Resistance and Resistivity

6 Key excerpts on "Resistance and Resistivity"

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  eBook - ePub

  Electrical Conductivity in Polymer-Based Composites

  Experiments, Modelling, and Applications

  • Reza Taherian, Ayesha Kausar(Authors)
  • 2018(Publication Date)
  • William Andrew

    (Publisher)

  −8 (Ωm) but the resistance of a piece of copper depends on the dimension of sample under test.

  The three most common resistance measurements are

  • • Surface resistivity or sheet resistance
  • • Bulk or volume resistivity
  • • Contact resistance

  12.2.3.1 Surface Resistivity

  Surface resistivity or sheet resistance is the measurement of resistance across the surface of a material in contact with the electrodes. In simple form, two equal-sized electrodes in good contact with the surface of the sample is used for measuring surface resistivity. Distance between electrodes is equal to width of the electrode. This type of measurement is very applied for measuring the electrical resistivity of flat materials. Regardless of the size of the electrodes the unit of surface resistivity is ohms per square (Ω/ ) or only Ω. To avoid confusion with volume resistance (which is expressed in the unit of ohm), sheet resistance is expressed in ohms per square (Ω/ ). Fig. 12.4 shows the test configuration for surface resistivity.

  Figure 12.4 Simple method for measuring surface resistivity.

  In this method surface resistivity calculated from:

  ρ = R

  l W

  (12.9)

  (12.9)

  where, ρ is the surface resistivity, l is the distance between two electrodes, R is the measured resistance, and W is the width of the sample.

  12.2.3.2 Bulk Resistivity

  Bulk resistivity is the measurement of resistance between the two electrodes that placed in the two ends of the sample. Bulk resistivity is also called as volume resistivity. The unit of bulk resistivity is Ωm. In this method the electrodes are in contact with both sides of the material. The simplest configuration of bulk resistivity measurement is shown in Fig. 12.5

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  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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  Electrical, Electronics, and Digital Hardware Essentials for Scientists and Engineers

  • Ed Lipiansky(Author)
  • 2012(Publication Date)
  • Wiley-IEEE Press

    (Publisher)

  So if the length of a conductor is doubled, all other factors remaining equal, the resistance of such conductor doubles. If the thickness (i.e., cross section) of a conductor doubles, while all other factors remain equal, the resistance of the conductor becomes half of the original resistance.

  Resistivity ρ , is a temperature-dependent parameter, and it is a characteristic of the material. A good empirical approximation of how resistivity varies with temperature is

  (1.55)  

  where α is called the temperature coefficient of resistivity, ρ 0 is the resistivity at the reference temperature, usually 20°C (or 293K [kelvin degrees]), T 0 is the reference temperature (20°C in our case), and ρ and T are respectively the resistivity and the temperature of the conductor at the temperature of interest, or at the unknown temperature. Equation (1.55) is linear and remains linear for most engineering problems over a wide temperature range around 20°C. Table 1.5 lists the temperature coefficient of resistivity α for some metals.

  Table 1.5  Temperature coefficients of resistivity for some metals [2]

  Metal	(α ) Temperature Coefficient of Resistivity [K−1 ]
  Silver	4.1 × 10−3
  Copper	4.3 × 10−3
  Gold	4.0 × 10−3
  Aluminum	4.4 × 10−3
  Manganina	0.002 × 10−3
  Tungsten	4.5 × 10−3
  Iron	6.5 × 10−3
  Platinum	3.9 × 10−3

  a  

   An alloy with an extremely low value of α .

  1.4  OHM’S LAW, POWER DELIVERED AND POWER CONSUMED

  A voltage source happens to behave very much like a constant pressure water pump. The voltage source pushes the current through the electric circuit very much like a water pump pushes a volume of water through the closed-loop hydraulic case as depicted in Figure 1.13 a, which shows an electrical circuit with a DC voltage source, a conductor or wire and a resistor, and Figure 1.13

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  Physics for Students of Science and Engineering

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

    (Publisher)

  ) to be one volt per ampere, or

  TABLE 14.2 Typical Resistivities of Common Metals at Room Temperature

  Substance	ρ(Ω · m)
  Aluminum	2.8 × 10−8
  Copper	1.7 × 10−8
  Iron	1.0 × 10−7
  Nickel	7.1 × 10−8
  Platinum	1.1 × 10−7
  Silver	1.6 × 10−8
  Tungsten	5.6 × 10−8

  1 Ω = 1

  V A

  (14-33)

  (14-33)

  Then the unit of resistivity ρ becomes the ohm-meter ( · m).

  Suppose, instead of considering the resistive character of a substance, we focus on a specific object. Let us consider the length L of wire with cross-sectional area A shown in Figure 14.13 . If we apply a difference in potential ΔV across the length and observe that the wire carries a current i , we define the resistance R of this particular length of wire to be

  Figure 14.13 A length L of wire with cross-sectional area A. The resistivity of the material of the wire is ρ. When a difference in potential ΔV is across the length of wire, it carries a current i , and the current density in the wire is J .

  R =

  Δ V

  i

  (14-34)

  (14-34)

  in which ΔV is measured in volts (V), i is measured in amperes (A), and the resistance R is measured in ohms ( ). Equation (14–34) is called Ohm’s law for a specific object . Thus, while resistivity ρ is a characteristic of a material, resistance R characterizes a particular specimen. We can relate the resistance of a given specimen to the resistivity of the material that constitutes that specimen. Consider again the wire with uniform cylindrical cross section, shown in Figure 14.13 . Because the difference in potential ΔV is across its length L , the material has within it an electric field with magnitude E = ΔV /L ;if the wire is carrying a current i , the current density has magnitude J = i /A . Putting these values for E and J into Equation (14–32) and substituting R for ΔV /i from Equation (14–34)

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  Physical Properties of Textile Fibres

  • J. W. S. Hearle, W E Morton(Authors)
  • 2008(Publication Date)
  • Woodhead Publishing

    (Publisher)

  22

  Electrical resistance

  22.1 Introduction

  When electricity was first intentionally conducted from one place to another (from an electrified tube to an ivory ball) by Stephen Gray in 1729, the material used as the conductor was hempen pack-thread. Gray eventually covered distances of up to 233 m along the corridors of his house. In order to do this, he had to support the packthread and, after an abortive attempt in which fine copper wires were used, he suspended the thread by silk filaments. Thus both the conductor and the insulator were textile fibres. Soon afterwards, Du Fay found that pack-thread was a better conductor when it was wet. Then, in 1734, Gray discovered metallic conductors, and, apart from some use for insulating purposes, interest in the electrical resistance of fibres did not revive for nearly 200 years [1 ].

  22.2 Definitions

  The electrical resistance of a specimen, i.e. the voltage across the specimen divided by the current through it, is determined both by the properties of the material and the dimensions of the specimen. For most substances, the property of the material is best given by the specific resistance ρ (in Ωm), which is defined as the resistance between opposite faces of a 1 m cube, but, as with mechanical properties (see Section 13.3.1 ), it is more convenient with fibres to base a definition on linear density (mass per unit length) than on area of cross-section. A mass -specific resistance R s is therefore defined as the resistance in ohms between the ends of a specimen 1 m long and of mass 1 kg, giving units of Ωkg/m2 . The two quantities are related as follows:

  R s

  = ρd

    (22.1)

  where d  = density of material in kg/m3 .

  In practice, it is more convenient to express R s in Ωg/cm2 , when the numerical values for most fibres will differ by less than 50% from the values of ρ expressed in Ωcm. With these units, the resistance R

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  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)

  Ω . Under these conditions, what voltage would produce a current of 1.0 mA (the value that a person can barely feel)?

  17.3.1 Factors That Influence Resistance

  On the atomic level, resistance arises when electrons collide with the atoms of the material. Thus, resistance depends on the type of material involved. However, geometrical factors also influence resistance. To summarize, the electrical resistance of an object of uniform cross-section, such as a length of uniform wire, depends on four properties: (1) the type of material, (2) length, (3) cross-sectional area, and (4) temperature ( ▶ Figure 17.12 ).

  ▲ Figure 17.12 Resistance factors The physical factors that directly affect the electrical resistance of a cylindrical conductor are: (a) type of material, (b) length (L ), (c) cross-sectional area (A ), and (d) temperature (T ).

  As might be expected, the resistance (R ) of an object is inversely proportional to its cross-sectional area (A ), and directly proportional to its length (L ); that is, R ∝ L /A. For example, a uniform metal wire 4.0 m long offers twice as much resistance as a similar wire 2.0 m long, but a wire with a cross-sectional area of 0.50 mm2 has only half the resistance of one with an area of 0.25 mm2 . These geometrical resistance conditions are analogous to those for liquid flow in a pipe. The longer the pipe, the greater its resistance (drag), but the larger its cross-sectional area, the more liquid it can carry per second.

  17.3.2 Resistivity

  The resistance of an object is partly determined by its material’s atomic properties, quantitatively described by the material’s resistivity ( ρ ) . Instead of the proportionality relation (R  ∝  L /A

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