Resistivity

7 Key excerpts on "Resistivity"

• 

  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)

  26 Electrical Conductivity and Resistivity Michael B. Heaney Huladyne Research and Consulting

  1. 26.1 Basic Concepts
  2. 26.2 Simple Model and Theory
  3. 26.3 Experimental Techniques for Measuring Resistivity
     • Two-Point Technique
     • Four-Point Technique
     • Common Experimental Errors
     • Sheet Resistance Measurements
     • Instrumentation for Four-Point Resistivity Measurements
     • Instrumentation for High-Resistivity Measurements
     • van der Pauw Technique
  4. Defining Terms
  5. Acknowledgments
  6. References
  7. Further Readings

  Electrical Resistivity is a key physical property of all materials. It is often necessary to accurately measure the Resistivity of a given material. The electrical Resistivity of different materials at room temperature can vary by over 20 orders of magnitude. No single technique or instrument can measure resistivities over this wide range. This chapter describes a number of different experimental techniques and instruments for measuring resistivities. The emphasis is on explaining how to make practical measurements and avoid common experimental errors. More theoretical and detailed discussions can be found in the sources listed at the end of this chapter.

  26.1 Basic Concepts

  The electrical Resistivity of a material is a number describing how much that material resists the flow of electricity. Resistivity is measured in units of ohmmeters (ω m). If electricity can flow easily through a material, that material has low Resistivity. 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 × 1018

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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 Materials, Third Edition

  • Mary Anne White(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  Part IVElectrical and Magnetic Properties of Materials

  The missing link between electricity and magnetism was found in 1820, by Hans Christian Ørsted, who noticed that a magnetic compass needle is influenced by current in a nearby conductor. His discovery literally set the wheels of modern industry in motion.

  Rodney Cotterill The Cambridge Guide to the Material World

  Passage contains an image

  12

  Electrical Properties

  12.1 Introduction

  Although all the properties of materials—optical, thermal, electrical, magnetic, and mechanical—are related, it is perhaps the electrical properties that most distinguish one material from another. This distinction can be as simple as metal versus nonmetal, or it can involve more exotic properties such as superconductivity. The aim of this chapter is to expose the principles that determine electrical properties of matter.

  12.2 Metals, Insulators, and Semiconductors: Band Theory

  The resistance to flow of electric current in a material, designated R , is determined by the dimensions of the material (length L and cross-sectional area A ) and the intrinsic Resistivity (also known as Resistivity , and represented by ρ) of the material:*

  R = ρ

  (

  L A

  )

   

  ( 12.1 )

  where R is in units of ohms† (abbreviated Ω) and ρ is typically in units Ω m. The intrinsic Resistivity depends not just on the specific material but also on the temperature. (We will see later how the temperature dependence of Resistivity can be used to produce electronic thermometers.) Some typical resistivities are given in Table 12.1 .

  TABLE 12.1 Electrical Resistivities, ρ, and Conductivities, σ (= ρ−1 ), of Selected Materials at 25 °C

  The electrical conductivity , σ, of a material is the reciprocal of its Resistivity, ρ:

  σ =

  1 ρ

   

  ( 12.2 )

  so typical units of σ are Ω−1 m−1 (≡S m−1 , where S represents Siemens* and 1 S = 1 Ω−1 ). Electrical conductivity also can be equivalently expressed in terms of current density, J (units A m−2 , where A is amperes† ) and electric field, ε (units V m−1 , where V is volts‡

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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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  eBook - ePub

  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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  On the Origin of Natural Constants

  Axiomatic Ideas with References to the Measurable Reality

  • Hans Peter Good(Author)
  • 2018(Publication Date)
  • De Gruyter

    (Publisher)

  The inverse of R meas is also called electrical conductance. The resistance value or the conductance should not be confused with the intensive quantities specific resistance (volume resistance or Resistivity) and specific conductance, which for macroscopic samples are almost independent of the system size. These macroscopic characteristics are subject to units, are material dependent and do not constitute dimensionless constants. For two-dimensional resistance systems, it is a common practice to consider the film thickness as constant and to specify the surface or sheet resistance of the film in units of ohm per unit area. The resistance is then determined as the number of unit squares in series. High-resistance values are achieved either by a material with a high sheet resistance and/or by a large number of squares in series. In the production of two-dimensional resistance systems, the last method is usually applied and the geometrical dimensions are reduced to the limit of the lithographic process to achieve a large number of squares. The scaling of the sheet resistance by changing the film thickness or the material composition by doping has similar practical limitations as the lithography. In any case, the interaction between film thickness and material composition (doping) is most interesting for materials science. All measurements were made on samples that consisted of an insulating carrier substrate of dimension 50 mm × 50 mm, on which eight resistors were patterned into an area smaller than 4 mm × 1 mm. The size of the magnetron sputtering plant ensured that within this small area, the chemical composition and the interior structure of the amorphous layers can be considered as very homogeneous. Figure 16.1 : Sample geometry. Note: A typical 50 mm × 50 mm test sample with eight patterned resistors of amorphous layers with various magnifications of some details

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