Conductance

5 Key excerpts on "Conductance"

• 

  eBook - ePub

  An Introduction to Electrical Science

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

    (Publisher)

  losses , which, of course, are undesirable.

  We can modify the natural resistance of any circuit by adding resistors . These are circuit components, which are manufactured to have specific values of resistance. By changing the resistance of a circuit using resistors, we can, for example, modify or limit the current flowing through that circuit.

  Conductance

  You may come across the term Conductance (symbol: G ). Conductance is the reciprocal of resi stance, that is:

  G =

  1 R

  Until the adoption of SI, the unit of measurement of Conductance was the mho – that’s ‘ohm’, spelt backwards (proving that some scientists do, indeed, have a sense of humour)! The SI unit of measurement for Conductance, however, is the siemens (symbol: S ).

  Conductance is a particularly useful concept to use when we study a.c. theory in a later chapter.

  The unit of resistance: the ohm

  The SI unit of measurement of resistance is the ohm (symbol: Ω), named in honour of Georg Simon Ohm.

  The ohm is defined as ‘the electrical resistance between two points along a conductor such that, when a constant potential difference of one volt is applied between those points, a current of one ampere results’ .

  In other words, an ohm is equivalent to a volt per ampere , and we should understand the significance of this very important definition, as it will become important when we study Ohm’s Law in a later chapter.

  The resistance of any material depends upon the following factors:

  • its length (symbol: l )
  • its cross-sectional area (symbol: A )
  • its resistivity (symbol: ρ , pronounced ‘rho’ ).

  Length

  The resistance of a material is directly proportional to its length . In other words, doubling the length of a conductor will double its resistance, while halving its length will halve

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  eBook - ePub

  Electrical Engineering

  Fundamentals

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

    (Publisher)

  A conductor has a resistance of 1 Ω when a voltage V = 1 V drives a current of I = 1 A through the conductor. 18 The technically used resistors can generally be divided into two groups: wire resistors and sheet resistors. The materials of the wire filaments or coatings, usually attached to cylindrical ceramic bodies, have specific resistances with low temperature dependence. The resistance is determined by measuring current and voltage. Instead of stating the resistance of an object, sometimes the reciprocal dimension, the Conductance G is given (e.g. to compare the conductivity of different conductors). G = 1 R G  Electrical Conductance in S (Siemens) 1.10.2 Temp. dependence of R, resistivity ϱ, conductivity σ, temperature coefficient α The resistance of conductor materials changes with the temperature (e.g. increases for metals). This change in resistance is non-linear and the accurate characteristic curve can be approximated using a polynomial. The resistance R 2 of a conductor at the temperature ϑ 2 can be calculated if its resistance R 1 is known at the temperature ϑ 1 : R 2 = R 1 ⋅ 1 + α 1 ⏟ l i n e a r T C ϑ 2 − ϑ 1 + β 1 ⏟ q u a d r a t i c T C ϑ 2 − ϑ 1 2 + γ 1 ϑ 2 − ϑ 1 3 … Up to ϑ 2 = 100 °C, generally, only the linear temperature coefficient α 1 is. used. R 2 = R 1 ⋅ 1 + α 1 ϑ 2 − ϑ 1 ⏟ v i t a l t e r m f o r c h a n g e For most pure metals the linear temperature coefficient α 20 is around 4 ⋅ 10 − 3 C − 1 and the quadratic temperature coefficient β 20 is around 0.6 ⋅ 10 − 6 C − 1. Pure metals have the highest temperature coefficients and therefore are not suitable as standard or measuring resistor. They can, however, be used as measured-value transmitter (resistance thermometer). Through alloys, the temperature coefficients can be reduced in such a way that temperature dependence practically does not exist anymore. These materials are used for standard and measuring resistors (e.g

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  eBook - ePub

  Measurement, Instrumentation, and Sensors Handbook

  Electromagnetic, Optical, Radiation, Chemical, and Biomedical Measurement

  • John G. Webster, Halit Eren, John G. Webster, Halit Eren(Authors)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  If electricity has great difficulty flowing through a material, that material has high resistivity. The electrical wires in overhead power lines and buildings are made of copper or aluminum. This is because copper and aluminum are materials with very low resistivities (about 20 nω m), allowing electrical power to flow very easily. If these wires were made of high-resistivity material like some types of plastic (which can have resistivities about 1 Eω m [1 × 10 18 ω m]), very little electrical power would flow. Electrical resistivity is represented by the Greek letter ρ. Electrical conductivity is represented by the Greek letter Σ and is defined as the inverse of the resistivity. This means a high resistivity is the same as a low conductivity and a low resistivity is the same as a high conductivity: Σ ≡ 1 ρ (26.1) This chapter will discuss everything in terms of resistivity, with the understanding that conductivity can be obtained by taking the inverse of resistivity. The electrical resistivity of a material is an intrinsic physical property, independent of the particular size or shape of the sample. This means a thin copper wire in a computer has the same resistivity as the Statue of Liberty, which is also made of copper. 26.2 Simple Model and Theory Figure 26.1 shows a simple microscopic model of electricity flowing through a material [ 1 ]. While this model is oversimplified and incorrect in several ways, it is still a very useful conceptual model for understanding resistivity and making rough estimates of some physical properties. A more correct understanding of the electrical resistivity of materials requires a thorough understanding of quantum mechanics [ 2 ]. On a microscopic level, electricity is simply the movement of electrons through a material. The smaller white circle in Figure 26.1 represents one electron flowing through the material. For ease of explanation, only one electron is shown

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  eBook - ePub

  Understanding Solids

  The Science of Materials

  • Richard J. D. Tilley(Author)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  The effective mass is not a constant, but depends upon temperature and the direction in the crystal that the electron is travelling. It is invariably expressed as a fraction of the electron rest mass m e, i.e. 0.067 m e.) The current in a conductor is steady, and not ever increasing, as would be expected if the electrons were accelerating. To account for this, it is assumed that the electrons constantly collide with the atoms and defects in the material and that each collision resets the drift velocity to zero. In this case the current will decay to zero in a time τ, the relaxation time, after the voltage is turned off, where τ is equivalent to the time between successive collisions. The mean free path of the electron, which is the length of the path between successive collisions, is given by: where is the electron velocity at the Fermi surface. In addition, the drift velocity of the electrons is: Substituting for the acceleration from Eq. (11.1) (11.2) The total current flowing is therefore: If the length of the conductor is L, the electric field can be replaced by V / L, where V is the voltage applied to the conductor, to give: Ohm's law can be written: so that: (11.3) where σ is the conductivity and ρ the resistivity of the solid. The conductivity is often written in terms of another variable, the mobility of the electrons, μ e, defined as the drift velocity gained per unit electric field, that is: Comparing this with Eq. (11.2) makes it apparent that: This is sometimes called the drift mobility, to distinguish it from mobility measured via the Hall effect (Section 11.2.5). The conductivity and the mobility are then related by substituting Eq. (11.3) into (11.2) to give: 11.1.3 Resistivity Scattering is the main cause of resistivity. The electron wave can be scattered by interaction with phonons (lattice vibrations), called thermal scattering. As the temperature increases so do the lattice vibrations, and the resistivity rises

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  eBook - ePub

  Heat Transfer 1

  Conduction

  • Michel Ledoux, Abdelkhalak El Hami(Authors)
  • 2021(Publication Date)
  • Wiley-ISTE

    (Publisher)

  www.iste.co.uk/ledoux/heat1.zip

  This coefficient, a property of the material, is known as the thermal conductibility of the material. It is expressed in J s−1 m−1 K−1 or much more frequently in W s−1 K−1

  In many situations, we can consider this conductibility to be constant. The experiment demonstrates that this conductibility depends on the temperature. In certain problems, in particular in the case of high temperatures and heterogeneous thermal fields, we must take into account the spatial variation of the thermal conductibility within the material, which can be expressed explicitly as:

  [2.3]

  or more often by a relationship between the conductibility and the temperature:

  [2.4]

  Materials with high values of λ are known as conductors. Materials with low values of λ are known as insulators.

  Here are a few values to set out the general idea: Metals are conductors of heat:

  Many solids (including refractory ones) are insulators: For example, for a light resinous wood:

  Liquids are relatively poor conductors of heat. For example, for water at 20°C:

  Gases are poor conductors of heat. For example, for air at 20°C:

  REMARK.– Air is thus one of the best thermal insulators. However, between two faces, separated by a layer of air of thickness of the order of 2 cm, natural convection phenomena leads to a “parasitic” thermal transfer. Our solution is thus to trap air in alveolar structures, such as networks of mineral threads (glass fiber or rock “wool”). The solid material then leads to parasitic thermal conduction, known as a “thermal bridge”, which explains how rock wool presents a thermal conductibility of the order of λ = 0.4 W s−1 K−1 , higher than that of air. If the faces are made of glass (double glazing), the distance between the two panes must be small.

  We can also observe that strictly speaking, a vacuum is an absolute insulator, since there are no molecules that are likely to propagate impacts. We will see later on however, that a vacuum is ideal for the propagation of radiation and in that sense does not present an obstacle to the transmission of heat. This explains the structure of a thermos flask, whose internal walls, positioned face to face, are made of reflective glass.

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