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| {{electromagnetism|cTopic=[[Electrical network|Electrical Network]]}}
| | El Tingon Tire Shop gives all main manufacturers of latest and used tires in Tucson, AZ. We offer top quality tires and skilled workmanship on transmissions and auto repair. Our objective is to exceed buyer's expectations in time and value.<br><br>Rumor is that Sears is searching for a chief marketing officer for its appliance line whose responsibilities will include selling equipment purchases by external teams reminiscent of Costco Wholesale Corp., which not too long ago struck a deal to hold the Craftsman line. This possible action by Sears seems to me as an act of desperation to sell its best manufacturers wherever it may well get the gross sales which could end up being a disaster for the company in the long term. 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| The '''electrical resistance''' of an [[electrical conductor]] is the opposition to the passage of an [[electric current]] through that conductor; the inverse quantity is '''electrical conductance''', the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical notion of [[friction]]. The [[International System of Units|SI]] unit of electrical resistance is the [[ohm]] ([[Omega|Ω]]), while electrical conductance is measured in [[siemens (unit)|siemens]] (S).
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| An object of uniform cross section has a resistance proportional to its [[resistivity]] and length and inversely proportional to its cross-sectional area. All materials show some resistance, except for [[superconductor]]s, which have a resistance of zero.
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| The resistance (R) of an object is defined as the ratio of [[voltage]] across it (''V'') to [[Electric current|current]] through it (''I''), while the conductance (G) is the inverse:
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| :<math>R = {V\over I}, \qquad G = {I\over V}, \qquad G = \frac{1}{R}</math>
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| For a wide variety of materials and conditions, ''V'' and ''I'' are directly proportional to each other, and therefore ''R'' and ''G'' are [[Constant (mathematics)|constant]] (although they can depend on other factors like temperature or strain). This proportionality is called [[Ohm's law]], and materials that satisfy it are called "Ohmic" materials.
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| In other cases, such as a [[diode]] or [[battery (electricity)|battery]], ''V'' and ''I'' are ''not'' directly proportional, or in other words the [[I–V curve|''I–V'' curve]] is not a straight line through the origin, and Ohm's law does not hold. In this case, resistance and conductance are less useful concepts, and more difficult to define. The ratio V/I is sometimes still useful, and is referred to as a "chordal resistance" or "static resistance",<ref name=brown>{{cite book | title = Engineering System Dynamics | author = Forbes T. Brown | publisher = CRC Press | year = 2006 | isbn = 978-0-8493-9648-9 | page = 43 | url = http://books.google.com/books?id=UzqX4j9VZWcC&pg=PA43&dq=%22chordal+resistance%22&as_brr=3&ei=Z0x0Se2yNZHGlQSpjMyvDg }}</ref><ref name=kaiser>{{cite book | title = Electromagnetic Compatibility Handbook | author = Kenneth L. Kaiser | publisher = CRC Press | year = 2004 | isbn = 978-0-8493-2087-3 | pages = 13–52 | url = http://books.google.com/books?id=nZzOAsroBIEC&pg=PT1031&dq=%22static+resistance%22+%22dynamic+resistance%22+nonlinear&lr=&as_brr=3&ei=Kk50Ser1MJeOkAS9wNTwDg#PPT1031,M1 }}</ref> as it corresponds to the inverse slope of a chord between the origin and an [[I–V curve|''I–V'' curve]]. In other situations, the [[derivative]] <math> \frac{dV}{dI} \,\!</math> may be most useful; this is called the "differential resistance".
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| ==Introduction==
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| [[File:ResistanceHydraulicAnalogy.svg|thumb|The [[hydraulic analogy]] compares electric current flowing through circuits to water flowing through pipes. When a pipe (left) is filled with hair (right), it takes a larger pressure to achieve the same flow of water. Pushing electric current through a large resistance is like pushing water through a pipe clogged with hair: It requires a larger push ([[electromotive force]]) to drive the same flow ([[electric current]]).]]
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| In the [[hydraulic analogy]], current flowing through a wire (or [[resistor]]) is like water flowing through a pipe, and the [[voltage drop]] across the wire is like the [[pressure drop]] which pushes water through the pipe. Conductance is proportional to how much flow occurs for a given pressure, and resistance is proportional to how much pressure is required to achieve a given flow. (Conductance and resistance are [[Multiplicative inverse|reciprocals]].)
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| The [[voltage drop|voltage ''drop'']] (i.e., difference in voltage between one side of the resistor and the other), not the [[voltage]] itself, provides the driving force pushing current through a resistor. In hydraulics, it is similar: The pressure ''difference'' between two sides of a pipe, not the pressure itself, determines the flow through it. For example, there may be a large water pressure above the pipe, which tries to push water down through the pipe. But there may be an equally large water pressure below the pipe, which tries to push water back up through the pipe. If these pressures are equal, no water will flow. (In the image at right, the water pressure below the pipe is zero.)
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| The resistance and conductance of a wire, resistor, or other element is primarily determined by two factors: geometry (shape) and materials.
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| Geometry is important because it is more difficult to push water through a long, narrow pipe than a wide, short pipe. In the same way, a long, thin copper wire has higher resistance (lower conductance) than a short, thick copper wire.
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| Materials are important as well. A pipe filled with hair restricts the flow of water more than a clean pipe of the same shape and size. In a similar way, [[electron]]s can flow freely and easily through a [[copper]] wire, but cannot as easily flow through a [[steel]] wire of the same shape and size, and they essentially cannot flow at all through an [[insulator (electrical)|insulator]] like [[rubber]], regardless of its shape. The difference between, copper, steel, and rubber is related to their microscopic structure and [[electron configuration]], and is quantified by a property called [[resistivity]].
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| ==Conductors and resistors==
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| [[File:65-ohm resistor.jpg|thumb|250px|A 65 Ω [[resistor]], as identified by its [[electronic color code]] (blue–green–black-gold). <!-- This resistor uses the 4 band variant of the colour code so the bands represent 6 - 5 - 0 - x0.1 making 65Ω ---> An [[ohmmeter]] could be used to verify this value.]]
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| Those substances through which electricity can flow are called [[electrical conductor|conductors]]. A piece of conducting material of a particular resistance meant for use in a circuit is called a [[resistor]]. Conductors are made of high-[[Electrical resistivity and conductivity|conductivity]] materials such as metals, in particular copper and aluminium. Resistors, on the other hand, are made of a wide variety of materials depending on factors such as the desired resistance, amount of energy that it needs to dissipate, precision, and costs.
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| ==Ohm's law==
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| [[File:FourIVcurves.svg|thumb|500px|The [[current-voltage characteristic]]s of four devices: Two [[resistor]]s, a [[diode]], and a [[Battery (electricity)|battery]]. The horizontal axis is [[voltage drop]], the vertical axis is [[electric current|current]]. Ohm's law is satisfied when the graph is a straight line through the origin. Therefore, the two resistors are "ohmic", but the diode and battery are not.]]
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| {{main|Ohm's law}}
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| Ohm's law is an empirical law relating the voltage ''V'' across an element to the current ''I'' through it:
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| :<math>V \propto I</math>
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| (''V'' is directly proportional to ''I''). This law is not always true: For example, it is false for [[diode]]s, [[battery (electrical)|batteries]], etc. However, it ''is'' true to a very good approximation for wires and [[resistor]]s (assuming that other conditions, including temperature, are held fixed). Materials or objects where Ohm's law is true are called "ohmic", whereas objects which do not obey Ohm's law are '"non-ohmic".
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| == Relation to resistivity and conductivity ==
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| [[File:Resistivity geometry.png|thumb|A piece of resistive material with electrical contacts on both ends.]]
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| {{main|Electrical resistivity and conductivity}}
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| The resistance of a given object depends primarily on two factors: What material it is made of, and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area; for example, a thick copper wire has lower resistance than an otherwise-identical thin copper wire. Also, for a given material, the resistance is proportional to the length; for example, a long copper wire has higher resistance than an otherwise-identical short copper wire. The resistance {{math|R}} and conductance {{math|G}} of a conductor of uniform cross section, therefore, can be computed as
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| :<math>R = \rho \frac{\ell}{A},</math>
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| :<math>G= \sigma \frac{A}{\ell}.</math>
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| where <math>\ell</math> is the length of the conductor, measured in [[metre]]s [m], ''A'' is the cross-section area of the conductor measured in [[square metre]]s [m²], σ ([[Sigma (letter)|sigma]]) is the [[electrical conductivity]] measured in [[Siemens (unit)|siemens]] per meter (S·m<sup>−1</sup>), and ρ ([[Rho (letter)|rho]]) is the [[electrical resistivity]] (also called ''specific electrical resistance'') of the material, measured in ohm-metres (Ω·m). The resistivity and conductivity are proportionality constants, and therefore depend only on the material the wire is made of, not the geometry of the wire. Resistivity and conductivity are [[multiplicative inverse|reciprocals]]: <math>\rho=1/\sigma</math>. Resistivity is a measure of the material's ability to oppose electric current.
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| This formula is not exact: It assumes the [[current density]] is totally uniform in the conductor, which is not always true in practical situations. However, this formula still provides a good approximation for long thin conductors such as wires.
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| Another situation for which this formula is not exact is with [[alternating current]] (AC), because the [[skin effect]] inhibits current flow near the center of the conductor. Then, the ''geometrical'' cross-section is different from the ''effective'' cross-section in which current is actually flowing, so the resistance is higher than expected. Similarly, if two conductors are near each other carrying AC current, their resistances will increase due to the [[proximity effect (electromagnetism)|proximity effect]]. At [[utility frequency|commercial power frequency]], these effects are significant for large conductors carrying large currents, such as [[busbar]]s in an [[electrical substation]],<ref>Fink and Beaty, ''Standard Handbook for Electrical Engineers 11th Edition'', page 17-19</ref> or large power cables carrying more than a few hundred amperes.
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| ===What determines resistivity?===
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| {{main|Electrical resistivity and conductivity}}
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| The resistivity of different materials varies by an enormous amount: For example, the conductivity of [[PTFE|teflon]] is about 10<sup>30</sup> times lower than the conductivity of copper. Why is there such a difference? Loosely speaking, a metal has large numbers of "delocalized" electrons that are not stuck in any one place, but free to move across large distances, whereas in an insulator (like teflon), each electron is tightly bound to a single molecule, and a great force is required to pull it away. [[Semiconductor]]s lie between these two extremes. More details can be found in the article: [[Electrical resistivity and conductivity]]. For the case of [[electrolyte]] solutions, see the article: [[Conductivity (electrolytic)]].
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| Resistivity varies with temperature. In semiconductors, resistivity also changes when light is shining on it. These are discussed below.
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| ==Measuring resistance==
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| {{main|ohmmeter}}
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| An instrument for measuring resistance is called an [[ohmmeter]]. Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes a voltage drop that interferes with the measurement, so more accurate devices use [[four-terminal sensing]].
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| ==Typical resistances==
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| {{see also|Electrical resistivities of the elements (data page)|Electrical resistivity and conductivity}}
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| {| class="wikitable"
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| |-
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| |'''Component'''
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| |'''Resistance''' (Ω)
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| |-
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| |1 meter of copper wire<br>with 1mm diameter
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| |0.02<ref>The resistivity of copper is about 1.7×10<sup>-8</sup>Ωm. See [http://hypertextbook.com/facts/2004/BridgetRitter.shtml].</ref>
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| |-
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| |1 km [[overhead power line]]<br>''(typical)''
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| |0.03<ref>''Electric power substations engineering'' by John Douglas McDonald, p 18-37, [http://books.google.com/books?id=e__hltcUQIQC&pg=PT363 google books link]</ref>
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| |-
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| |[[AA battery]] ''(typical<br>[[internal resistance]])''
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| |0.1<ref>[http://data.energizer.com/PDFs/BatteryIR.pdf] For a fresh Energizer E91 AA alkaline battery, the internal resistance varies from 0.9Ω at -40°C, to 0.1Ω at +40°C.</ref>
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| |[[Incandescent light bulb]]<br>filament ''(typical)''
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| |200-1000<ref>A 60W light bulb in the USA (120V [[mains electricity]]) draws RMS current 60W/120V=500mA, so its resistance is 120V/500mA=240 ohms. The resistance of a 60W light bulb in Europe (230V mains) would be 900 ohms. The resistance of a filament is temperature-dependent; these values are for when the filament is already heated up and the light is already glowing.</ref>
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| |Human body
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| |1000 to 100,000<ref>100,000 ohms for dry skin contact, 1000 ohms for wet or broken skin contact. Other factors and conditions are relevant as well. See [[electric shock]] article for more details. Also see: {{cite web|url=http://www.cdc.gov/niosh/docs/98-131/overview.html|accessdate=2008-08-16|title=Publication No. 98-131: Worker Deaths by Electrocution|publisher=[[National Institute for Occupational Safety and Health]]}}</ref>
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| |}
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| ==Static and differential resistance==
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| {{multiple image
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| | align = right
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| | direction = horizontal
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| | width = 200
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| | image1 = DifferentialChordalResistance.svg
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| | width1 = 110
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| | alt1 = Differential versus chordal resistance
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| | caption1 = The [[Current–voltage characteristic|IV curve]] of a non-ohmic device (purple). The '''static resistance''' at point ''A'' is the [[Multiplicative inverse|inverse]] [[slope]] of line ''B'' through the origin. The '''differential resistance''' at ''A'' is the inverse slope of [[tangent line]] ''C''.
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| | image2 = Negative_differential_resistance.svg
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| | width2 = 90
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| | alt2 = Negative differential resistance
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| | caption2 = The [[Current–voltage characteristic|IV curve]] of a component with [[negative resistance|negative differential resistance]], an unusual phenomenon where the IV curve is non-[[Monotonic function|monotonic]].}}
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| {{see also|Small-signal model}}
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| Many electrical elements, such as [[diode]]s and [[battery (electricity)|batteries]] do ''not'' satisfy [[Ohm's law]]. These are called ''non-ohmic'' or ''nonlinear'', and are characterized by an [[I–V curve|''I–V'' curve]] which is ''not'' a straight line through the origin.
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| Resistance and conductance can still be defined for non-ohmic elements. However, unlike ohmic resistance, nonlinear resistance is not constant but varies with the voltage or current through the device; its [[Biasing|operating point]]. There are two types:<ref name=brown/><ref name=kaiser/>
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| *'''Static resistance''' (also called ''chordal'' or ''DC resistance'') - This corresponds to the usual definition of resistance; the voltage divided by the current
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| :<math>R_\mathrm{static} = \frac {V}{I} \,</math>.
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| :It is the slope of the line ([[chord (geometry)|chord]]} from the origin through the point on the curve. Static resistance determines the power dissipation in an electrical component. Points on the ''IV'' curve located in the 2nd or 4th quadrants, for which the slope of the chordal line is negative, have ''negative static resistance''. [[Passivity (engineering)|Passive]] devices, which have no source of energy, cannot have negative static resistance. However active devices such as transistors or [[op-amp]]s can synthesize negative static resistance with feedback, and it is used in some circuits such as [[gyrator]]s.
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| *'''Differential resistance''' (also called ''dynamic'', ''incremental'' or ''small signal resistance'') - [[Electrical resistance#Static and differential resistance|Differential resistance]] is the derivative of the voltage with respect to the current; the [[slope]] of the ''IV'' curve at a point
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| :<math>R_\mathrm{diff} = \frac {dV}{dI} \,</math>.
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| :If the ''IV'' curve is non[[monotonic]] (with peaks and troughs), the curve will have a negative slope in some regions; so in these regions the device has ''negative differential resistance''. Devices with negative differential resistance can amplify a signal applied to them, and are used to make amplifiers and oscillators. These include [[tunnel diode]]s, [[Gunn diode]]s, [[IMPATT diode]]s, [[magnetron]] tubes, and [[unijunction transistor]]s.
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| ==AC circuits==
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| ===Impedance and admittance===
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| [[File:VI phase.png|thumb|right|300px|The voltage (red) and current (blue) versus time (horizontal axis) for a [[capacitor]] (top) and [[inductor]] (bottom). Since the [[amplitude]] of the current and voltage [[Sine wave|sinusoid]]s are the same, the [[absolute value]] of [[electrical impedance|impedance]] is 1 for both the capacitor and the inductor (in whatever units the graph is using). On the other hand, the [[phase (waves)|phase difference]] between current and voltage is -90° for the capacitor; therefore, the [[argument (complex analysis)|complex phase]] of the [[electrical impedance|impedance]] of the capacitor is -90°. Similarly, the [[phase (waves)|phase difference]] between current and voltage is +90° for the inductor; therefore, the complex phase of the impedance of the inductor is +90°.]]
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| {{main|Electrical impedance|Admittance}}
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| When an alternating current flows through a circuit, the relation between current and voltage across a circuit element is characterized not only by the ratio of their magnitudes, but also the difference in their [[Phase (waves)|phases]]. For example, in an ideal resistor, the moment when the voltage reaches its maximum, the current also reaches its maximum (current and voltage are oscillating in phase). But for a [[capacitor]] or [[inductor]], the maximum current flow occurs as the voltage passes through zero and vice-versa (current and voltage are oscillating 90° out of phase, see image at right). [[Complex number]]s are used to keep track of both the phase and magnitude of current and voltage:
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| :<math>V(t)=\text{Re}(V_0 e^{j\omega t}), \quad I(t)=\text{Re}(I_0 e^{j\omega t}), \quad Z=\frac{V_0}{I_0}, \quad Y=\frac{I_0}{V_0}</math>
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| where:
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| *''t'' is time,
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| *''V''(''t'') and ''I''(''t'') are, respectively, voltage and current as a function of time,
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| *''V<sub>0</sub>'', ''I<sub>0</sub>'', ''Z'', and ''Y'' are complex numbers,
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| *''Z'' is called [[electrical impedance|impedance]],
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| *''Y'' is called [[admittance]],
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| *Re indicates [[real part]],
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| *<math>\omega</math> is the [[angular frequency]] of the AC current,
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| *<math>j=\sqrt{-1}</math> is the [[imaginary unit]].
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| The impedance and admittance may be expressed as complex numbers which can be broken into real and imaginary parts:
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| :<math>Z=R+jX, \quad Y=G+jB</math>
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| where ''R'' and ''G'' are resistance and conductance respectively, ''X'' is [[electrical reactance|reactance]], and ''B'' is [[susceptance]]. For ideal resistors, ''Z'' and ''Y'' reduce to ''R'' and ''G'' respectively, but for AC networks containing [[capacitor]]s and [[inductor]]s, ''X'' and ''B'' are nonzero.
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| <math>Z=1/Y</math> for AC circuits, just as <math>R=1/G</math> for DC circuits.
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| ===Frequency dependence of resistance===
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| Another complication of AC circuits is that the resistance and conductance can be frequency-dependent. One reason, mentioned above is the [[skin effect]] (and the related [[proximity effect (electromagnetism)|proximity effect]]). Another reason is that the resistivity itself may depend on frequency (see [[Drude model]], [[deep-level trap]]s, [[resonant frequency]], [[Kramers–Kronig relations]], etc.)
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| ==Energy dissipation and Joule heating==
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| [[File:Cartridge-heater-hot.jpg|thumb|Running current through a material with high resistance creates heat, in a phenomenon called [[Joule heating]]. In this picture, a [[cartridge heater]], warmed by Joule heating, is [[Incandescence|glowing red hot]].]]
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| {{main|Joule heating}}
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| Resistors (and other elements with resistance) oppose the flow of electric current; therefore, electrical energy is required to push current through the resistance. This electrical energy is dissipated, heating the resistor in the process. This is called ''[[Joule heating]]'' (after [[James Prescott Joule]]), also called ''ohmic heating'' or ''resistive heating''.
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| The dissipation of electrical energy is often undesired, particularly in the case of [[electric power transmission|transmission losses]] in [[overhead power line|power lines]]. [[Electric power transmission|High voltage transmission]] helps reduce the losses by reducing the current for a given power.
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| On the other hand, Joule heating is sometimes useful, for example in [[electric stove]]s and other [[electric heating|electric heaters]] (also called ''resistive heaters''). As another example, [[incandescent lamp]]s rely on Joule heating: the filament is heated to such a high temperature that it glows "white hot" with [[thermal radiation]] (also called [[incandescence]]).
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| The formula for Joule heating is:
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| :<math>P=I^2R</math>
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| where ''P'' is the [[electric power|power]] (energy per unit time) converted from electrical energy to thermal energy, ''R'' is the resistance, and ''I'' is the current through the resistor.
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| == Dependence of resistance on other conditions ==
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| === Temperature dependence ===
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| {{main|Electrical resistivity and conductivity#Temperature dependence}}
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| Near room temperature, the resistivity of metals typically increases as temperature is increased, while the resistivity of semiconductors typically decreases as temperature is increased. The resistivity of insulators and electrolytes may increase or decrease depending on the system. For the detailed behavior and explanation, see [[Electrical resistivity and conductivity]].
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| As a consequence, the resistance of wires, resistors, and other components often change with temperature. This effect may be undesired, causing an electronic circuit to malfunction at extreme temperatures. In some cases, however, the effect is put to good use. When temperature-dependent resistance of a component is used purposefully, the component is called a [[resistance thermometer]] or [[thermistor]]. (A resistance thermometer is made of metal, usually platinum, while a thermistor is made of ceramic or polymer.)
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| Resistance thermometers and thermistors are generally used in two ways. First, they can be used as [[thermometer]]s: By measuring the resistance, the temperature of the environment can be inferred. Second, they can be used in conjunction with [[Joule heating]] (also called self-heating): If a large current is running through the resistor, the resistor's temperature rises and therefore its resistance changes. Therefore, these components can be used in a circuit-protection role similar to [[fuse (electrical)|fuse]]s, or for [[feedback]] in circuits, or for many other purposes. In general, self-heating can turn a resistor into a [[nonlinear element|nonlinear]] and [[hysteresis|hysteretic]] circuit element. For more details see [[Thermistor#Self-heating effects]].
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| If the temperature ''T'' does not vary too much, a [[linear approximation]] is typically used:
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| :<math>R(T) = R_0[1+\alpha (T - T_0)]</math>
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| where <math>\alpha</math> is called the ''temperature coefficient of resistance'', <math>T_0</math> is a fixed reference temperature (usually room temperature), and <math>R_0</math> is the resistance at temperature <math>T_0</math>. The parameter <math>\alpha</math> is an empirical parameter fitted from measurement data. Because the linear approximation is only an approximation, <math>\alpha</math> is different for different reference temperatures. For this reason it is usual to specify the temperature that <math>\alpha</math> was measured at with a suffix, such as <math>\alpha_{15}</math>, and the relationship only holds in a range of temperatures around the reference.<ref>Ward, MR, ''Electrical Engineering Science'', pp36–40, McGraw-Hill, 1971.</ref>
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| The temperature coefficient <math>\alpha</math> is typically +3×10<sup>−3</sup> K<sup>−1</sup> to +6×10<sup>−3</sup> K<sup>−1</sup> for metals near room temperature. It is usually negative for semiconductors and insulators, with highly variable magnitude.<ref>See [[Electrical resistivity and conductivity]] for a table. The temperature coefficient of resistivity is similar but not identical to the temperature coefficient of resistance. The small difference is due to [[thermal expansion]] changing the dimensions of the resistor.</ref>
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| === Strain dependence ===
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| {{main|Strain gauge}}
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| Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon [[strain (materials science)|strain]]. By placing a conductor under [[tension (mechanics)|tension]] (a form of [[stress (physics)|stress]] that leads to strain in the form of stretching of the conductor), the length of the section of conductor under tension increases and its cross-sectional area decreases. Both these effects contribute to increasing the resistance of the strained section of conductor. Under compression (strain in the opposite direction), the resistance of the strained section of conductor decreases. See the discussion on [[strain gauge]]s for details about devices constructed to take advantage of this effect.
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| === Light illumination dependence ===
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| {{main|Photoresistor|Photoconductivity}}
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| Some resistors, particularly those made from [[semiconductor]]s, exhibit ''[[photoconductivity]]'', meaning that their resistance changes when light is shining on them. Therefore they are called ''[[photoresistor]]s'' (or ''light dependent resistors''). These are a common type of [[photodetector|light detector]].
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| ==Superconductivity==
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| {{main|Superconductivity}}
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| [[Superconductor]]s are materials that have exactly zero resistance and infinite conductance, because they can have V=0 and I≠0. This also means there is no [[joule heating]], or in other words no [[dissipation]] of electrical energy. Therefore, if superconductive wire is made into a closed loop, current will keep flowing around the loop forever. Superconductors require cooling to temperatures near 4 K with [[liquid helium]] for most metallic superconductors like [[Niobium|Nb]][[Tin|Sn]] alloys, or cooling to temperatures near 77K with [[liquid nitrogen]] for the expensive, brittle and delicate ceramic [[high temperature superconductors]].
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| Nevertheless, there are many [[technological applications of superconductivity]], including [[superconducting magnet]]s.
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| ==See also==
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| {{Portal|Electronics}}
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| <div class= style="-moz-column-count:2; column-count:2;">
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| * [[Electrical measurements]]
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| * [[Resistor]]
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| * [[Electrical conduction]] for more information about the physical mechanisms for conduction in materials.
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| * [[Voltage divider]]
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| * [[Voltage drop]]
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| * [[Thermal resistance]]
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| * [[Sheet resistance]]
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| * [[SI electromagnetism units]]
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| * [[Quantum Hall effect]], a standard for high-accuracy resistance measurements.
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| * [[Series and parallel circuits]]
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| * [[Johnson–Nyquist noise]]
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| </div>
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://independent.academia.edu/Csoliverez/Papers/1848699/The_Notion_of_Electrical_Resistance_by_Soliverez The Notion of Electrical Resistance]. Review of the equations that determine the value of electrical resistance.
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| *[http://www.cvel.clemson.edu/emc/calculators/Resistance_Calculator/index.html''Clemson Vehicular Electronics Laboratory: Resistance Calculator'']
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| {{DEFAULTSORT:Electrical Resistance}}
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| [[Category:Electricity]]
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| [[Category:Physical quantities]]
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| [[Category:Electromagnetism]]
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