will be different. Unless otherwise stated, we shall assume that any given potential difference is applied as in Fig.
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 .
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
L i i A V Current is driven by a potential difference. If we know the resistivity of a substance such as copper, we can calculate the resistance of a length of wire made of that substance. Let A be the cross-sectional area of the wire, let L be its length, and let a potential difference V exist between its ends (Fig. 26-9). If the streamlines representing the current density are uniform throughout the wire, the electric field and the current density will be constant for all points within the wire and, from Eqs. 24-42 and 26-5, will have the values E = V/L and J = i/A. (26-14) We can then combine Eqs. 26-10 and 26-14 to write ρ = E J = V/L i/A . (26-15) Resistance is a property of an object. Resistivity is a property of a material. 755 26-3 Resistance and Resistivity However, V/i is the resistance R, which allows us to recast Eq. 26-15 as R = ρ L A . (26-16) Equation 26-16 can be applied only to a homogeneous isotropic conductor of uniform cross section, with the potential difference applied as in Fig. 26-8b. The macroscopic quantities V, i, and R are of greatest interest when we are making electrical measurements on specific conductors. They are the quantities that we read directly on meters. We turn to the microscopic quantities E, J, and when we are interested in the fundamental electrical properties of materials. Checkpoint 3 The figure here shows three cylindrical copper conductors along with their face areas and lengths. Rank them according to the current through them, greatest first, when the same potential difference V is placed across their lengths. (a) (b) A L (c) 1.5L A _ 2 A _ 2 L/2 Variation with Temperature The values of most physical properties vary with temperature, and resistivity is no exception. Figure 26-10, for example, shows the variation of this property for copper over a wide temperature range. The relation between temperature and resistivity for copper — and for metals in general — is fairly linear over a rather broad temperature range.
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.
- 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- 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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