36 Resistivity - incompressiblefluid, Interestingly,,...

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Ganago / Resistance and Resistivity / Resistance of Wires / Wiring Your Speakers Required Reading for HW 03 © 2010 Alexander Ganago Page 1 of 8 File: Resistivity 2.1.2 Resistance and resistivity We already mentioned that old theories of electricity described it as an invisible and incompressible fluid, and considered the electric voltage as the pressure difference. Interestingly, Ohm’s law is similar to Poiseuille’s law, which was formulated about 20 years later, in 1842, for the laminar flow of water through very small tubes: the flow rate is directly proportional to the pressure drop per unit length of the tube. For a flow of liquid, it is easy to predict that its rate would decrease if the tube gets longer and narrower. Similarly, a simple theory for electric current maintains that the electric resistance R of a uniform cylindrical sample is directly proportional to the length L of the sample and inversely proportional to its cross‐section area A, as sketched in Figure 2‐9. Figure 2‐9. For a uniform cylindrical conductor, resistance is proportional to its length L and inversely proportional to its cross‐ section area A. Mathematically: R = ρ L A [equation 2‐6] The coefficient ρ in equation [2‐6] is called resistivity and strongly depends on the material of the sample. Learning Objective: Define resistivity and explain the dependence of electric resistance on the length and cross‐section of a uniform cylindrical sample.
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Ganago / Resistance and Resistivity / Resistance of Wires / Wiring Your Speakers Required Reading for HW 03 © 2010 Alexander Ganago Page 2 of 8 File: Resistivity The SI unit of resistivity is ohm meter ( Ω⋅ m); the numerical values of resistivity range from 1.59 10 ‐8 Ω⋅ m for silver to ~10 13 Ω⋅ m for hard rubber to ~ 10 22 Ω⋅ m for Teflon (note the impressive difference by 30 orders of magnitude). Materials with low resistivity are called conductors; these are metals, of which we make wires: copper has ρ = 1.72 10 ‐8 Ω⋅ m; much cheaper and lighter aluminum has ρ = 2.82 10 ‐8 Ω⋅ m. Materials with high resistivity are called insulators: we use them to wrap wires in order to avoid unwanted electric connection, shock and electrocution of the users of electric appliances, etc. Learning Objective: Explain the difference between conductors and insulators; provide numerical examples. Resistivity of semiconductors is variable: in pure germanium, it equals 0.46 Ω⋅ m; in pure silicon, ρ = 640 Ω⋅ m, but these numbers can decrease by several orders of magnitude in the presence of impurity atoms. The actual values of resistivity depend on a variety of factors, including: (a) parameters of the semiconductor material such as density and type of impurity atoms, (b) operation conditions such as the polarity and magnitude of applied voltage, (c) environmental parameters such as temperature, illumination of the sample, etc. We will consider examples later in the book.
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