Physics
Ohmic Conductor
An ohmic conductor is a material that obeys Ohm's law, which states that the current passing through the conductor is directly proportional to the voltage applied across it. In an ohmic conductor, the resistance remains constant regardless of the applied voltage. This behavior allows for a predictable and linear relationship between current and voltage.
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7 Key excerpts on "Ohmic Conductor"
- 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)
If you are designing a coaxial cable, how does the resistance between the two conductors depend on these variables? View this simulation (https://openstaxcollege.org/l/21batteryresist) to see how the voltage applied and the resistance of the material the current flows through affects the current through the material. You can visualize the collisions of the electrons and the atoms of the material effect the temperature of the material. Chapter 9 | Current and Resistance 405 9.4 | Ohm's Law Learning Objectives By the end of this section, you will be able to: • Describe Ohm’s law • Recognize when Ohm’s law applies and when it does not We have been discussing three electrical properties so far in this chapter: current, voltage, and resistance. It turns out that many materials exhibit a simple relationship among the values for these properties, known as Ohm’s law. Many other materials do not show this relationship, so despite being called Ohm’s law, it is not considered a law of nature, like Newton’s laws or the laws of thermodynamics. But it is very useful for calculations involving materials that do obey Ohm’s law. Description of Ohm’s Law The current that flows through most substances is directly proportional to the voltage V applied to it. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied: I ∝ V . This important relationship is the basis for Ohm’s law. It can be viewed as a cause-and-effect relationship, with voltage the cause and current the effect. This is an empirical law, which is to say that it is an experimentally observed phenomenon, like friction. Such a linear relationship doesn’t always occur. Any material, component, or device that obeys Ohm’s law, where the current through the device is proportional to the voltage applied, is known as an ohmic material or ohmic component.
eBook - PDF- David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
A potential difference V is applied across a cylindrical conductor of length L and cross-sectional area A, es- tablishing a current i. L i i ∆V A field E V/L. If the current density is also uniform over the area A, then j i /A. The resistivity is then (29-11) The quantity V/i that appears in this equation is defined as the resistance R: (29-12) Combining Eqs. 29-11 and 29-12, we obtain an expression for the resistance R: (29-13) The resistance R is characteristic of a particular object and depends on the material of which it is made as well as on its length and cross-sectional area; the resistivity is char- acteristic of the material in general. The units of resistance are ohms (). Equation 29-12 gives us another basis for stating Ohm’s law. For a particular object, we can measure the current i for various applied potential differences and plot i as a function of V. If this plot gives a straight line, then the ob- ject is ohmic and obeys Ohm’s law. An equivalent state- ment of Ohm’s law is: The resistance of an object is independent of the magni- tude or sign of the applied potential difference. Ordinary resistors that are found in electric circuits are ohmic for the range of potential differences that are normally used in circuits. Semiconducting devices, such as diodes and tran- sistors, usually are nonohmic. Figure 29-7 compares the cur- rent – voltage plots for ohmic and non-ohmic devices. Keep in mind that the relationship V iR is not a statement of Ohm’s law. This equation defines the resis- tance and is true for both ohmic and nonohmic objects. Even for nonohmic devices, we can find a value of the re- sistance R for a particular value of V; for a different V, a different value of R will be obtained. For ohmic devices, we get the same value of R for any value of V. R L A . R V i . E j V/L i/A . V, i, and R are macroscopic quantities, applying to a particular body or extended region.
eBook - PDF- Pradeep Fulay, Jung-Kun Lee(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
52 Electronic, Magnetic, and Optical Materials The distinction between resistance and resistivity is also important in situations where the resis-tivity of a material or a component changes across the thickness of the component. Thus, if we know the resistivity values and the geometry for different regions, we can calculate the total resistance of a component or a device. Let us now derive the point form of Ohm’s law (Equation 2.11). The conduction electrons in metals move at very high speeds (~10 6 m/s). We can expect that, as temperature increases, the kinetic energy of electrons should also increase, causing the electrons to move at higher speeds. However, as we will see in Section 2.7, this speed is largely independent of the temperature. When no electric field is applied, the motions of the conduction electron are in random directions and do not result in an electrical current (Figure 2.7). This is similar to ions drift-ing around in an electroplating solution. A less-technical analogy is that of small schoolchildren running around without the supervision of their teacher! Now consider a voltage V applied across the length ( L ) of a conductor. The electric field is given by E V L = (2.12) When we apply a DC electric field to a conductor, the electrons in the material flow from the negative to the positive terminal of the voltage supply (Figure 2.7b). This current is known as the electron current . As a matter of convention, we state that the current or the conventional current flows from the positive to the negative terminal of the battery (Figure 2.7c).
eBook - PDFFundamentals of Materials Science and Engineering
An Integrated Approach
- William D. Callister, Jr., David G. Rethwisch(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
The dielectric characteristics of insulating materials are also treated. The final sections are devoted to the phenomena of ferroelectricity and piezoelectricity. 12.1 INTRODUCTION Electrical Conduction One of the most important electrical characteristics of a solid material is the ease with which it transmits an electric current. Ohm’s law relates the current I—or time rate of charge passage—to the applied voltage V as follows: V = IR (12.1) where R is the resistance of the material through which the current is passing. The units for V, I, and R are, respectively, volts (J/C), amperes (C/s), and ohms (V/A). The value Ohm’s law Ohm’s law expression 12.2 OHM’S LAW 12.3 Electrical Conductivity • 505 of R is influenced by specimen configuration and for many materials is independent of current. The electrical resistivity ρ is independent of specimen geometry but related to R through the expression ρ = RA l (12.2) where l is the distance between the two points at which the voltage is measured and A is the cross-sectional area perpendicular to the direction of the current. The units for ρ are ohm-meters (Ω∙m). From the expression for Ohm’s law and Equation 12.2, ρ = VA Il (12.3) Figure 12.1 is a schematic diagram of an experimental arrangement for measuring elec- trical resistivity. electrical resistivity Electrical resistivity— dependence on resistance, specimen cross-sectional area, and distance between measuring points Electrical resistivity— dependence on applied voltage, current, specimen cross-sectional area, and distance between measuring points Sometimes, electrical conductivity σ is used to specify the electrical character of a mate- rial. It is simply the reciprocal of the resistivity, or σ = 1 ρ (12.4) and is indicative of the ease with which a material is capable of conducting an electric current. The units for σ are reciprocal ohm-meters [(Ω∙m) –1 ]. 1 The following discussions on electrical properties use both resistivity and conductivity.
eBook - PDFMaterials Science and Engineering
An Introduction
- William D. Callister, Jr., David G. Rethwisch(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
We opted to use (Ω·m) −1 on the basis of convention—these units are traditionally used in introductory materials science and engineering texts. 18.5 Energy Band Structures in Solids • 651 The demonstration of the equivalence of the two Ohm’s law expressions (Equations 18.1 and 18.5) is left as a homework exercise. Solid materials exhibit an amazing range of electrical conductivities, extending over 27 orders of magnitude; probably no other physical property exhibits this breadth of variation. In fact, one way of classifying solid materials is according to the ease with which they conduct an electric current; within this classification scheme there are three groupings: conductors, semiconductors, and insulators. Metals are good conductors, typically having conductivities on the order of 10 7 ( Ω· m) −1 . At the other extreme are materials with very low conductivities, ranging between 10 −10 and 10 −20 ( Ω· m) −1 ; these are electrical insulators. Materials with intermediate conductivities, generally from 10 −6 to 10 4 ( Ω· m) −1 , are termed semiconductors. Electrical conductivity ranges for the various material types are compared in the bar chart of Figure 1.8. metal insulator semiconductor An electric current results from the motion of electrically charged particles in response to forces that act on them from an externally applied electric field. Positively charged particles are accelerated in the field direction, negatively charged particles in the direc- tion opposite. Within most solid materials a current arises from the flow of electrons, which is termed electronic conduction. In addition, for ionic materials, a net motion of charged ions is possible that produces a current; this is termed ionic conduction. The present discussion deals with electronic conduction; ionic conduction is treated briefly in Section 18.16.
- Wei Gao, Nigel M Sammes;;;(Authors)
- 1999(Publication Date)
- WSPC(Publisher)
Two Classical Theory of Electrical Conduction and Conducting Materials In this chapter, the free electron conduction theory is described. This description is then used to explain the conduction properties of materials. Finally, materials which are used for electrical conduction in electrical and electronic industries are introduced. In classical electron conduction theory, an electron is treated as a very small particle with certain mass and electric charge: Electron mass m e = 9.1 x 10~ 31 kg Electron charge e = -1.6 x 10 19 C. Because electrons behave like particles in this theory, they obey Newton's Laws of motion. In Sections 2.3 to 2.5, we will apply this theory to describe the electron conduction behaviour in conductors. 2.1. Resistivity and Temperature Coefficient of Resistivity (TCR), Matthiessen's Rule 2.1.1. Resistivity The electrical resistance, R, of a material is defined as R oc l/A (2.1) 8 Classical Theory of Electrical Conduction and Conducting Materials 9 or R = pi IA , (2.2) where I is the length, A is the area of the cross-section of the conductor and p is called electrical resistivity. Equation (2.2) indicates that p is the resistance of a material in unit length and unit cross-section area. 2.1.2. Matthiessen's Rule and TCR For pure metals, resistivity p is the sum of two items: a residual part, p r , and a thermal part, p t (see Fig. 2.1). This is called Matthiessen's rule: P(total) = Pr + Pt P = Pr(l+Pt/Pr) Pt/Pr = f(T) P = /V[1 + /(T)]. (2.3) (2.4) (2.5) (2.6) For most metals and alloys, p is approximately proportional to temperature T and can be written as (see Fig. 2.2) p = p 0 (l + aAT), (2.7) where a is called the temperature coefficient of resistivity (TCR). Temperature, K Fig. 2.1. Resistivity versus temperature for a typical metal, Matthiessen's Rule. 10 An Introduction to Electronic and Ionic Materials -273 -200 0 100 200 Temperature. C Fig.2.2. The effect of temperature on the resistivity of selected metals.
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