7 Key excerpts on "Electric Potential"

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  eBook - ePub

  Electromagnetics Explained

  A Handbook for Wireless/ RF, EMC, and High-Speed Electronics

  • Ron Schmitt(Author)
  • 2002(Publication Date)
  • Newnes

    (Publisher)

  * Without any aether, there is no way to measure absolute velocity. All movement is therefore relative.

  Figure 2.2 Two balls attached by a spring. The spring exerts an attractive force when the balls are pulled apart.

  VOLTAGE AND POTENTIAL ENERGY

  A quantity that goes hand in hand with the electric field is voltage. Voltage is also called potential, which is an accurate description since voltage quantifies potential energy. Voltage, like the electric field, is normalized per unit charge.

  Voltage = Potential energy of a unit charge

  In other words, multiplying voltage by charge gives the potential energy of that charge, just as multiplying the electric field by charge gives the force felt by the charge. Mathematically we represent this by

  Potential energy is always a relative term; therefore voltage is always relative. Gravity provides a great visual analogy for potential. Let’s define ground level as zero potential. A ball on the ground has zero potential, but a ball 6 feet in the air has a positive potential energy. If the ball were to be dropped from 6 feet, all of its potential energy will have been converted to kinetic energy (i.e., motion) just before it reaches the ground. Gravity provides a good analogy, but the electric field is more complicated because there are both positive and negative charges, whereas gravity has only positive mass. Furthermore, some particles and objects are electrically neutral, whereas all objects are affected by gravity. For instance, an unconnected wire is electrically neutral, therefore, it will not be subject to movement when placed in an electrical potential. (However, there are the secondary effects of electrostatic induction, which are described later in the chapter.)

  Consider another example, a vacuum tube diode, as shown in Figure 2.3

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  eBook - ePub

  Radiation Detection

  Concepts, Methods, and Devices

  • Douglas McGregor, J. Kenneth Shultis(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  potential, which is defined as the potential energy per unit charge,

  V = U Q ′ = 1 4 π ϵ o ∑ i = 1 n Q i r i ,	(8.16)

  and is expressed in units of volts (or joules per coulomb). Note that the potential is no longer dependent upon the “test” charge Q′ .3 The force exerted upon Q′ may also be expressed in terms of the electric field, produced by one or more point charges, in which

  F =

  Q ′

  E

  . Substitution of

  q ′

  E

  into Eq. (8.13 ) and division by Q′ gives the potential difference between two points within the electric field. Hence, the potential difference between arbitrary locations a and b is

  V a b = Δ V = ∫ a b E ⋅ d l = ∫ a b E cos ⁡ θ d l .	(8.17)

  In summary, Eq. (8.17 ) is the voltage that an experimenter would measure between two points (a and b) within an electric field. The work done on a unit test charge moving from some point a to another point b in the electric field is Q′ V

  ab

  .

  8.3Capacitance

  Consider the arrangement depicted in Fig. 8.6 . Two conductive plates, separated by a distance d, have equal, but opposite, charges. An electric field is produced between the plates by the charges on the plates. The positively charged plate (or terminal) has a voltage V1 and the negatively charged plate has a voltage V2 . The capacitance of the two plates is defined as the ratio of the charge magnitude on either plate to the magnitude of the potential difference between the plates,

  C = | Q Δ V | .	(8.18)

  If ΔV is taken as the applied voltage V between the electrodes, then the above definition gives the important relation

  C V = Q	(8.19)

  The SI unit for capacitance is the farad (one coulomb per volt). The reader should understand that the charge stored in a capacitor has a summed positive charge on one terminal and an equal summed negative charge stored on the opposite terminal; hence, a capacitor with stored charge Q actually has +Q on one terminal and −Q

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  eBook - ePub

  Electrical Engineering

  Fundamentals

  • Viktor Hacker, Christof Sumereder(Authors)
  • 2020(Publication Date)
  • De Gruyter Oldenbourg

    (Publisher)

  φ of the field at that point.

  Defining equation:

  φ =

  W p

  Q +

  1.9  Voltage V

  Voltage is the difference in Electric Potential between two points. In a static electric field, voltage is defined as the work needed to move a unit charge between two points.

  The necessary charge to transport a charge

  Q +

  from object 1 to object 2 equals the difference of the potential energies

  W

  1 , 2

  =

  W

  p , 2

  −

  W

  p , 1  

  of the charges on the two objects.

  The potential difference equals the work for the unit charge

  Q +

  = 1   A s

  :

  φ 2

  −

  φ 1

  =

  W

  1 , 2

  Q

  It is called voltage V (14 ).

  Defining equation:

  V =

  W

  1 , 2

  Q +

  V = V  

  V o l t

  15 SI unit:

  V =

  J

  A s

  The voltage between two objects therefore is the work that is necessary to transport the unit charge

  Q +

  = 1  

  A s

  from the negatively charged object to the positively charged object. If this voltage is expended, the charges are separated.

  Voltage can cause electric current: If there is a voltage between two particles and these two particles are connected through a conductor, current flows. (More specifically: There is an electric field between the two particles. This field exerts force on the free charge carriers, which causes them to move.)

  Voltage is connected to force:

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  eBook - ePub

  An Introduction to Electrical Science

  • Adrian Waygood(Author)
  • 2018(Publication Date)
  • Routledge

    (Publisher)

  always be 50 V.

  Potential differences or voltages are never described as being ‘positive’ or ‘negative’ in the sense of electric ‘charge ’.

  However, you will frequently hear the terms applied in the sense of the ‘direction ’ in which they act. For example, a voltage which acts, say, in a clockwise direction around a circuit might be arbitrarily-described as acting in a ‘positive ’ direction , whereas another voltage which acts in a counter clockwise direction would then be described as acting in a ‘negative ’ direction .

  Summary

  ‘Voltage ’ is simply another word for ‘potential difference ’; i.e. they are synonyms. ‘Voltage ’ is not another term for ‘potential ’.

  • It is correct to say, ‘The voltage across a resistor is so-many volts’.
  • It is incorrect to say, ‘The voltage at a point is so-many volts’; instead, we should say, ‘The potential at a point….’.
  • It is correct to say, ‘The voltage between line conductor and earth is 230 V’.
  • It is incorrect to say, ‘The voltage of the line conductor with respect to earth is 230 V’; instead, we should say, ‘The potential of the line conductor with respect to earth is 230 V’.

  Table 5.1

  potential difference	The difference in potentials between any two points in a circuit. Symbol :E or U – depending on context.
  voltage	A synonym for ‘potential difference’. Symbol; E or U – depending on context.
  electromotive force	The potential difference produced, internally, by a battery, generator, etc., and which appears across its terminals when it is not supplying a load. Symbol: E .
  voltage drop	The potential difference across an individual circuit component, such as a resistor, responsible for current through that component. Symbol: U 1 , U 2 , etc.
  potential	Potential exists at a single point in a circuit, and is measured relative to another randomly chosen point (in practice, often earth). Potential is either negative or positive with respect to the point of reference. Symbol: U.

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  eBook - ePub

  Introduction to Electrophysiological Methods and Instrumentation

  • Franklin Bretschneider, Jan R. de Weille(Authors)
  • 2018(Publication Date)
  • Academic Press

    (Publisher)

    V) but allow far larger currents to be drawn (hundreds of amperes in the case of a car battery).

  This brings us to the most important quantities to describe electrical phenomena: the unit of tension, the volt (V), and the unit of current, the ampere (A). Note that the correct spelling of the units is in lowercase letters when spelled out, but abbreviated as a single capital. In Anglo-Saxon countries, tension is often called “voltage.” Both units have practical values, that is, it is perfectly normal to have circuits under a tension of 1  V or carrying 1  A in the lab or even at home. The definitions are derived from other fundamental physical quantities:

  • Charge (Q): 1  coulomb is defined as the charge of 6.2415  ×  1018 electrons.
  • Current (I): 1  ampere is a current that transports 1  coulomb of charge per second.

  An overview of electrical quantities, their units, and symbols is given in the Appendix .

  The origin of the definition of tension, or potential difference, is a bit more intricate. The electrical forces that act on charges (or charged objects) depend not only on the field strength but also on the distance traveled. Thus, the electrical potential (abbreviated as U) is defined in terms of the amount of energy, or work (abbreviation W), involved in the movement of the charge from a certain point in the electric field to infinity (where the electrical forces are zero by definition). If one does not move to infinity, but from one point in the field to another point, less energy is involved. This is called the potential difference between the two points. Where to choose the two points will be a matter of practical, quantitative discussion.

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  eBook - ePub

  Standard Potentials in Aqueous Solution

  • Allen J. Bard, Roger Parsons, Joseph Jordan(Authors)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Chapter 1 .

  However, the classical definition of potential causes difficulty as soon as an attempt is made to consider the potential difference between two points in different media: for example, between a point in vacuum and a point in a condensed phase. This may be made clear by noting that the energy change in taking a test charge from one point to the other depends on the nature of the test charge because of the short-range “chemical” interaction between the test charge and the condensed phase. There is no complete solution to this problem because there is no method for the separation of “chemical” and “electrical” forces since they are both essentially electrical in nature.

  Nevertheless, some useful separations can be carried out on the basis of well-defined operations either on the real system or on a simple model of it. In the former case the quantities obtained are measurable, in the latter they are calculable in principle. These two cases can be illustrated first using the simple system of a piece of conducting material β of uniform bulk composition surrounded by free space. The work of inserting a charged particle of species i from a point distant from the conductor into a point in the bulk of the conductor is the electrochemical potential

  u ˜

  i β

  . This is a measurable quantity that depends on the nature of the phase β, on the nature of the charged particle i, and on the state of charge of β. Experimentally, it is possible to reduce the electrostatic charge on β to zero. This may be verified by the absence of a field in the free space around β. Under these conditions the electrochemical potential takes a particular value which has become known as the real potential

  α i β

  . The best known example of a real potential is the electronic work function. (Since the latter is a work of extraction, not a work of insertion, it is

  −

  α e β

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  eBook - ePub

  Electrical Engineering Fundamentals

  • S. Bobby Rauf(Author)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  1 Fundamental Electrical Engineering Concepts and Principles

  Introduction

  In this first chapter of the Electrical Engineering Fundamentals text, we will explore fundamental electrical engineering terms, concepts, principles, and analytical techniques and impart knowledge that is considered elemental in the discipline of electrical engineering. Readers who invest time and effort in studying this text are likely to do so for the key purpose of gaining an introduction into the field of electricity. In this chapter, we will lay the foundations in the electrical engineering realm by covering basic electrical engineering terms, concepts, and principles, without the understanding of which, discussion and study of terms that bear important practical significance, such as power factor, real power, reactive power, apparent power, and load factor, would be untenable.

  Most of the material in this chapter pertains to DC, or direct current, electricity. However, some entities discussed in this chapter such as capacitive reactance, inductive reactance, and impedance are fundamentally entrenched in the AC, alternating current, realm.

  This text affirms that electrical engineering is rooted in the field of physics and chemistry. Physics, chemistry, and electrical engineering, as most other subject matters in science, depend on empirical proof of principles and theories. Empirical analysis and verification require tools and instruments for measurement of various parameters and entities. Hence, after gaining a better understanding of the basic electrical concepts, we will conclude this chapter with an introduction to three of the most common and basic electrical instruments, namely, multi-meter, clamp-on ammeter, and a scope meter or oscilloscope.

  Voltage or EMF (Electromotive Force)

  Voltage can be defined as a “force” that moves or pushes electrically charged particles like electrons, holes, negatively charged ions, or positively charged ions by forming an electric field. The term “electromotive” force stems from the early recognition of electrical current as something that consisted, strictly, of the movement of “electrons.” Nowadays, however, with the more recent breakthroughs in the renewable and non-traditional electrical power generating methods and systems like microbial fuel cells and hydrocarbon fuel cells, electrical power is being harnessed, more and more, in the form of charged particles that may not be electrons. In batteries, such as those used in automobiles, as we will see in the batteries chapter, the flow of current driven by voltage potential difference consists not only of negatively charged electrons, e− , but also types of ions, including H+ and HSO4 − ions.1

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