Capacitor Charge

8 Key excerpts on "Capacitor Charge"

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  eBook - ePub

  An Introduction to Electrical Science

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

    (Publisher)

  electric field .

  So we can say that

  a capacitor is a circuit component that stores energy

  .

  Perhaps we should replace the terms, ‘charging’ and ‘discharging’ with ‘energising’ and ‘de-energising’? Well, unfortunately, the terms ‘charging’ and ‘discharging’ are too well established for us to change them at this stage!

  Despite this, many textbooks continue to insist that a capacitor ‘stores charge’, but this is misleading because, as we have learnt, there is no increase in the overall charge on the plates whenever a capacitor is charged. All that has happened is that charge has been separated , and has been moved from one plate across to the other; no additional charge has been introduced or stored .

  Actually, these textbooks aren’t really ‘wrong’ because what they mean (as opposed to what they say !) is that a capacitor is a circuit component which ‘stores separated charges’ which, of course, is quite correct!

  Circuit symbols for capacitors and capacitance

  Capacitors may be fixed value or variable value . A special type of variable capacitor is the trimmer

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  eBook - ePub

  Introductory Electrical Engineering With Math Explained in Accessible Language

  • Magno Urbano(Author)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  8.4 Electric Characteristics

  These are the main characteristics of capacitors:

  • They store electric charges in the form of an electric field.
  • An ideal capacitor can store an electric charge indefinitely. In real life, they discharge slowly through the dielectric (leakage), because dielectrics are not perfect insulators and let a little bit of current flow.
  • Capacitors block direct current.
  • Capacitors let alternating current (AC) pass.

  Like resistors, capacitors are passive components, because they do not have an active role inside a circuit.

  8.5 Electric Field

  Considering that the plates of a capacitor have an area equal to A and are separated by a distance d, the electric field between the plates can be found by using the following equation.

  ELECTRIC FIELD

  • E is the electric field, in Newtons per Coulomb or volts per meter.
  • q is the amount of stored charge, in Coulombs.
  • ε is the dielectric permittivity, in Farads per meter (F/m).
  • A is the plate area, in squared meters.
  • d is the distance between the plates, in meters.

  8.6 Capacitance

  Capacitance is the ratio of the change in an electric charge in a system to the corresponding change in its electric potential.

  CAPACITANCE

  • C is the capacitance, in Farads.
  • q is the amount of charge, in Coulombs.
  • V is the electric potential, in Volts.

  Capacitance is measured in Farads3 and represented by the uppercase letter F in the SI.

  According to this formula, a capacitor of 1 F can store a charge of 1 C when subjected to 1 V.

  There are two kinds of capacitance: one produced by the object itself and one produced by proximity to other objects. Any object that can be electrically charged will have its own value of capacitance. Also, any object in the proximity of others will generate mutual capacitance.

  Every component in a circuit has capacitance. Most of the time this is a parasitic characteristic.

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  eBook - ePub

  Electrical Engineering Fundamentals

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

    (Publisher)

  anode . This separation of charge and the quantity of charge separated determine the electrical potential – or voltage – developed across the electrodes of the capacitor, as well as the amount of electrical energy stored in a given capacitor. Therefore, as energy storage devices – with a potential difference – capacitors are analogous to mechanical pressure energy storage devices like air receivers and pneumatic cylinders; pressure differential wherein can be used to perform mechanical work.

  Construction of a simple capacitor is depicted in Figure 1.6 . As shown in the figure, a simple capacitor can be constructed with two parallel square plates, of equal size, separated by a dielectric substance like air, glass, mica, paper, etc. The separation between the two plates (electrodes), “r ,” in conjunction with the area of the plates determines the “capacitance ” of the capacitor. Capacitance, “C ,” of a capacitor is defined as the charge storage capacity of the capacitor.

  FIGURE 1.6 A simple parallel plate capacitor.

  Capacitance can be defined, mathematically, through Eq. 1.16.

  C = ∈

  A r

  (1.16)

  where

  • C = Capacitance is quantified or specified in farads.
  • A = The area of cross-section – or simply area – of the capacitor electrode plates.
  • Є = Permittivity of the dielectric medium between the plates.

  and

  • Є = Єr ∙ Є0

  where Є r = Relative permittivity of a specific dielectric medium and Є 0 = Permittivity in vacuum or in air = 8.854 × 10−12 farads per meter (F·m−1 ).

  One farad is rather large amount of capacitance for most common capacitor applications. Therefore, many capacitors – especially, at the circuit board level – are specified or labeled in terms of smaller units, such as mF (milli-Farad), µF (micro-Farad), or nF (nano-Farad). The capacitor shown in Figure 1.7

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  eBook - ePub

  Engineering Science

  • W. Bolton(Author)
  • 2015(Publication Date)
  • Routledge

    (Publisher)

  Chapter 13 Capacitance

  13.1 Introduction

  This chapter is about capacitors, these being components which are widely used in electronic circuits. The concept of an electric field is reviewed and the basic principles and use of capacitors considered.

  13.1.1 Electric fields

  If we pick up an object and then let go, it falls to the ground. We can explain this by saying that there are attractive gravitational forces between two masses, the earth and the object. There is another way of explaining this. We can say that the earth produces in its surroundings a gravitational field and that when the object is in that field it experiences a force which causes it to fall. A mass is thus said to produce a gravitational field. Other masses placed in that field experience forces.

  A charged body is said to produce an electric field in the space around it. Any other charged body placed in the electric field experiences a force. The direction of the electric field at a point is defined as being the direction the force would be if a positive charge was placed at the point. The field can be visualised by drawing lines representing the directions of the field, these lines being called lines of force. Figure 13.1 shows the field patterns for isolated positive and negative charges.

  Figure 13.1 Field patterns of (a) an isolated positive charge, (b) an isolated negative charge

  13.1.2 Forces on charged bodies

  As indicated in Chapter 9 , like charges repel, unlike charges attract. Thus, by the definition given above for field direction, a positive charge when placed in an electric field will move in the direction of that field, i.e. away from another positive charge or towards a negative charge, while a negative charge in an electric field will move in the opposite direction. We can define the electric field strength E as the force F experienced per unit charge placed in a field and so for a charge q :

  13.2 Capacitor

  If a pair of parallel plates separated by an insulator, e.g. air, are connected to a direct voltage supply such as a battery (Figure 13.2

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  eBook - ePub

  Fundamental Electrical and Electronic Principles

  • C R Robertson(Author)
  • 2008(Publication Date)
  • Routledge

    (Publisher)

  conventional current flow.

  Fig. 3.21

  However, if a discharge current flows then work must be done (energy is being dissipated). The only possible source of this energy in these circumstances must be the capacitor itself. Thus the charged capacitor must store energy.

  If a graph is plotted of capacitor p.d. to the charge it receives, the area under the graph represents the energy stored. Assuming a constant charging current, the graph will be as shown in Fig. 3.22 .

  Fig. 3.22

  Worked Example 3.16

  Q        A 3 μF capacitor is charged from a 250 V d.c. supply. Calculate the charge and energy stored. The charged capacitor is now removed from the supply and connected across an uncharged 6 μF capacitor. Calculate the p.d. between the plates and the energy now stored by the combination. A

  When the two capacitors are connected in parallel the 3 μF will share its charge with 6 μF capacitor. Thus the total charge in the system will remain unchanged, but the total capacitance will now be different:

  Note: The above example illustrates the law of conservation of charge, since the charge placed on the first capacitor is simply redistributed between the two capacitors when connected in parallel. The total charge therefore remains the same. However, the p.d. now existing between the plates has fallen, and so too has the total energy stored. But there is also a law of conservation of energy, so what has happened to the ‘lost’ energy? Well, in order for the 3 μF capacitor to share its charge with the 6 μF capacitor a charging current had to flow from one to the other. Thus this ‘lost’ energy was used in the charging process.

  Worked Example 3.17

  Q        Consider the circuit of Fig. 3.23

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  eBook - ePub

  Reactive Power Compensation

  A Practical Guide

  • Wolfgang Hofmann, Jürgen Schlabbach, Wolfgang Just(Authors)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  The ‘plates’ in industrial production are manufactured from very thin plastic foils (dielectric) with a very thin vaporized metallic layer (electrode) on one side only. Two of the ‘plates’ are wound in rolls and packed in metallic or plastic cups. Manufacturers deliver them in standardized sizes for assembling compensation banks of any requested size.

  The unit of measure for capacitance is the farad1 (F). A capacitor with 1 F of capacitance becomes 1 V of voltage if it is charged up with a current of 1 A for just 1 s. Since 1 A s represents 1 coulomb (C), the mathematical description runs as follows:

  (7.5)

  As 1 F is a very large unit, divisions of the unit are in use:

  1 μF (microfarad) = 10−6 F

  1 nF (nanofarad) = 10−9 F

  1 pF (picofarad) = 10−12 F

  The electric charge stored on a capacitor depends on its capacitance and the supplied voltage:

  (7.6)

  where

  C = capacitance of the capacitor, unit A s/V U = supplied voltage, unit V Q = electric charge, unit A s

  7.3 Reactive Power of Capacitors

  The reactive power

  QC

  in single-phase operation depends on three factors, namely voltage U , capacitance C and frequency f , written mathematically as

  (7.7a)

  (7.7b)

  (7.7c)

  Regarding Equation 7.7 c, one can recognize that the reactive power mainly depends on the supplied voltage in a squared manner. This means that an increase of 10% due to the rated voltage causes a 21% higher reactive power than rated. The frequency, however, influences the reactive power in a linear manner only. This means that a capacitor with a defined capacitance supplied by an AC voltage of 60 Hz results in 20% more reactive power compared with 50 Hz grids. The nominal reactive power

  Qr

  of a capacitor printed on a factory nameplate always refers to the rated supply voltage

  Ur

  (sinusoidal waveform) and the rated frequency

  fr

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  eBook - ePub

  Engineering Energy Storage

  • Odne Stokke Burheim(Author)
  • 2017(Publication Date)
  • Academic Press

    (Publisher)

  Whenever electrochemical energy storage of mobile applications is discussed, the terms supercapacitor, ultracapacitor, double-layer capacitor, or electrochemical capacitor are likely to be brought up. These are synonyms for the term supercapacitor. The reason for considering supercapacitors is their extremely high power density in terms of both mass and volume. Albeit supercapacitors are electrochemical, they do not include red-ox reactions. At the same time they are sensitive to changes in concentration. Since there is no red-ox reactions and thus no friction for charge transfer, these systems can take enormous loads in very short time and with high efficiency. For the same reasons (i.e., no red-ox reactions), these systems store very little energy. This chapter explains the principles of conventional capacitors, supercapacitors, energy and power dimensioning, and some very interesting features of salinity gradient energy extraction.

  9.1 Conventional Capacitors

  A conventional double plate capacitor consists of two parallel plates, typically of aluminum, separated by a thin polymer film. These capacitors are therefore often referred to as thin-film capacitors. The capacitance of a capacitor or capacitor system is defined as how much the charge can change for a given change in potential:

  C =

  Δ Q

  Δ E

  .

  (9.1)

  The polymer film thickness represents an internal distance d. When applying a current I for some time Δt or charging this pair of plates to a certain voltage E, one of the plates will experience a deficit of electrons, and the other a surplus relative to the natural being of these plates. This is illustrated (left) in Fig. 9.1 . The corresponding charge is the product of the time and current applied:

  Q = I Δ t .

  (9.2)

  The potential is then given as

  E =

  Q ⋅ d

  ϵ

  0

  ϵ

  i

  A

  ,

  (9.3)

  where

  ϵ 0

  ,

  ϵ i

  , and A are the dielectric constant of vacuum, the dielectric constant of the body between the parallel plates, and the cross-sectional area. The dielectric constant in vacuum is the lowest dielectric constant. If the volume between the two plates truly were almost vacuum (e.g., in a satellite in space), then

  ϵ i

  would become

  ϵ 0

  . For all practical purposes, a spacer is needed to prevent physical contact and short circuit discharge. Thus, the dielectric material must also be electrically insulating. The capacitor plate pair is depicted with (right) and without (left) a dielectric material in Fig. 9.1 . The foremost reason for this body to be embedded between the two plates is for spacing or separation since the material inevitably lowers the potential for any given charge Q. However, when taking a charged conventional capacitor with some dielectric material and replacing its dielectric body with a dielectric constant of

  ϵ 1

  by another material with a dielectric constant of

  ϵ 2

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  eBook - ePub

  Energy Storage

  Systems and Components

  • Alfred Rufer(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  5 Energy Storage by Means of Supercapacitors

  5.1 GENERAL CHARACTERISTICS ON SUPERCAPACITORS

  5.1.1 PRINCIPLE AND PROPERTIES

  In Chapter 3 , supercapacitors have been briefly introduced as new storage components with lower energy capacity (or energy density) than batteries but which can be realized at a high capacity scale of several thousand farads. In addition, they can be utilized with a significantly higher number of possible cycles or higher lifetimes than conventional batteries. These new components, also called ultracapacitors or formerly EDLC (electric double-layer capacitors), can be charged or discharged much faster than batteries, thus defining a relatively high power density.

  Relation 5.1 is a standard formula for the calculation of the capacity of conventional capacitors:

  (5.1)

  Accordingly, capacitance C is greatest in capacitors made from materials with a high permittivity ε, large electrode plate surface areas A, and small distance between plates d.

  As a result, double-layer capacitors have much higher capacitance values than conventional capacitors, arising from the extremely large surface area of activated carbon electrodes and the extremely thin double-layer distance in the order of a few ångströms (0.3–0.8 nm). The amount of charge stored per unit voltage in an electrochemical capacitor is primarily a function of the electrode size [1 ].

  Figure 5.1 shows the principle and structure of both a conventional capacitor with plan electrodes and a double-layer capacitor.

  5.1.1.1 Lifetime

  Since no chemical changes take place within the electrodes or electrolyte, charging and discharging EDLCs is in principle unlimited. Real supercapacitors’ lifetimes are only limited by electrolyte evaporation effects.

  Figure 5.2 shows the position of EDLC capacitors with regard to the number of cycles, along with an indication of their efficiency. This image represents the order of magnitude of the life cycle of the first available elements (around y 2000); modern components are able to achieve more than one million cycles [2

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