Physics
Electrical Resistance
Electrical resistance is a measure of how much a material opposes the flow of electric current. It is determined by the material's properties and is measured in ohms. Conductors have low resistance, allowing easy flow of current, while insulators have high resistance, impeding the flow of current. Resistance can be calculated using Ohm's law, which relates resistance, current, and voltage.
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11 Key excerpts on "Electrical Resistance"
- 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)
KEY IDEAS • The resistance R of a conductor is defned as R = V i , where V is the potential difference across the conductor and i is the current. • The resistivity and conductivity of a material are related by = 1 = E J , where E is the magnitude of the applied electric feld and J is the magnitude of the current density. • The electric feld E and the current density J are related to the resistivity by E = J. • The resistance R of a conducting wire of length L and uniform cross section is R = L A , where A is the cross‐sectional area. • 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 ( T − T 0 ) . Here T 0 is a reference temperature, 0 is the resistivity at T 0 , and is the temperature coeffcient of resistivity for the material. Pdf_Folio:577 CHAPTER 26 Current and resistance 577 If we apply the same potential difference between the ends of geometrically similar rods of copper and of glass, very different currents result. The reason is that the current depends on a characteristic of the conductor called the Electrical Resistance. We determine the resistance between any two points of a conductor by applying a potential difference V between those points and measuring the current i that results. The resistance R is then R = V i . (26.11) The equation shows that the SI unit for resistance is the volt per ampere, but this combination occurs so frequently that it has a special name, the ohm (symbol Ω); that is, 1 ohm = 1 Ω = 1 volt per ampere = 1 V∕A. (26.12) A conductor whose function in a circuit is to provide a specified resistance is called a resistor. Figure 26.8 shows an assortment of resistors, with the circular bands around them indicating colour‐coding marks that identify the value of each resistance.
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 - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
• Electrical signals travel at speeds about 10 12 times greater than the drift velocity of free electrons. 20.2 Ohm’s Law: Resistance and Simple Circuits • A simple circuit is one in which there is a single voltage source and a single resistance. • One statement of Ohm’s law gives the relationship between current I , voltage V , and resistance R in a simple circuit to be I = V R . • Resistance has units of ohms ( Ω ), related to volts and amperes by 1 Ω = 1 V/A . • There is a voltage or IR drop across a resistor, caused by the current flowing through it, given by V = IR . 20.3 Resistance and Resistivity • The resistance R of a cylinder of length L and cross-sectional area A is R = ρL A , where ρ is the resistivity of the material. • Values of ρ in Table 20.1 show that materials fall into three groups—conductors, semiconductors, and insulators. • Temperature affects resistivity; for relatively small temperature changes ΔT , resistivity is ρ = ρ 0 (1 + αΔT ) , where ρ 0 is the original resistivity and α is the temperature coefficient of resistivity. • Table 20.2 gives values for α , the temperature coefficient of resistivity. • The resistance R of an object also varies with temperature: R = R 0 (1 + αΔT ) , where R 0 is the original resistance, and R is the resistance after the temperature change. 20.4 Electric Power and Energy • Electric power P is the rate (in watts) that energy is supplied by a source or dissipated by a device. • Three expressions for electrical power are 798 Chapter 20 | Electric Current, Resistance, and Ohm's Law This OpenStax book is available for free at http://cnx.org/content/col11406/1.9 P = IV, P = V 2 R , and P = I 2 R. • The energy used by a device with a power P over a time t is E = Pt . 20.5 Alternating Current versus Direct Current • Direct current (DC) is the flow of electric current in only one direction. It refers to systems where the source voltage is constant.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
● The resistance R of a conducting wire of length L and uniform cross section is R = ρ L __ A , where A is the cross-sectional area. ● 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 ). 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. TopFoto 798 CHAPTER 26 CURRENT AND RESISTANCE As we have done several times in other connections, we often wish to take a general view and deal not with particular objects but with materials. Here we do so by focusing not on the potential difference V across a particular resistor but on the electric field E → at a point in a resistive material. Instead of dealing with the current i through the resistor, we deal with the current den- sity J → at the point in question. Instead of the resistance R of an object, we deal with the resistivity of the material: ρ = E __ J (definition of ). (26.3.3) (Compare this equation with Eq. 26.3.1.) If we combine the SI units of E and J according to Eq. 26.3.3, we get, for the unit of , the ohm-meter (Ω · m): unit (E) ________ unit (J) = V / m _____ A / m 2 = V __ A m = Ω ⋅ m. (Do not confuse the ohm-meter, the unit of resistivity, with the ohmmeter, which is an instrument that measures resistance.) Table 26.3.1 lists the resis- tivities of some materials. We can write Eq. 26.3.3 in vector form as E → = ρ J → . (26.3.4) Equations 26.3.3 and 26.3.4 hold only for isotropic materials—materials whose electrical properties are the same in all directions. We often speak of the conductivity σ of a material. This is simply the reciprocal of its resistivity, so σ = 1 __ ρ (definition of σ). (26.3.5) The SI unit of conductivity is the reciprocal ohm-meter, (Ω · m) –1 . The unit name mhos per meter is sometimes used (mho is ohm backwards).
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
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. 26-8b. 753 26-3 RESISTANCE AND RESISTIVITY ● The resistance R of a conductor is defined as R = V i , where V is the potential difference across the conductor and i is the current. ● The resistivity and conductivity σ of a material are related by ρ = 1 σ = E J , where E is the magnitude of the applied electric field and J is the magnitude of the current density. ● The electric field and current density are related to the resistivity by E → = ρ J → . ● The resistance R of a conducting wire of length L and uniform cross section is R = ρ L A , where A is the cross-sectional area. ● 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 ). 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. Key Ideas Figure 26-7 An assortment of resistors. The circular bands are color-coding marks that identify the value of the resistance.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
(26.3.2) A conductor whose function in a circuit is to provide a specified resistance is called a resistor (see Fig. 26.3.1). In a circuit diagram, we represent a resistor and a resistance with the symbol . If we write Eq. 26.3.1 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 potential difference is applied to it. Figure 26.3.2, 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. 26.3.2b. Figure 26.3.1 An assortment of resis- tors. The circular bands are color- coding marks that identify the value of the resistance. Figure 26.3.2 Two ways of applying a potential difference to a conducting rod. The gray connectors are assumed to have negligible resistance. When they are arranged as in (a) in a small region at each rod end, the measured resistance is larger than when they are arranged as in (b) to cover the entire rod end. ( a) ( b ) Key Ideas ● The resistance R of a conductor is defined as R = V __ i , where V is the potential difference across the conduc- tor and i is the current. ● The resistivity and conductivity σ of a material are related by ρ = 1 __ σ = E __ J , where E is the magnitude of the applied electric field and J is the magnitude of the current density. ● The electric field and current density are related to the resistivity by E → = ρ J → . ● The resistance R of a conducting wire of length L and uniform cross section is R = ρ L __ A , where A is the cross-sectional area. ● 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 ).
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
(26.3.2) A conductor whose function in a circuit is to provide a specified resistance is called a resistor (see Fig. 26.3.1). In a circuit diagram, we represent a resistor and a resistance with the symbol . If we write Eq. 26.3.1 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 potential difference is applied to it. Figure 26.3.2, 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. 26.3.2b. Figure 26.3.1 An assortment of resis- tors. The circular bands are color- coding marks that identify the value of the resistance. Figure 26.3.2 Two ways of applying a potential difference to a conducting rod. The gray connectors are assumed to have negligible resistance. When they are arranged as in (a) in a small region at each rod end, the measured resistance is larger than when they are arranged as in (b) to cover the entire rod end. ( a) ( b ) Key Ideas ● The resistance R of a conductor is defined as R = V __ i , where V is the potential difference across the conduc- tor and i is the current. ● The resistivity and conductivity σ of a material are related by ρ = 1 __ σ = E __ J , where E is the magnitude of the applied electric field and J is the magnitude of the current density. ● The electric field and current density are related to the resistivity by E → = ρ J → . ● The resistance R of a conducting wire of length L and uniform cross section is R = ρ L __ A , where A is the cross-sectional area. ● 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 ).
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
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. 26-8b. ● The resistance R of a conductor is defined as R = V i , where V is the potential difference across the conductor and i is the current. ● The resistivity and conductivity σ of a material are related by ρ = 1 σ = E J , where E is the magnitude of the applied electric field and J is the magnitude of the current density. ● The electric field and current density are related to the resistivity by E → = ρ J → . ● The resistance R of a conducting wire of length L and uniform cross section is R = ρ L A , where A is the cross-sectional area. ● 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 ). 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. Key Ideas Figure 26-7 An assortment of resistors. The circular bands are color-coding marks that identify the value of the resistance. Figure 26-8 Two ways of applying a potential difference to a conducting rod. The gray connectors are assumed to have negligible resistance. When they are arranged as in (a) in a small region at each rod end, the measured resistance is larger than when they are arranged as in (b) to cover the entire rod end. (a ) (b ) 654 CHAPTER 26 CURRENT AND RESISTANCE As we have done several times in other connections, we often wish to take a general view and deal not with particular objects but with materials.
- 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 - ePub- J. W. S. Hearle, W E Morton(Authors)
- 2008(Publication Date)
- Woodhead Publishing(Publisher)
22Electrical Resistance
22.1 Introduction
When electricity was first intentionally conducted from one place to another (from an electrified tube to an ivory ball) by Stephen Gray in 1729, the material used as the conductor was hempen pack-thread. Gray eventually covered distances of up to 233 m along the corridors of his house. In order to do this, he had to support the packthread and, after an abortive attempt in which fine copper wires were used, he suspended the thread by silk filaments. Thus both the conductor and the insulator were textile fibres. Soon afterwards, Du Fay found that pack-thread was a better conductor when it was wet. Then, in 1734, Gray discovered metallic conductors, and, apart from some use for insulating purposes, interest in the Electrical Resistance of fibres did not revive for nearly 200 years [1 ].22.2 Definitions
The Electrical Resistance of a specimen, i.e. the voltage across the specimen divided by the current through it, is determined both by the properties of the material and the dimensions of the specimen. For most substances, the property of the material is best given by the specific resistance ρ (in Ωm), which is defined as the resistance between opposite faces of a 1 m cube, but, as with mechanical properties (see Section 13.3.1 ), it is more convenient with fibres to base a definition on linear density (mass per unit length) than on area of cross-section. A mass -specific resistance R s is therefore defined as the resistance in ohms between the ends of a specimen 1 m long and of mass 1 kg, giving units of Ωkg/m2 . The two quantities are related as follows:R s= ρd(22.1)where d = density of material in kg/m3 .In practice, it is more convenient to express R s in Ωg/cm2 , when the numerical values for most fibres will differ by less than 50% from the values of ρ expressed in Ωcm. With these units, the resistance R
eBook - ePubCircuit Analysis with PSpice
A Simplified Approach
- Nassir H. Sabah(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
2 Fundamentals of Resistive CircuitsObjective and Overview
This chapter introduces (1) the two ideal circuit elements of dc circuits, namely, resistors and sources; (2) the two basic circuit laws, namely, Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL); and (3) the two basic connections between circuit elements, namely, series and parallel connections.The nature of Electrical Resistance is first explained using a simplified model, following which, the very basic Ohm’s law defining an ideal resistor is presented. Ideal, independent and dependent, voltage and current sources are then discussed, with emphasis on their defining and essential properties.Kirchhoff’s laws are introduced as laws derived from conservation of charge and conservation of energy, but which provide a much simpler means of analyzing circuit behavior. Series and parallel connections of circuit elements are then discussed and linked to Kirchhoff’s laws.PSpice simulations are introduced in this chapter and are included in all numerical examples, whenever appropriate, to illustrate and verify the results of analytical solutions. This chapter concludes with a very helpful problem-solving approach and illustrating it with examples.⋆ 2.1Nature of ResistanceConcept: Resistance is fundamentally due to impediments to the movement of current carriers in a conductor under the influence of an applied electric field.A sample of a metallic conductor typically consists of a large number of crystals in which the rest positions of the metal atoms at 0 K are arranged in a regular manner that is characteristic of the type of crystal. At temperatures above 0 K, (1) the crystal atoms vibrate, in randomly oriented directions, about their rest positions, with an amplitude of vibration that increases with temperature, and (2) some electrons, referred to as conduction electrons have sufficient energy to detach from their parent atoms and move freely in the crystal, in randomly oriented directions, at thermal velocities of the order of 107
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