Resistance

12 Key excerpts on "Resistance"

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  eBook - PDF

  Halliday's Fundamentals of Physics, 1st Australian & New Zealand Edition

  • 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.

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  College Physics Essentials, Eighth Edition

  Electricity and Magnetism, Optics, Modern Physics (Volume Two)

  • Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  Resistors in use A printed circuit board, typically used in many electrical devices, can include resistors of different values. The striped cylinders are resistors; their banded color code indicates their Resistance value in ohms.

  But how is Resistance quantified? For example, if a large voltage applied across an object produces only a small current, it is clear that the object has a high electrical Resistance. Keeping this notion in mind, the electrical Resistance of any object is defined as the ratio of the voltage applied across it to the resulting current in it, or

  R   =   Δ V I     ( electrical Resistance definition )	(17.2)

  SI unit of Resistance: volt per ampere (V/A), or ohm (Ω )

  Resistance units are volts per ampere (V/A), named the ohm (Ω ) in honor of the German physicist Georg Ohm (1789–1854), who investigated the relationship between current and voltage. Large values of Resistance are expressed as kilohms (kΩ ) and even megohms (MΩ ). A schematic circuit diagram showing how, in principle, Resistance is determined is illustrated in ▼ Figure 17.10 .

  ▲ Figure 17.10 Measuring Resistance In principle, any object’s electrical Resistance can be determined by dividing the voltage across it by the resulting current through it.

  For some materials, the Resistance may be constant over a range of voltages. A resistor that exhibits constant Resistance is said to obey Ohm ’s law , or to be ohmic. The law was named after Ohm, who found that many materials, particularly metals, possessed this property. A plot of voltage versus resulting current for an ohmic material is linear with a slope equal to its Resistance R (▼ Figure 17.11 ). In most of our study, it will be assumed that the resistors are ohmic. Remember however, that current will be directly proportional to the applied voltage only if R is constant

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  Fundamentals of Physics, Volume 2

  • 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 ).

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  Fundamentals of Physics

  • 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 ).

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  College Physics

  • Paul Peter Urone, Roger Hinrichs(Authors)
  • 2012(Publication Date)
  • Openstax

    (Publisher)

  20.2 Ohm’s Law: Resistance and Simple Circuits What drives current? We can think of various devices—such as batteries, generators, wall outlets, and so on—which are necessary to maintain a current. All such devices create a potential difference and are loosely referred to as voltage sources. When a voltage source is connected to a conductor, it applies a potential difference V that creates an electric field. The electric field in turn exerts force on charges, causing current. 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: (20.12) I ∝ V . This important relationship is known as 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 like that for friction—an experimentally observed phenomenon. Such a linear relationship doesn’t always occur. Resistance and Simple Circuits If voltage drives current, what impedes it? The electric property that impedes current (crudely similar to friction and air Resistance) is called Resistance R . Collisions of moving charges with atoms and molecules in a substance transfer energy to the substance and limit current. Resistance is defined as inversely proportional to current, or (20.13) I ∝ 1 R . Thus, for example, current is cut in half if Resistance doubles. Combining the relationships of current to voltage and current to Resistance gives (20.14) I = V R . This relationship is also called Ohm’s law. Ohm’s law in this form really defines Resistance for certain materials. Ohm’s law (like Hooke’s law) is not universally valid. The many substances for which Ohm’s law holds are called ohmic. These include good conductors like copper and aluminum, and some poor conductors under certain circumstances.

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  Fundamentals of Physics, Extended

  • 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.

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  University Physics Volume 2

  • William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
  • 2016(Publication Date)
  • Openstax

    (Publisher)

  All such devices create a potential difference and are referred to as voltage sources. When a voltage source is connected to a conductor, it applies a potential difference V that creates an electrical field. The electrical field, in turn, exerts force on free charges, causing current. The amount of current depends not only on the magnitude of the voltage, but also on the characteristics of the material that the current is flowing through. The material can resist the flow of the charges, and the measure of how much a material resists the flow of charges is known as the resistivity. This resistivity is crudely analogous to the friction between two materials that resists motion. Resistivity When a voltage is applied to a conductor, an electrical field E → is created, and charges in the conductor feel a force due to the electrical field. The current density J → that results depends on the electrical field and the properties of the material. This dependence can be very complex. In some materials, including metals at a given temperature, the current density is approximately proportional to the electrical field. In these cases, the current density can be modeled as J → = σ E → , where σ is the electrical conductivity. The electrical conductivity is analogous to thermal conductivity and is a measure of a material’s ability to conduct or transmit electricity. Conductors have a higher electrical conductivity than insulators. Since the electrical conductivity is σ = J /E , the units are σ = [J ] [E] = A/m 2 V/m = A V · m . Here, we define a unit named the ohm with the Greek symbol uppercase omega, Ω . The unit is named after Georg Simon Ohm, whom we will discuss later in this chapter. The Ω is used to avoid confusion with the number 0. One ohm equals one volt per amp: 1 Ω = 1 V/A . The units of electrical conductivity are therefore ( Ω · m) −1 . Conductivity is an intrinsic property of a material.

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  Halliday and Resnick's Principles of Physics

  • 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.

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  Electricity

  • Leslie Basford(Author)
  • 2013(Publication Date)
  • Made Simple

    (Publisher)

  Materials which have practically no Resistance at extremely low temperatures are described as superconducting. The Resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area. The relationship is given by the formula where p is the resistivity of the conducting material. The combined Resistance R of any number of resistors Ri 9 R2 9 R3, etc., in series is given by R = R± + R2 + R3 + . . . The combined Resistance R of any number of resistors Ri 9 Ife, ife, etc., in parallel is given by ^ = ^ + j ^ + j ^ + --' Kirchhoff's first law states that the sum of the currents flowing into any junction in a circuit is equal to the sum of the currents flowing out of it. KirchhofF's second law states that the total e.m.f. in any closed loop of a circuit is equal to the sum of the potential differences across the Resistances in the loop. Resistance 37 Resistance can be measured accurately with a Wheatstone bridge. The condition for a balanced bridge is S ~~ h where h is the length of bridge wire between the sliding contact and the (unknown) Resistance whose value is X 9 h is the length of bridge wire between the sliding contact and the (standard) resistor whose value is S.

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  Principles of Physics: Extended, International Adaptation

  • 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).

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  Circuit Analysis with PSpice

  A Simplified Approach

  • Nassir H. Sabah(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Joule heating.

  2.2Ideal Resistor

  Definition: An ideal resistor is a purely dissipative circuit element that obeys Ohm’s law.

  As mentioned in Section 1.8 , an ideal resistor only dissipates energy. It does not store electric or magnetic energy. According to Ohm’s law, the voltage drop across an ideal resistor is directly proportional to the current through the resistor. Thus,

  (2.1)

  v = R i

  where R is the Resistance of the given resistor. When v is in volts and i is in amperes, R is in ohms and is denoted by Ω, the Greek capital omega. For an ideal resistor, R is a constant, independent of voltage, current, time, and temperature.

  According to Equation 2.1 , the plot of v against i is a straight line of slope R passing through the origin, irrespective of the magnitude or direction of current (Figure 2.2 a). The graphical symbol for a resistor is illustrated in Figure 2.2 b together with the direction of i that is associated with the polarity of v in Equation 2.1 . It is important to note that the current through an ideal resistor is always in the direction of the voltage drop across the resistor, so as to give a positive value of R in Equation 2.1 . Thus, with v and i in Equation 2.1 assigned the positive directions indicated in Figure 2.2 b, a positive value of i is in the direction of a positive value of voltage drop v, which gives a positive value of R in Equation 2.1 . This is also in accordance with the passive sign convention (Section 1.7

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  Physical Properties of Textile Fibres

  • J. W. S. Hearle, W E Morton(Authors)
  • 2008(Publication Date)
  • Woodhead Publishing

    (Publisher)

  22

  Electrical 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

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