Cable Capacitance

11 Key excerpts on "Cable Capacitance"

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  eBook - PDF

  Physics, Volume 2

  • David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  CHAPTER 30 679 CHAPTER 30 CAPACITANCE I n many applications of electric circuits, the goal is to store electrical charge or energy in an electrostatic field. A device that stores charge is called a capacitor, and the property that determines how much charge it can store is its capacitance. We shall see that the ca- pacitance depends on the geometrical properties of the device and not on the electric field or the potential. In this chapter we define capacitance and show how to calculate the capacitance of a few simple de- vices and of combinations of capacitors. We study the energy stored in capacitors and show how it is re- lated to the strength of the electric field. Finally, we investigate how the presence of a dielectric in a capaci- tor enhances its ability to store electric charge. 30-1 CAPACITORS A capacitor* is a device that stores energy in an electrosta- tic field. A flashbulb, for example, requires a short burst of electric energy that exceeds what a battery can generally provide. A capacitor can draw energy relatively slowly (over several seconds) from the battery, and it then can re- lease the energy rapidly (within milliseconds) through the bulb. Much larger capacitors are used to produce short laser pulses in attempts to induce thermonuclear fusion in tiny pellets of hydrogen. In this case the power level during the pulse is about 10 14 W, about 200 times the entire electrical generating capacity of the United States, but the pulses typ- ically last only for 10 9 s. Capacitors are also used to produce electric fields, such as the parallel-plate device that gives the very nearly uni- form electric field that deflects beams of electrons in a TV or oscilloscope tube. In circuits, capacitors are often used to smooth out the sudden variations in line voltage that can damage computer memories. In another application, the tuning of a radio or TV receiver is usually done by varying the capacitance of the circuit.

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  Fundamentals of Physics, Extended

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  The physics of capacitors can be generalized to other devices and to any situation involving electric fields. For example, Earth’s atmo- spheric electric field is modeled by meteorologists as being produced by a huge spherical capacitor that partially discharges via lightning. The charge that skis collect as they slide along snow can be modeled as being stored in a capacitor that frequently discharges as sparks (which can be seen by nighttime skiers on dry snow). The first step in our discussion of capacitors is to determine how much charge can be stored. This “how much” is called capacitance. Capacitance Figure 25.1.1 shows some of the many sizes and shapes of capacitors. Figure 25.1.2 shows the basic elements of any capacitor—two isolated conductors of any shape. No matter what their geometry, flat or not, we call these conductors plates. Figure 25.1.1 An assortment of capacitors. Paul Silvermann/Fundamental Photographs 760 CHAPTER 25 CAPACITANCE Figure 25.1.3a shows a less general but more conventional arrangement, called a parallel-plate capacitor, consisting of two parallel conducting plates of area A separated by a distance d. The symbol we use to represent a capacitor (⫞⊦) is based on the structure of a parallel-plate capacitor but is used for capacitors of all geometries. We assume for the time being that no material medium (such as glass or plastic) is present in the region between the plates. In Module 25.5, we shall remove this restriction. When a capacitor is charged, its plates have charges of equal magnitudes but opposite signs: +q and –q. However, we refer to the charge of a capacitor as being q, the absolute value of these charges on the plates. (Note that q is not the net charge on the capacitor, which is zero.) Because the plates are conductors, they are equipotential surfaces; all points on a plate are at the same electric potential. Moreover, there is a potential dif- ference between the two plates.

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  eBook - ePub

  Power Cable Technology

  • Sushil Kumar Ganguli, Vivek Kohli(Authors)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  −12 ). The capacity of retaining the electrical charge in the insulation depends on the thickness of the insulation and the diameter of the conductor and its length. The capacitance of a single-core cable, thus, depends on

   

  1. The dimensions of the cable, such as its length, radius of the conductor ro and radius over the insulation R

  2. Relative permittivity (dielectric constant), εr , of the homogenous insulation material

    Thus, the measure of capacitance is given by  

  (8.15)

    On simplification, it gives  

  (8.16)

    For round three-core belted cables,

  Star capacitance can be taken as C1 = 1.2C (conductor to neutral)

  Conductor to conductor C2 = 0.6C (other conductors are free floating)

  All conductors bunched to sheath C3 = 1.8C

  The relative permittivity of materials is shown in Table 8.4 .

  This capacity of retaining the charge per unit volume increases as the length of the cable increases, that is, the volume of insulation increases proportionately. This charge is absorbed from the flowing current, and this absorbed current is called the charging current (current absorbed by the insulation, when the cable is charged with power, i.e. current and voltage) and is given by

   

  (8.17)

    where

  ω = 2πf rad/s

  f is the frequency

  Vo is the operating voltage

   

  It can be seen that as the length of the cable increases, the absorption of power also increases within the insulation, which means that the value of C

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  University Physics Volume 2

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

    (Publisher)

  8 | CAPACITANCE Figure 8.1 The tree-like branch patterns in this clear Plexiglas® block are known as a Lichtenberg figure, named for the German physicist Georg Christof Lichtenberg (1742–1799), who was the first to study these patterns. The “branches” are created by the dielectric breakdown produced by a strong electric field. (credit: modification of work by Bert Hickman) Chapter Outline 8.1 Capacitors and Capacitance 8.2 Capacitors in Series and in Parallel 8.3 Energy Stored in a Capacitor 8.4 Capacitor with a Dielectric 8.5 Molecular Model of a Dielectric Introduction Capacitors are important components of electrical circuits in many electronic devices, including pacemakers, cell phones, and computers. In this chapter, we study their properties, and, over the next few chapters, we examine their function in combination with other circuit elements. By themselves, capacitors are often used to store electrical energy and release it when needed; with other circuit components, capacitors often act as part of a filter that allows some electrical signals to pass while blocking others. You can see why capacitors are considered one of the fundamental components of electrical circuits. 8.1 | Capacitors and Capacitance Learning Objectives By the end of this section, you will be able to: • Explain the concepts of a capacitor and its capacitance • Describe how to evaluate the capacitance of a system of conductors A capacitor is a device used to store electrical charge and electrical energy. It consists of at least two electrical conductors separated by a distance. (Note that such electrical conductors are sometimes referred to as “electrodes,” but more correctly, Chapter 8 | Capacitance 345 they are “capacitor plates.”) The space between capacitors may simply be a vacuum, and, in that case, a capacitor is then known as a “vacuum capacitor.” However, the space is usually filled with an insulating material known as a dielectric.

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  Fundamentals of Physics, Extended

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  717 C H A P T E R 2 5 Capacitance What Is Physics? One goal of physics is to provide the basic science for practical devices designed by engineers. The focus of this chapter is on one extremely common example—the capacitor, a device in which electrical energy can be stored. For example, the batteries in a camera store energy in the photoflash unit by charg- ing a capacitor. The batteries can supply energy at only a modest rate, too slowly for the photoflash unit to emit a flash of light. However, once the capacitor is charged, it can supply energy at a much greater rate when the photoflash unit is triggered—enough energy to allow the unit to emit a burst of bright light. The physics of capacitors can be generalized to other devices and to any situ- ation involving electric fields. For example, Earth’s atmospheric electric field is modeled by meteorologists as being produced by a huge spherical capacitor that partially discharges via lightning. The charge that skis collect as they slide along snow can be modeled as being stored in a capacitor that frequently discharges as sparks (which can be seen by nighttime skiers on dry snow). The first step in our discussion of capacitors is to determine how much charge can be stored. This “how much” is called capacitance. Capacitance Figure 25-1 shows some of the many sizes and shapes of capacitors. Figure 25-2 shows the basic elements of any capacitor — two isolated conductors of any 25-1 CAPACITANCE Learning Objectives After reading this module, you should be able to . . . 25.01 Sketch a schematic diagram of a circuit with a parallel-plate capacitor, a battery, and an open or closed switch. 25.02 In a circuit with a battery, an open switch, and an uncharged capacitor, explain what happens to the conduction electrons when the switch is closed.

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  Halliday and Resnick's Principles of Physics

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  C H A P T E R 2 5 Capacitance What Is Physics? One goal of physics is to provide the basic science for practical devices designed by engineers. The focus of this chapter is on one extremely common example—the capacitor, a device in which electrical energy can be stored. For example, the batteries in a camera store energy in the photoflash unit by charging a capacitor. The batteries can supply energy at only a modest rate, too slowly for the photoflash unit to emit a flash of light. However, once the capaci- tor is charged, it can supply energy at a much greater rate when the photoflash unit is triggered—enough energy to allow the unit to emit a burst of bright light. The physics of capacitors can be generalized to other devices and to any sit- uation involving electric fields. For example, Earth’s atmospheric electric field is modeled by meteorologists as being produced by a huge spherical capacitor that partially discharges via lightning. The charge that skis collect as they slide along snow can be modeled as being stored in a capacitor that frequently dis- charges as sparks (which can be seen by nighttime skiers on dry snow). The first step in our discussion of capacitors is to determine how much charge can be stored. This “how much” is called capacitance. Capacitance Figure 25-1 shows some of the many sizes and shapes of capacitors. Figure 25-2 shows the basic elements of any capacitor — two isolated conductors 25-1 CAPACITANCE Learning Objectives After reading this module, you should be able to . . . 25.01 Sketch a schematic diagram of a circuit with a parallel-plate capacitor, a battery, and an open or closed switch. 25.02 In a circuit with a battery, an open switch, and an uncharged capacitor, explain what happens to the conduction electrons when the switch is closed.

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  Electrical Power Cable Engineering

  • William A. Thue(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  In coaxial cables, three kinds of inductance must be taken into account: space inductance, inductance within the inner conductor, and inductance within the outer conductor. Above 50 kilohertz, only space inductance needs to be considered for results with less than 0.5% error. The equation for a coaxial cable with a tubular outer conductor becomes:

  L f = 4.6 log 10 r 2 r 1 × 10 − 9

  (4.36)

  where

  Lf = inductance in henries per centimeter

  r2 = inner radius of outer conductor in inches

  r1 = radius of inner conductor in inches.

  If the outer conductor is stranded or braided, the inductance is slightly higher. 4.20  CAPACITANCE

  This is the property of an electric system comprising insulated conductors and associated dielectric materials that determines, for a given time rate of change of potential difference between the conductors, the displacement currents in the system.

  The unit of capacitance is the farad and it is that capacitance of a circuit whose potential difference will be raised 1 V by the addition of a charge of 1 coulomb.

  4.20.1  CAPACITANCE OF A CABLE

  The electrostatic capacitance of an insulated conductor 1 cm in length, in absolute units, is:

  C = ε 2 log ε D d

  (4.37)

  where

  C = capacitance

  ε = dielectric constant of the insulating material

  D = outer diameter of the insulation

  d = inside diameter of the insulation.

  In more common terms, the equation is:

  C = 7.354 ε log 10 1 + 2 t / d

  (4.38)

  4.21  REACTANCE

  Reactance is the product of the sine of the angular phase difference between the current and potential difference times the ratio of the effective potential difference to the effective current because there is no source of power in the portion of the circuit under consideration. The total reactance of a circuit is the sum of the inductive and capacitive reactances.

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  eBook - ePub

  Physics for Students of Science and Engineering

  • A. L. Stanford, J. M. Tanner(Authors)
  • 2014(Publication Date)
  • Academic Press

    (Publisher)

  capacitance C of a two-conductor system is defined by

  Figure 14.1 Two electrical conductors, A and B . A positive charge Q has been transferred fromB toA , leaving B with a negative charge –Q .

  C =

  Q

  Δ V

  (14-1)

  (14-1)

  which is an inherently positive quantity because both Q and ΔV are positive. As we will see, the ratio of charge Q to potential difference ΔV is a constant value for a fixed-configuration capacitor. Thus, the capacitance of a given capacitor with fixed conductors is a constant value; if the transferred charge Q of a given capacitor is changed, the potential difference ΔV changes proportionately.

  The unit of capacitance, as indicated by Equation (14–1) , is a coulomb (C) per volt (V), which is defined to be a farad (F), or

  1 F = 1

  C V

  (14-2)

  (14-2)

  Convenient values of capacitance are considerably smaller than a farad, and the most frequently encountered measures of capacitance are the microfarad (1 μF= 10−6 F) and the picofarad (1 pF = 10−12 F).

  Capacitance of Symmetrical Capacitors

  The most common capacitor is the parallel-plate capacitor, illustrated in Figure 14.2 . In this arrangement, the separation d

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  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)

  CHAPTER 25 Capacitance 25.1 Capacitance LEARNING OBJECTIVES After reading this module, you should be able to: 25.1.1 sketch a schematic diagram of a circuit with a parallel‐plate capacitor, a battery, and an open or closed switch 25.1.2 in a circuit with a battery, an open switch, and an uncharged capacitor, explain what happens to the conduction electrons when the switch is closed 25.1.3 for a capacitor, apply the relationship between the magnitude of charge q on either plate (‘the charge on the capacitor’), the potential difference V between the plates (‘the potential across the capacitor’), and the capacitance C of the capacitor. KEY IDEAS • A capacitor consists of two isolated conductors (the plates) with charges +q and −q. Its capacitance C is defned from q = CV, where V is the potential difference between the plates. • When a circuit with a battery, an open switch, and an uncharged capacitor is completed by closing the switch, conduction electrons shift, leaving the capacitor plates with opposite charges. Why study physics? People in Australia and New Zealand who install timber flooring deal with many consumer complaints arising from moisture problems. Capacitance moisture meters determine the amount of moisture in the timber based upon the change in the dielectric constant of the timber. This varies with timber density and moisture content. 1 One goal of physics is to provide the basic science for practical devices designed by engineers. The focus of this chapter is on one extremely common example — the capacitor, a device in which electrical energy can be stored. The first step in our discussion of capacitors is to determine how much charge can be stored. This ‘how much’ is called capacitance. Capacitance Figure 25.1 shows some of the many sizes and shapes of capacitors. Figure 25.2 shows the basic elements of any capacitor — two isolated conductors of any shape, which, flat or not, are called plates.

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  eBook - ePub

  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)

  capacitance :

  Q = C   ⋅   Δ V   or   C = Q Δ V   (definition   of   capacitance)	(16.9)

  SI unit of capacitance is the coulomb per volt (C/V) or the farad (F)

  The coulomb per volt is named the farad after Michael Faraday, a famous physicist of the nineteenth century, thus 1 C/V = 1 F. The farad is a large unit (see Example 16.6), so the microfarad (1 µ F = 10− 6 F), the nanofarad (1 nF = 10− 9 F), and the picofarad (1 pF = 10− 12 F) are commonly used.

  Capacitance represents the charge Q that can be stored per volt . If a capacitor has a large capacitance value, this means it is capable of holding a large charge per volt compared to one of smaller capacitance. Thus if you connect the same battery to two different capacitors, the one with the larger capacitance stores more charge and energy.

  Capacitance depends only on the geometry (size, shape, and spacing) of the plates (and possibly any material between the plates – see Section 16.5) but specifically not the charge on the plates. To understand this, consider again a set of parallel plates which is now called a parallel plate capacitor. The electric field between the plates given by Equation 16.5:

  E =

  4 π k Q

  A

  The potential difference between the plates can be computed from Equation 16.2 as follows:

  Δ V = E d =

  4 π k Q d

  A

  The capacitance of a parallel plate arrangement is then

  C = Q Δ V = ( 1 4 π k ) A d   ( parallel   plates   only )	(16.10)

  It is common to replace the constants in the parentheses in Equation 16.10 with a single constant called the permittivity of free space ( ε o ) . Knowing k , the permittivity has a value of

  ε o = 1 4 π k = 8.85 × 10 − 12 C 2 N   ⋅   m 2   (permittivity   of free   space )	(16.11)

  ε o

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  Fundamentals of Electromagnetics

  1Internal Behavior of Lumped Elements

  • David Voltmer(Author)
  • 2022(Publication Date)
  • Springer

    (Publisher)

  91 C H A P T E R 2 Capacitors 2.1 CAPACITORS: A FIRST GLANCE The basic function of a capacitor is as a storage element for electric energy. Its configuration is designed to enhance this function. Properly selected materials minimize its power dissipation as well. As you recall from circuits, the terminal behavior of an ideal capacitor is given by I C = C dV C dt (2.1) where I C is the current flowing into the capacitor in the direction of the voltage drop across the capacitor, V C , and C is the capacitance value of the capacitor expressed in Farads and abbreviated as F . Its terminal behavior is more complicated than that of a resistor due to the presence of the derivative of voltage. As with resistors, we will investigate the internal, electromagnetic behavior of capacitors to better understand them. The simplest capacitor configuration has many similarities with that of resistors, see Fig. 2.1. Two metallic wire leads provide the connection between a capacitor and the external circuit. Current enters the element at one end through the wire lead and flows directly onto a metallic electrode. An equal current flows from the other electrode out of the capacitor via the other wire lead. The flux guiding material is located between the two metal electrodes. An insulator serves as the electric flux guide in a capacitor similar to the way conductive material in a resistor guides the current flux. The charges that enter the capacitor do not flow to the opposite electrode and leave via the other lead because the conductivity of the insulator is zero. Instead, they accumulate on the electrode while an equal charge flows from the other electrode out of the other wire lead. This leaves equal but opposite charges on the two electrodes. The use of an insulating flux guide instead of one that is conductive is the chief reason for the marked difference in behavior between capacitors and resistors.

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