Cable Capacitance
Cable capacitance refers to the ability of a cable to store electrical energy in the form of an electric field between its conductors. It is measured in farads per unit length and is influenced by the cable's geometry and dielectric material. Cable capacitance can cause signal distortion in high-frequency applications and is a key consideration in designing transmission lines.
7 Key excerpts on "Cable Capacitance"
- Magno Urbano(Author)
- 2019(Publication Date)
- Wiley(Publisher)
...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. Capacitance can also be expressed by the following formula. CAPACITANCE C is the capacitance, in Farads. ε is the dielectric permittivity, in Farads per meter (F/m). A is the plate's area, in squared meters. d is the distance between the plates, in meters. 8.7 Stored Energy Capacitors can store a large amount of energy in the form of electric field in a relatively short amount of time, differently from batteries that take a long time to charge. However, capacitors cannot supply energy or hold their electric charge for a long time because they slowly discharge through their own dielectrics or through the circuit they are connected. However, their charge and discharge characteristics can be utilized to create very interesting circuits, like audio filters, blinkers, and timers. Capacitors are frequently used to stabilize voltage levels on power supplies. The energy stored inside a capacitor can be expressed in terms of work to move charges from a plate to another. In other words, the energy stored inside a capacitor is equivalent to the work necessary to keep positive and negative charges, +q and −q, in their respective plates. Mathematically, this work and its equivalent charge can be related by the following equation. STORED ENERGY OR WORK W is the work, in Joules. q is the stored charge, in Coulombs. C is the capacitance, in Farads. To find the total energy, we can integrate the previous equation: MATH CONCEPT The integral of The constant of integration (C) can be ignored when dealing with defined integrals...
eBook - ePub- Adrian Waygood(Author)
- 2018(Publication Date)
- Routledge(Publisher)
...It is claimed that this can lead to energy savings of up to 50%. Wind turbines and solar panels are also using supercapacitors to stabilise their energy output when wind gusts or clouds would otherwise cause fluctuations. Natural capacitance It’s not just capacitors that exhibit capacitance. Both overhead lines and underground cables behave as ‘natural capacitors’! In the case of overhead lines, adjacent conductors (and each conductor and the earth) behave like the plates of a capacitor, and the air acts as the dielectric. In the case of underground cables (in fact, any long length of cable), adjacent conductors (or individual conductors and earth) act like plates, while the conductors’ insulation acts as the dielectric. The ‘capacitance’ of cables is significantly higher than for overhead lines, due to the extreme closeness of their conductors (‘plates’), and care must be taken to fully discharge long lengths of cable that may have accumulated appreciable charge separation during an insulation test using a Megger (a high voltage test instrument), in order to avoid a shock hazard! Electrical cables used for residential wiring have a capacitance of around 100 pF per metre length and the resulting capacitive currents can be responsible for some odd behaviours that occasionally occur in electrical installations, such as CFLs (compact fluorescent lamps) which continue to flicker after they have been switched off. Capacitors in series and parallel Capacitors in series Figure 22.34 In accordance with Kirchhoff’s Voltage Law, the sum of the voltage drops across each capacitor will equal the supply...
eBook - ePub- William A. Thue, William A. Thue(Authors)
- 2017(Publication Date)
- CRC Press(Publisher)
...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 L f = inductance in henries per centimeter r 2 = inner radius of outer conductor in inches r 1 = 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 C APACITANCE OF A C ABLE 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...
eBook - ePub- J. W. S. Hearle, W E Morton(Authors)
- 2008(Publication Date)
- Woodhead Publishing(Publisher)
...21 Dielectric properties 21.1 General introduction The electrical properties of fibres are of less obvious technical importance than, for example, the mechanical properties. Apart from their intrinsic interest, the first stimulus for their investigation came from the use of fibres as insulating materials, and much important work was done in the Bell Telephone Laboratories. Later, the use of resistance and capacity methods for measuring the moisture condition of textile materials, and of capacity methods for measuring irregularity, increased the interest in electrical properties. With the introduction of synthetic fibres, the troubles due to static charges, both in processing and in use, became more frequent and more severe. The electrical properties are interrelated. The liability of materials to static charges is determined by their electrical resistance. The electrical resistance is, on what seems to be the most likely theory, mainly determined by the permittivity of the material. It is, therefore, most appropriate to consider first the dielectric properties, then the electrical resistance, and finally static. 21.2 Definitions of dielectric properties The permittivity, ε, of a material may be defined either in terms of the capacitance, C, of a condenser with the material between parallel plates of area A and separation d, or in terms of the force F between two charges Q 1 and Q 2 at a distance r in the material. Expressed in SI units as kg −1 m −3 s 4 A 2 (A = ampere) or F/m (F = farad), the relations contain no arbitrary numerical factors and are: C = εA d (21.1) F = Q 1 Q 2 4 πε r 2 (21.2) This does, however, mean that in vacuo the equations become: C = ε 0 A d (21.3) F = Q 1 Q 2 4 π ε 0 r 2 (21.4) where ε 0 is the permittivity of a vacuum, which is a fundamental physical quantity with the value 8 · 854 × 10 − 12 F/m...
eBook - ePubPrinciples of Electrical Transmission Lines in Power and Communication
The Commonwealth and International Library: Applied Electricity and Electronics Division
- J. H. Gridley, P. Hammond(Authors)
- 2014(Publication Date)
- Pergamon(Publisher)
...The stipulation that the line is “remote from the earth” is to be interpreted as meaning that the spacing between conductors is small compared with their heights above earth and that the electric field in the vicinity of the conductors can be calculated solely from consideration of the charges on the conductors, without regard to any induced charges on the earth. Figure 16.1 illustrates the system. FIG. 16.1 Illustrating calculation of capacitance of parallel-wire go-and-return circuit remote from earth. If the conductors are imagined to carry charges +q and – q coulombs per metre length, the electric field at a point distance x from the centre of one conductor and on the plane containing the conductors is ε x = q 2 π ε 0 x + q 2 π ε 0 (D − x), (Consider each conductor individually; a cylindrical surface radius x, coaxial with a conductor, is uniformly permeated by a flux q coulombs per metre length. This gives an electric flux density q /2π x.) The potential of conductor A above B is V A B = ∫ r D − r ε x d x, the integration being taken along a straight line joining the conductors and normal to both. The integration begins and ends at the surface of a conductor, of course, since there is no electric field inside the conductors. Then V A B = q 2 π ε 0 ∫ r D − r { 1 x + 1 D − x } d x = q 2 π ε 0 [ log x − log (D − x) ] r D − r = q π ε 0 log D − r r. The capacitance q/V is accordingly given as C = π ε 0 /log (D − r r) farads/metre. Normally, D is so much larger. than r that it is sufficient to write C = π ε 0 /log D r farads/metre. 16.2.2 Capacitance between a single wire and a conducting plane Some transmission circuits include one wire only, the return path being through earth. For such circuits we shall require to know the capacitance between a long wire and a parallel conducting plane, the plane being at earth potential. The core of the problem is to relate the charges, say + q on the wire and – q in the earth, to the potential difference V of the wire above earth...
eBook - ePubPower System Grounding and Transients
An Introduction
- A.P. Sakis Meliopoulis(Author)
- 2017(Publication Date)
- Routledge(Publisher)
...4 Transmission Line Modeling Line Capacitance 4.1 Introduction In this chapter we discuss methods by which the capacitance of a transmission line can be computed. For this purpose we employ an approach analogous to the one for computing the inductive reactance of a transmission line. Recall that for the computation of the inductive reactance, the magnetic field around the transmission line was examined. For the computation of the line capacitance, the electric field around the line will be examined. The source of this electric field is electric charge, which is deposited on the surface of the line conductors. The analysis of the electric field results in a model relating the electric charge and the conductor voltage. The time derivative of the total electric charge on the surface of the conductors is by definition the capacitive current (or the charging current) of the line. Utilizing this definition, the model can be transformed into a relationship between the line voltage and the capacitive current. The line capacitance can be extracted from this model. This general approach will be utilized to introduce the analysis of capacitive phenomena in lines in a step-by-step procedure. Specifically, first the simplest case of a single circular conductor will be examined to establish the basic equation. Then the analysis will be extended to two parallel conductors and the general n-conductor line configuration. 4.2 Electric Field Around a Circular Infinitely Long Conductor In this section we examine the simple case of one circular infinitely long conductor. We shall assume that the conductor is electrically charged and we shall seek the relationship between the electric charge and the conductor voltage. Specifically, assume that the conductor is charged with electric charge q (coulombs per meter). Because of symmetry, the electric charge is uniformly distributed on the conductor surface. The electric charge generates an electric field around the conductor...
eBook - ePub- 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...
