2251:
2201:
1493:
67:
2907:
3798:
1774:
2066:
1603:
4481:
2644:
1650:
3491:
2571:
3237:
3960:
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
1540:
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
3952:
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
1500:
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:
2027:
is about 10 times lower than the conductivity of copper. Loosely speaking, this is because metals have large numbers of "delocalized" electrons that are not stuck in any one place, so they are free to move across large distances. In an insulator, such as Teflon, each electron is tightly bound to a
1781:
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
2902:{\displaystyle {\begin{array}{cl}u(t)&=\operatorname {\mathcal {R_{e}}} \left(U_{0}\cdot e^{j\omega t}\right)\\i(t)&=\operatorname {\mathcal {R_{e}}} \left(I_{0}\cdot e^{j(\omega t+\varphi )}\right)\\Z&={\frac {U}{\ I\ }}\\Y&={\frac {\ 1\ }{Z}}={\frac {\ I\ }{U}}\end{array}}}
3652:, which does no useful work at a load. In a simple case with an inductive load (causing the phase to increase), a capacitor may be added for compensation at one frequency, since the capacitor's phase shift is negative, bringing the total impedance phase closer to 0° again.
4347:
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
2402:) from the origin through the point on the curve. Static resistance determines the power dissipation in an electrical component. Points on the currentâvoltage curve located in the 2nd or 4th quadrants, for which the slope of the chordal line is negative, have
1872:
3817:
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
1541:
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 flows. (In the image at right, the water pressure below the pipe is zero.)
1634:
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.
1940:) 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
1555:
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.
3980:(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
1164:
990:
2513:
3486:{\displaystyle {\begin{aligned}R&={\frac {G}{\ G^{2}+B^{2}\ }}\ ,\qquad &X={\frac {-B~}{\ G^{2}+B^{2}\ }}\ ,\\G&={\frac {R}{\ R^{2}+X^{2}\ }}\ ,\qquad &B={\frac {-X~}{\ R^{2}+X^{2}\ }}\ ,\end{aligned}}}
3202:
1336:
2310:
Resistance and conductance can still be defined for non-ohmic elements. However, unlike ohmic resistance, non-linear resistance is not constant but varies with the voltage or current through the device; i.e., its
2618:
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
1742:
Other components and materials used in electronics do not obey Ohm's law; the current is not proportional to the voltage, so the resistance varies with the voltage and current through them. These are called
1800:
1795:
1529:
that 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.
2080:. 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
1782:
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
3242:
3133:
1478:
2395:
1719:
over a wide range of voltages and currents. Therefore, the resistance and conductance of objects or electronic components made of these materials is constant. This relationship is called
3602:
2004:
cross-section in which current actually flows, so resistance is higher than expected. Similarly, if two conductors near each other carry AC current, their resistances increase due to the
1985:
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.
3115:
624:
4970:
4437:
of electrical energy. Therefore, if superconductive wire is made into a closed loop, current flows around the loop forever. Superconductors require cooling to temperatures near
3069:
2093:
1077:
1976:
597:
4280:
1236:. The nature of a material is not the only factor in resistance and conductance, however; it also depends on the size and shape of an object because these properties are
4088:
1717:
609:
3700:
3531:
3915:
3008:
4303:
4253:
4233:
4213:
4108:
2982:
4462:
4193:
4166:
4139:
3734:
1894:
5128:
4737:
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
2450:
4992:
Zhai, Chongpu; Gan, Yixiang; Hanaor, Dorian; Proust, Gwénaëlle (2018). "Stress-dependent electrical transport and its universal scaling in granular materials".
3128:
1272:
2635:, 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 below).
1090:
1240:. For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. All objects resist electrical current, except for
5095:
860:
923:
629:
4700:. 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.
2526:. Devices with negative differential resistance can amplify a signal applied to them, and are used to make amplifiers and oscillators. These include
639:
1559:
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. Similarly,
4734:
4517:
3954:
3947:
2627:, the moment when the voltage reaches its maximum, the current also reaches its maximum (current and voltage are oscillating in phase). But for a
2097:
2033:
1768:
1631:
1233:
35:
464:
4915:
4890:
4804:
4774:
101:
1590:
In addition to geometry and material, there are various other factors that influence resistance and conductance, such as temperature; see
30:
This article is about specific applications of conductivity and resistivity in electrical elements. For other types of conductivity, see
5138:
3764:
2340:
2005:
2300:
2257:
2207:
1732:
1654:
1426:
1237:
359:
91:
1191:, measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical
1360:(although they will depend on the size and shape of the object, the material it is made of, and other factors like temperature or
4458:
2522:
3976:: by measuring the resistance, the temperature of the environment can be inferred. Second, they can be used in conjunction with
3648:
respectively. In general, AC systems are designed to keep the phase angle close to 0° as much as possible, since it reduces the
2410:
devices, which have no source of energy, cannot have negative static resistance. However active devices such as transistors or
274:
5107:
853:
619:
96:
4321:
for metals near room temperature. It is usually negative for semiconductors and insulators, with highly variable magnitude.
3736:
for DC circuits containing only resistors, or AC circuits for which either the reactance or susceptance happens to be zero (
2614:
between current and voltage is +90° for the inductor; therefore, the complex phase of the impedance of the inductor is +90°.
4931:
3756:
3755:
A key feature of AC circuits is that the resistance and conductance can be frequency-dependent, a phenomenon known as the
1579:, regardless of its shape. The difference between copper, steel, and rubber is related to their microscopic structure and
1196:
634:
339:
31:
5060:
Meyer, Sebastian; et al. (2022), "Characterization of the deformation state of magnesium by electrical resistance",
4352:(strain in the opposite direction), the resistance of the strained section of conductor decreases. See the discussion on
3780:
4544:
1442:
499:
489:
474:
239:
106:
539:
229:
3848:
3840:
3537:
2603:
2041:
792:
667:
564:
459:
4336:
4215:
is an empirical parameter fitted from measurement data. Because the linear approximation is only an approximation,
3969:. (A resistance thermometer is made of metal, usually platinum, while a thermistor is made of ceramic or polymer.)
3125:
The impedance and admittance may be expressed as complex numbers that can be broken into real and imaginary parts:
292:
4523:
3542:
1867:{\displaystyle {\begin{aligned}R&=\rho {\frac {\ell }{A}},\\G&=\sigma {\frac {A}{\ell }}\,.\end{aligned}}}
4554:
846:
807:
334:
324:
264:
259:
199:
4014:
1696:
1677:. Ohm's law is satisfied when the graph is a straight line through the origin. Therefore, the two resistors are
5099:
4235:
is different for different reference temperatures. For this reason it is usual to specify the temperature that
3884:
777:
657:
344:
1544:
The resistance and conductance of a wire, resistor, or other element is mostly determined by two properties:
4507:
3084:
2598:
is 1 for both the capacitor and the inductor (in whatever units the graph is using). On the other hand, the
2520:(with peaks and troughs), the curve has a negative slope in some regionsâso in these regions the device has
2407:
2160:
2047:
Resistivity varies with temperature. In semiconductors, resistivity also changes when exposed to light. See
1917:
1361:
782:
752:
184:
174:
169:
4335:
Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon
4466:
3962:
2543:
2219:
1941:
1933:
1580:
1572:
1357:
1180:
604:
374:
149:
4499:
4349:
3870:
rely on Joule heating: the filament is heated to such a high temperature that it glows "white hot" with
3043:
2280:
2081:
2017:
1666:
1611:
1384:
702:
389:
379:
329:
319:
66:
42:
2023:
The resistivity of different materials varies by an enormous amount: For example, the conductivity of
1232:
like metals tend to have very low resistance and high conductance. This relationship is quantified by
1049:
5133:
5011:
4874:
4829:
4008:
3825:
3219:
3031:
2607:
2595:
2561:
1947:
1623:
1229:
1221:
1083:
916:
827:
727:
692:
444:
309:
209:
194:
129:
2250:
234:
4528:
4494:
4340:
3972:
Resistance thermometers and thermistors are generally used in two ways. First, they can be used as
3844:
3604:
is the phase difference between the voltage and current passing through a component with impedance
2261:
2148:
2127:
1989:
1736:
1626:. A piece of conducting material of a particular resistance meant for use in a circuit is called a
1502:
787:
767:
762:
569:
554:
439:
409:
304:
4384:, meaning that their resistance changes when light is shining on them. Therefore, they are called
4258:
5075:
5027:
5001:
4855:
4559:
4512:
4486:
3776:
2414:
can synthesize negative static resistance with feedback, and it is used in some circuits such as
2265:
2190:
1220:
The resistance of an object depends in large part on the material it is made of. Objects made of
662:
402:
204:
164:
4415:
are materials that have exactly zero resistance and infinite conductance, because they can have
2200:
3665:
3496:
4911:
4886:
4800:
4770:
4738:
4637:
4407:
4380:
4369:
3989:
3981:
3871:
3867:
2993:
2985:
2009:
1514:
1497:
722:
4288:
4238:
4218:
4198:
4093:
3988:
in circuits, or for many other purposes. In general, self-heating can turn a resistor into a
2967:
5065:
5019:
4845:
4837:
4549:
4344:
3859:
3806:
2399:
1756:
1674:
1506:
1492:
1422:
1259:
1176:
822:
737:
697:
687:
574:
529:
512:
429:
364:
134:
58:
4446:
4171:
4144:
4117:
3705:
2337:
This corresponds to the usual definition of resistance; the voltage divided by the current
1879:
4716:
for wet or broken skin contact. High voltage breaks down the skin, lowering resistance to
4564:
4454:
3772:
1982:
757:
682:
677:
544:
419:
384:
279:
244:
144:
797:
5015:
4963:
4833:
3801:
Running current through a material with resistance creates heat, in a phenomenon called
4721:
4412:
3922:
3855:
3231:
3118:
3076:
2636:
2591:
1921:
1913:
1536:(i.e., difference between voltages on one side of the resistor and the other), not the
1241:
1210:
717:
712:
534:
424:
349:
299:
249:
222:
179:
154:
124:
117:
4879:
2012:, these effects are significant for large conductors carrying large currents, such as
1159:{\displaystyle {\mathsf {M}}^{-1}{\mathsf {L}}^{-2}{\mathsf {T}}^{3}{\mathsf {I}}^{2}}
5122:
5079:
5070:
4442:
4430:
4395:
4386:
4375:
4365:
3977:
3875:
3839:
The dissipation of electrical energy is often undesired, particularly in the case of
3820:
3810:
3802:
3792:
2620:
2611:
2599:
2029:
1526:
832:
817:
802:
742:
454:
369:
354:
269:
254:
159:
17:
5031:
4859:
3797:
1773:
1571:
wire of the same shape and size, and they essentially cannot flow at all through an
4850:
4604:
For a fresh
Energizer E91 AA alkaline battery, the internal resistance varies from
4569:
4353:
4330:
4282:, and the relationship only holds in a range of temperatures around the reference.
2535:
2527:
2238:
1929:
1905:
1670:
1602:
1533:
1522:
1028:
904:
812:
707:
672:
614:
549:
434:
314:
189:
2288:
1720:
1644:
1365:
985:{\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}{\mathsf {I}}^{-2}}
469:
41:"Resistive" redirects here. For the term used when referring to touchscreens, see
4794:
4764:
1978:. Resistivity is a measure of the material's ability to oppose electric current.
4434:
3973:
3768:
3760:
3747:, respectively) (if one is zero, then for realistic systems both must be zero).
3227:
2649:
2037:
1993:
1735:
of an ohmic device consists of a straight line through the origin with positive
1584:
1376:
732:
584:
414:
76:
4938:
4720:. Other factors and conditions are relevant as well. For more details, see the
4520:
for more information about the physical mechanisms for conduction in materials.
4480:
2639:
are used to keep track of both the phase and magnitude of current and voltage:
5023:
4476:
3997:
3993:
3966:
3767:). Another reason is that the resistivity itself may depend on frequency (see
3035:
2565:
2531:
2142:
1437:
449:
1996:
inhibits current flow near the center of the conductor. For this reason, the
1228:
tend to have very high resistance and low conductance, while objects made of
3609:
3072:
2628:
2587:
2583:
2575:
2539:
2517:
2508:{\displaystyle R_{\mathrm {diff} }={{\mathrm {d} V} \over {\mathrm {d} I}}.}
2065:
772:
747:
559:
484:
81:
3925:(energy per unit time) converted from electrical energy to thermal energy,
3533:
is only true in the special cases of either DC or reactance-free current.
2032:
lie between these two extremes. More details can be found in the article:
1649:
4539:
4534:
3985:
3649:
3613:
2632:
2624:
2579:
2574:
The voltage (red) and current (blue) versus time (horizontal axis) for a
2077:
2070:
2060:
1728:
1658:
1627:
1615:
1607:
1560:
1518:
1192:
524:
519:
139:
4356:
for details about devices constructed to take advantage of this effect.
3197:{\displaystyle {\begin{aligned}Z&=R+jX\\Y&=G+jB~.\end{aligned}}}
1331:{\displaystyle R={\frac {V}{I}},\qquad G={\frac {I}{V}}={\frac {1}{R}}.}
4820:
Fink & Beaty (1923). "Standard
Handbook for Electrical Engineers".
2415:
2312:
1790:
of a conductor of uniform cross section, therefore, can be computed as
1537:
1252:
1017:
893:
494:
5098:. Vehicular Electronics Laboratory. Clemson University. Archived from
2602:
between current and voltage is â90° for the capacitor; therefore, the
4841:
3948:
Electrical resistivity and conductivity § Temperature dependence
3854:
On the other hand, Joule heating is sometimes useful, for example in
2443:
It is the derivative of the voltage with respect to the current; the
2411:
2013:
1576:
1564:
1225:
579:
86:
2570:
1777:
A piece of resistive material with electrical contacts on both ends.
5006:
3851:
helps reduce the losses by reducing the current for a given power.
3796:
2569:
2444:
2276:
2222:
2064:
2020:, or large power cables carrying more than a few hundred amperes.
1897:
1772:
1752:
1662:
1568:
1380:
1205:
4141:
is a fixed reference temperature (usually room temperature), and
5108:"Electron conductance models using maximal entropy random walks"
4910:(2nd ed.). Boca Raton, Florida: CRC Press. pp. 363ff.
2962:
indicate the amplitude of the voltage and current, respectively;
2942:
are the voltage and current as a function of time, respectively;
2024:
2264:, an unusual phenomenon where the currentâvoltage curve is non-
4766:
Engineering System
Dynamics: A Unified Graph-Centered Approach
2028:
single molecule so a great force is required to pull it away.
1988:
Another situation for which this formula is not exact is with
1200:
4769:(2nd ed.). Boca Raton, Florida: CRC Press. p. 43.
3961:
a component is used purposefully, the component is called a
3054:
3050:
2753:
2749:
2676:
2672:
1175:
of an object is a measure of its opposition to the flow of
3020:
are the complex-valued voltage and current, respectively;
1904:
is the cross-sectional area of the conductor measured in
3624:
are nonzero. Ideal resistors have an angle of 0°, since
3616:, this angle is exactly -90° or +90°, respectively, and
4531:, a standard for high-accuracy resistance measurements.
1727:
materials. Examples of ohmic components are wires and
1348:
are directly proportional to each other, and therefore
1213:(S) (formerly called the 'mho' and then represented by
1445:
5064:, Scripta Materialia, vol. 215, p. 114712,
4971:
National
Institute for Occupational Safety and Health
4291:
4261:
4241:
4221:
4201:
4174:
4147:
4120:
4096:
4017:
3887:
3708:
3668:
3545:
3499:
3240:
3131:
3087:
3046:
2996:
2970:
2647:
2453:
2343:
1950:
1882:
1798:
1699:
1275:
1093:
1052:
926:
2094:
Electrical resistivities of the elements (data page)
2076:
An instrument for measuring resistance is called an
1689:
through the material is proportional to the voltage
1622:
Substances in which electricity can flow are called
2048:
1591:
1473:{\textstyle {\frac {\mathrm {d} V}{\mathrm {d} I}}}
1413:is sometimes still useful, and is referred to as a
1082:
1039:
1026:
1016:
1004:
999:
915:
902:
892:
880:
875:
4878:
4799:. Boca Raton, Florida: CRC Press. pp. 13â52.
4297:
4274:
4247:
4227:
4207:
4187:
4160:
4133:
4102:
4082:
3909:
3728:
3694:
3596:
3525:
3485:
3196:
3109:
3063:
3002:
2976:
2901:
2507:
2390:{\displaystyle R_{\mathrm {static} }={V \over I}.}
2389:
1970:
1888:
1866:
1711:
1472:
1330:
1158:
1071:
984:
1421:, since it corresponds to the inverse slope of a
4457:for the expensive, brittle and delicate ceramic
1521:) is like water flowing through a pipe, and the
1340:For a wide variety of materials and conditions,
27:Opposition to the passage of an electric current
4463:technological applications of superconductivity
2116:1 meter of copper wire with 1 mm diameter
2103:Typical resistance values for selected objects
1209:), while electrical conductance is measured in
4885:(2nd ed.). New York: Wiley. p. 559.
34:. For electrical conductivity in general, see
4374:Some resistors, particularly those made from
1981:This formula is not exact, as it assumes the
854:
8:
3597:{\displaystyle \ \theta =\arg(Z)=-\arg(Y)\ }
1896:is the length of the conductor, measured in
1368:, and materials that satisfy it are called
1567:wire, but cannot flow as easily through a
861:
847:
65:
49:
5069:
5005:
4849:
4290:
4266:
4260:
4240:
4220:
4200:
4179:
4173:
4152:
4146:
4125:
4119:
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4068:
4037:
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3898:
3886:
3718:
3707:
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3667:
3544:
3512:
3498:
3461:
3448:
3427:
3400:
3387:
3374:
3342:
3329:
3308:
3281:
3268:
3255:
3241:
3239:
3132:
3130:
3094:
3086:
3053:
3048:
3047:
3045:
2995:
2969:
2877:
2856:
2826:
2785:
2772:
2752:
2747:
2746:
2708:
2695:
2675:
2670:
2669:
2648:
2646:
2610:of the capacitor is â90°. Similarly, the
2491:
2490:
2481:
2480:
2478:
2459:
2458:
2452:
2374:
2349:
2348:
2342:
1960:
1949:
1881:
1856:
1846:
1816:
1799:
1797:
1723:, and materials which obey it are called
1698:
1583:, and is quantified by a property called
1459:
1449:
1446:
1444:
1395:are not directly proportional. The ratio
1315:
1302:
1282:
1274:
1150:
1144:
1143:
1136:
1130:
1129:
1119:
1113:
1112:
1102:
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1092:
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950:
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942:
936:
935:
928:
927:
925:
4937:(Report). Energizer Corp. Archived from
4788:
4786:
4741:changing the dimensions of the resistor.
4449:alloys, or cooling to temperatures near
2447:of the currentâvoltage curve at a point
2101:
1763:Relation to resistivity and conductivity
1648:
1601:
1491:
1251:of an object is defined as the ratio of
4758:
4756:
4752:
4735:Electrical resistivity and conductivity
4580:
4518:Electrical resistivity and conductivity
4445:for most metallic superconductors like
4255:was measured at with a suffix, such as
3955:Electrical resistivity and conductivity
2098:Electrical resistivity and conductivity
2034:Electrical resistivity and conductivity
1769:Electrical resistivity and conductivity
1480:may be most useful; this is called the
610:Electromagnetism and special relativity
57:
36:Electrical resistivity and conductivity
4908:Electric Power Substations Engineering
4796:Electromagnetic Compatibility Handbook
3996:circuit element. For more details see
3110:{\displaystyle j\equiv {\sqrt {-1\ }}}
1145:
1131:
1114:
1097:
996:
968:
951:
937:
929:
872:
5129:Electrical resistance and conductance
4112:temperature coefficient of resistance
3933:is the current through the resistor.
3759:. One reason, mentioned above is the
3493:which are true in all cases, whereas
2315:. There are two types of resistance:
2210:of a non-ohmic device (purple). The
1563:can flow freely and easily through a
1517:, current flowing through a wire (or
1199:unit of electrical resistance is the
630:Maxwell equations in curved spacetime
7:
3787:Energy dissipation and Joule heating
2516:If the currentâvoltage curve is non-
2317:
2000:cross-section is different from the
1681:, but the diode and battery are not.
4587:The resistivity of copper is about
2307:straight lines through the origin.
1618:could be used to verify this value.
1614:(violetâgreenâblackâgoldâred). An
1244:, which have a resistance of zero.
5114:. Wolfram Demonstrantions Project.
3881:The formula for Joule heating is:
3064:{\displaystyle {\mathcal {R_{e}}}}
2492:
2482:
2469:
2466:
2463:
2460:
2365:
2362:
2359:
2356:
2353:
2350:
2275:Many electrical elements, such as
2185:Static and differential resistance
1460:
1450:
1364:). This proportionality is called
1265:through it, while the conductance
25:
4168:is the resistance at temperature
5071:10.1016/j.scriptamat.2022.114712
4964:"Worker Deaths by Electrocution"
4479:
4459:high temperature superconductors
2523:negative differential resistance
2262:negative differential resistance
2249:
2199:
1685:For many materials, the current
1072:{\displaystyle G={\frac {1}{R}}}
4828:(2788) (11th ed.): 17â19.
4724:article, and NIOSH 98-131.
4461:. Nevertheless, there are many
4339:. By placing a conductor under
3998:Thermistor#Self-heating effects
3418:
3299:
1971:{\displaystyle \rho =1/\sigma }
1655:currentâvoltage characteristics
1295:
1238:extensive rather than intensive
5049:. McGraw-Hill. pp. 36â40.
5047:Electrical Engineering Science
4429:. This also means there is no
4394:). These are a common type of
4077:
4074:
4055:
4043:
4027:
4021:
3953:behavior and explanation, see
3937:Dependence on other conditions
3809:, warmed by Joule heating, is
3588:
3582:
3567:
3561:
2804:
2789:
2738:
2732:
2661:
2655:
1938:specific electrical resistance
1630:. Conductors are made of high-
1:
4633:light bulb (in the USA, with
4360:Light illumination dependence
3757:universal dielectric response
2398:It is the slope of the line (
635:Relativistic electromagnetism
4545:Series and parallel circuits
4285:The temperature coefficient
4275:{\displaystyle \alpha _{15}}
3702:) for all circuits, just as
2040:solutions, see the article:
1525:across the wire is like the
4932:Battery internal resistance
4793:Kaiser, Kenneth L. (2004).
2623:. For example, in an ideal
2586:of the current and voltage
2427:
2325:
2042:Conductivity (electrolytic)
1501:It requires a larger push (
1436:. In other situations, the
1234:resistivity or conductivity
5155:
5139:Electromagnetic quantities
4906:McDonald, John D. (2016).
4405:
4363:
4328:
4083:{\displaystyle R(T)=R_{0}}
4007:does not vary too much, a
3945:
3790:
3010:is the displacement angle;
2559:
2404:negative static resistance
2188:
2091:
2058:
2010:commercial power frequency
1766:
1712:{\displaystyle I\propto V}
1642:
1505:) to drive the same flow (
1425:between the origin and an
1375:In other cases, such as a
360:LiĂ©nardâWiechert potential
40:
29:
5024:10.1016/j.eml.2018.05.005
4994:Extreme Mechanics Letters
4763:Brown, Forbes T. (2006).
4555:SI electromagnetism units
4392:light dependent resistors
3849:High voltage transmission
3695:{\displaystyle \ Z=1/Y\ }
3526:{\displaystyle \ R=1/G\ }
2110:
2107:
1669:. The horizontal axis is
625:Mathematical descriptions
335:Electromagnetic radiation
325:Electromagnetic induction
265:Magnetic vector potential
260:Magnetic scalar potential
4973:. Publication No. 98-131
3910:{\displaystyle P=I^{2}R}
3781:KramersâKronig relations
3003:{\displaystyle \varphi }
2556:Impedance and admittance
2237:is the inverse slope of
2229:through the origin. The
1598:Conductors and resistors
5096:"Resistance calculator"
4851:2027/mdp.39015065357108
4664:, so its resistance is
4508:Electrical measurements
4467:superconducting magnets
4433:, or in other words no
4298:{\displaystyle \alpha }
4248:{\displaystyle \alpha }
4228:{\displaystyle \alpha }
4208:{\displaystyle \alpha }
4103:{\displaystyle \alpha }
3929:is the resistance, and
3866:). As another example,
2977:{\displaystyle \omega }
2544:unijunction transistors
2438:small-signal resistance
2422:Differential resistance
2231:differential resistance
2161:Incandescent light bulb
1918:electrical conductivity
1673:, the vertical axis is
1610:, as identified by its
1482:differential resistance
175:Electrostatic induction
170:Electrostatic discharge
4712:for dry skin contact,
4692:light bulb in Europe (
4688:. The resistance of a
4299:
4276:
4249:
4229:
4209:
4189:
4162:
4135:
4104:
4084:
3963:resistance thermometer
3942:Temperature dependence
3911:
3814:
3730:
3696:
3598:
3527:
3487:
3198:
3111:
3065:
3004:
2978:
2903:
2615:
2509:
2391:
2301:currentâvoltage curves
2073:
1972:
1934:electrical resistivity
1890:
1868:
1778:
1713:
1682:
1619:
1581:electron configuration
1510:
1474:
1332:
1187:electrical conductance
1160:
1073:
986:
605:Electromagnetic tensor
4524:JohnsonâNyquist noise
4500:Von Klitzing constant
4300:
4277:
4250:
4230:
4210:
4190:
4188:{\displaystyle T_{0}}
4163:
4161:{\displaystyle R_{0}}
4136:
4134:{\displaystyle T_{0}}
4105:
4085:
3912:
3805:. In this picture, a
3800:
3731:
3729:{\displaystyle R=1/G}
3697:
3658:is the reciprocal of
3599:
3528:
3488:
3199:
3112:
3066:
3005:
2979:
2904:
2573:
2510:
2392:
2258:currentâvoltage curve
2208:currentâvoltage curve
2082:four-terminal sensing
2068:
2018:electrical substation
1973:
1924:per meter (S·m), and
1891:
1889:{\displaystyle \ell }
1869:
1776:
1733:currentâvoltage graph
1714:
1657:of four devices: Two
1652:
1612:electronic color code
1605:
1548:geometry (shape), and
1495:
1475:
1333:
1230:electrical conductors
1222:electrical insulators
1173:electrical resistance
1161:
1074:
987:
598:Covariant formulation
390:Synchrotron radiation
330:Electromagnetic pulse
320:Electromagnetic field
43:Resistive touchscreen
18:Electrical resistance
4640:) draws RMS current
4289:
4259:
4239:
4219:
4199:
4172:
4145:
4118:
4094:
4015:
4009:linear approximation
3885:
3826:James Prescott Joule
3751:Frequency dependence
3706:
3666:
3543:
3497:
3238:
3230:. These lead to the
3129:
3085:
3044:
2994:
2968:
2645:
2582:(bottom). Since the
2562:Electrical impedance
2451:
2341:
2260:of a component with
1948:
1880:
1796:
1697:
1443:
1273:
1091:
1050:
1000:Electric conductance
924:
640:Stressâenergy tensor
565:Reluctance (complex)
310:Displacement current
5045:Ward, M.R. (1971).
5016:2018ExML...22...83Z
4875:Johnson, Kenneth W.
4834:1923Natur.111..458R
4529:Quantum Hall effect
4495:Conductance quantum
4011:is typically used:
4003:If the temperature
3841:transmission losses
3628:is zero (and hence
2291:. These are called
2149:internal resistance
2128:overhead power line
2104:
1990:alternating current
1751:. Examples include
1693:applied across it:
1638:
1503:electromotive force
1269:is the reciprocal:
876:Electric resistance
555:Magnetomotive force
440:Electromotive force
410:Alternating current
345:Jefimenko equations
305:Cyclotron radiation
4944:on 11 January 2012
4873:Cutnell, John D.;
4560:Thermal resistance
4513:Contact resistance
4487:Electronics portal
4295:
4272:
4245:
4225:
4205:
4185:
4158:
4131:
4100:
4080:
3907:
3868:incandescent lamps
3815:
3777:resonant frequency
3726:
3692:
3594:
3523:
3483:
3481:
3194:
3192:
3107:
3061:
3000:
2988:of the AC current;
2974:
2899:
2897:
2616:
2590:are the same, the
2505:
2387:
2191:Small-signal model
2102:
2074:
2036:. For the case of
1992:(AC), because the
1968:
1886:
1864:
1862:
1779:
1709:
1683:
1620:
1511:
1470:
1415:chordal resistance
1328:
1156:
1069:
1030:SI base units
982:
906:SI base units
403:Electrical network
240:Gauss magnetic law
205:Static electricity
165:Electric potential
4917:978-1-4200-0731-2
4892:978-0-471-52919-4
4806:978-0-8493-2087-3
4776:978-0-8493-9648-9
4739:thermal expansion
4638:mains electricity
4593:10 Ω⋅m
4408:Superconductivity
4402:Superconductivity
4381:photoconductivity
4370:Photoconductivity
4325:Strain dependence
3872:thermal radiation
3864:resistive heaters
3834:resistive heating
3763:(and the related
3691:
3671:
3593:
3548:
3522:
3502:
3475:
3471:
3469:
3443:
3438:
3414:
3410:
3408:
3382:
3356:
3352:
3350:
3324:
3319:
3295:
3291:
3289:
3263:
3186:
3105:
3104:
2986:angular frequency
2893:
2888:
2882:
2872:
2867:
2861:
2842:
2840:
2834:
2500:
2382:
2320:Static resistance
2212:static resistance
2182:
2181:
1854:
1824:
1757:fluorescent lamps
1515:hydraulic analogy
1498:hydraulic analogy
1468:
1419:static resistance
1323:
1310:
1290:
1169:
1168:
1067:
995:
994:
871:
870:
570:Reluctance (real)
540:Gyratorâcapacitor
485:Resonant cavities
375:Maxwell equations
16:(Redirected from
5146:
5115:
5103:
5102:on 11 July 2010.
5083:
5082:
5073:
5057:
5051:
5050:
5042:
5036:
5035:
5009:
4989:
4983:
4982:
4980:
4978:
4968:
4960:
4954:
4953:
4951:
4949:
4943:
4936:
4928:
4922:
4921:
4903:
4897:
4896:
4884:
4870:
4864:
4863:
4853:
4842:10.1038/111458a0
4817:
4811:
4810:
4790:
4781:
4780:
4760:
4742:
4731:
4725:
4719:
4715:
4711:
4707:
4701:
4699:
4695:
4691:
4687:
4683:
4681:
4680:
4679:
4675:
4672:
4671:
4663:
4659:
4657:
4656:
4655:
4651:
4648:
4647:
4636:
4632:
4627:
4621:
4619:
4615:
4611:
4607:
4602:
4596:
4594:
4592:
4585:
4550:Sheet resistance
4502:(its reciprocal)
4489:
4484:
4483:
4452:
4440:
4428:
4421:
4320:
4318:
4312:
4310:
4304:
4302:
4301:
4296:
4281:
4279:
4278:
4273:
4271:
4270:
4254:
4252:
4251:
4246:
4234:
4232:
4231:
4226:
4214:
4212:
4211:
4206:
4195:. The parameter
4194:
4192:
4191:
4186:
4184:
4183:
4167:
4165:
4164:
4159:
4157:
4156:
4140:
4138:
4137:
4132:
4130:
4129:
4109:
4107:
4106:
4101:
4089:
4087:
4086:
4081:
4073:
4072:
4042:
4041:
4006:
3932:
3928:
3920:
3916:
3914:
3913:
3908:
3903:
3902:
3860:electric heaters
3807:cartridge heater
3773:deep-level traps
3765:proximity effect
3746:
3739:
3735:
3733:
3732:
3727:
3722:
3701:
3699:
3698:
3693:
3689:
3685:
3669:
3661:
3657:
3647:
3643:
3639:
3635:
3631:
3627:
3623:
3619:
3607:
3603:
3601:
3600:
3595:
3591:
3546:
3532:
3530:
3529:
3524:
3520:
3516:
3500:
3492:
3490:
3489:
3484:
3482:
3473:
3472:
3470:
3467:
3466:
3465:
3453:
3452:
3441:
3439:
3436:
3428:
3412:
3411:
3409:
3406:
3405:
3404:
3392:
3391:
3380:
3375:
3354:
3353:
3351:
3348:
3347:
3346:
3334:
3333:
3322:
3320:
3317:
3309:
3293:
3292:
3290:
3287:
3286:
3285:
3273:
3272:
3261:
3256:
3225:
3217:
3214:is conductance,
3213:
3209:
3203:
3201:
3200:
3195:
3193:
3184:
3116:
3114:
3113:
3108:
3106:
3102:
3095:
3070:
3068:
3067:
3062:
3060:
3059:
3058:
3057:
3030:are the complex
3029:
3025:
3019:
3015:
3009:
3007:
3006:
3001:
2983:
2981:
2980:
2975:
2961:
2952:
2941:
2930:
2917:
2908:
2906:
2905:
2900:
2898:
2894:
2889:
2886:
2880:
2878:
2873:
2868:
2865:
2859:
2857:
2843:
2841:
2838:
2832:
2827:
2813:
2809:
2808:
2807:
2777:
2776:
2759:
2758:
2757:
2756:
2724:
2720:
2719:
2718:
2700:
2699:
2682:
2681:
2680:
2679:
2612:phase difference
2600:phase difference
2514:
2512:
2511:
2506:
2501:
2499:
2495:
2489:
2485:
2479:
2474:
2473:
2472:
2440:
2396:
2394:
2393:
2388:
2383:
2375:
2370:
2369:
2368:
2334:
2253:
2203:
2126:
2105:
2006:proximity effect
1977:
1975:
1974:
1969:
1964:
1927:
1911:
1903:
1895:
1893:
1892:
1887:
1873:
1871:
1870:
1865:
1863:
1855:
1847:
1825:
1817:
1789:
1786:and conductance
1785:
1718:
1716:
1715:
1710:
1692:
1688:
1507:electric current
1479:
1477:
1476:
1471:
1469:
1467:
1463:
1457:
1453:
1447:
1433:
1429:
1412:
1411:
1409:
1408:
1405:
1402:
1394:
1390:
1355:
1351:
1347:
1343:
1337:
1335:
1334:
1329:
1324:
1316:
1311:
1303:
1291:
1283:
1268:
1264:
1257:
1250:
1216:
1208:
1189:
1188:
1177:electric current
1165:
1163:
1162:
1157:
1155:
1154:
1149:
1148:
1141:
1140:
1135:
1134:
1127:
1126:
1118:
1117:
1110:
1109:
1101:
1100:
1078:
1076:
1075:
1070:
1068:
1060:
1043:other quantities
1041:Derivations from
1031:
1012:
997:
991:
989:
988:
983:
981:
980:
972:
971:
964:
963:
955:
954:
947:
946:
941:
940:
933:
932:
907:
888:
873:
863:
856:
849:
530:Electric machine
513:Magnetic circuit
475:Parallel circuit
465:Network analysis
430:Electric current
365:London equations
210:Triboelectricity
200:Potential energy
69:
59:Electromagnetism
50:
21:
5154:
5153:
5149:
5148:
5147:
5145:
5144:
5143:
5119:
5118:
5106:
5094:
5091:
5086:
5059:
5058:
5054:
5044:
5043:
5039:
4991:
4990:
4986:
4976:
4974:
4966:
4962:
4961:
4957:
4947:
4945:
4941:
4934:
4930:
4929:
4925:
4918:
4905:
4904:
4900:
4893:
4872:
4871:
4867:
4819:
4818:
4814:
4807:
4792:
4791:
4784:
4777:
4762:
4761:
4754:
4750:
4745:
4732:
4728:
4717:
4713:
4709:
4708:
4704:
4697:
4693:
4689:
4685:
4677:
4676:
4673:
4669:
4668:
4667:
4665:
4661:
4653:
4652:
4649:
4645:
4644:
4643:
4641:
4634:
4630:
4628:
4624:
4617:
4613:
4609:
4605:
4603:
4599:
4590:
4588:
4586:
4582:
4578:
4565:Voltage divider
4485:
4478:
4475:
4455:liquid nitrogen
4450:
4438:
4423:
4416:
4413:Superconductors
4410:
4404:
4372:
4364:Main articles:
4362:
4333:
4327:
4316:
4314:
4308:
4306:
4287:
4286:
4262:
4257:
4256:
4237:
4236:
4217:
4216:
4197:
4196:
4175:
4170:
4169:
4148:
4143:
4142:
4121:
4116:
4115:
4092:
4091:
4064:
4033:
4013:
4012:
4004:
3950:
3944:
3939:
3930:
3926:
3918:
3894:
3883:
3882:
3856:electric stoves
3828:), also called
3811:glowing red hot
3795:
3789:
3753:
3741:
3737:
3704:
3703:
3664:
3663:
3659:
3655:
3645:
3641:
3637:
3633:
3629:
3625:
3621:
3617:
3605:
3541:
3540:
3495:
3494:
3480:
3479:
3457:
3444:
3440:
3429:
3419:
3396:
3383:
3379:
3367:
3361:
3360:
3338:
3325:
3321:
3310:
3300:
3277:
3264:
3260:
3248:
3236:
3235:
3223:
3215:
3211:
3210:is resistance,
3207:
3191:
3190:
3165:
3159:
3158:
3139:
3127:
3126:
3083:
3082:
3049:
3042:
3041:
3038:, respectively;
3027:
3023:
3017:
3013:
2992:
2991:
2966:
2965:
2960:
2954:
2951:
2945:
2932:
2921:
2915:
2896:
2895:
2879:
2858:
2851:
2845:
2844:
2831:
2821:
2815:
2814:
2781:
2768:
2767:
2763:
2748:
2741:
2726:
2725:
2704:
2691:
2690:
2686:
2671:
2664:
2643:
2642:
2637:Complex numbers
2568:
2560:Main articles:
2558:
2553:
2454:
2449:
2448:
2423:
2344:
2339:
2338:
2321:
2313:operating point
2273:
2272:
2271:
2270:
2269:
2254:
2246:
2245:
2204:
2193:
2187:
2124:
2111:Resistance (Ω)
2100:
2090:
2063:
2057:
1983:current density
1946:
1945:
1925:
1909:
1901:
1878:
1877:
1861:
1860:
1836:
1830:
1829:
1806:
1794:
1793:
1787:
1783:
1771:
1765:
1695:
1694:
1690:
1686:
1647:
1641:
1600:
1490:
1458:
1448:
1441:
1440:
1431:
1427:
1406:
1403:
1400:
1399:
1397:
1396:
1392:
1388:
1353:
1349:
1345:
1341:
1271:
1270:
1266:
1262:
1255:
1248:
1247:The resistance
1242:superconductors
1214:
1204:
1186:
1185:
1142:
1128:
1111:
1094:
1089:
1088:
1048:
1047:
1044:
1042:
1029:
1010:
1007:
965:
948:
934:
922:
921:
905:
886:
883:
867:
838:
837:
653:
645:
644:
600:
590:
589:
545:Induction motor
515:
505:
504:
420:Current density
405:
395:
394:
385:Poynting vector
295:
293:Electrodynamics
285:
284:
280:Right-hand rule
245:Magnetic dipole
235:BiotâSavart law
225:
215:
214:
150:Electric dipole
145:Electric charge
120:
46:
39:
28:
23:
22:
15:
12:
11:
5:
5152:
5150:
5142:
5141:
5136:
5131:
5121:
5120:
5117:
5116:
5104:
5090:
5089:External links
5087:
5085:
5084:
5052:
5037:
4984:
4955:
4923:
4916:
4898:
4891:
4865:
4812:
4805:
4782:
4775:
4751:
4749:
4746:
4744:
4743:
4726:
4722:electric shock
4702:
4622:
4597:
4579:
4577:
4574:
4573:
4572:
4567:
4562:
4557:
4552:
4547:
4542:
4537:
4532:
4526:
4521:
4515:
4510:
4505:
4504:
4503:
4491:
4490:
4474:
4471:
4406:Main article:
4403:
4400:
4396:light detector
4387:photoresistors
4376:semiconductors
4361:
4358:
4329:Main article:
4326:
4323:
4294:
4269:
4265:
4244:
4224:
4204:
4182:
4178:
4155:
4151:
4128:
4124:
4110:is called the
4099:
4079:
4076:
4071:
4067:
4063:
4060:
4057:
4054:
4051:
4048:
4045:
4040:
4036:
4032:
4029:
4026:
4023:
4020:
3946:Main article:
3943:
3940:
3938:
3935:
3906:
3901:
3897:
3893:
3890:
3791:Main article:
3788:
3785:
3752:
3749:
3725:
3721:
3717:
3714:
3711:
3688:
3684:
3680:
3677:
3674:
3650:reactive power
3590:
3587:
3584:
3581:
3578:
3575:
3572:
3569:
3566:
3563:
3560:
3557:
3554:
3551:
3519:
3515:
3511:
3508:
3505:
3478:
3464:
3460:
3456:
3451:
3447:
3435:
3432:
3426:
3423:
3420:
3417:
3403:
3399:
3395:
3390:
3386:
3378:
3373:
3370:
3368:
3366:
3363:
3362:
3359:
3345:
3341:
3337:
3332:
3328:
3316:
3313:
3307:
3304:
3301:
3298:
3284:
3280:
3276:
3271:
3267:
3259:
3254:
3251:
3249:
3247:
3244:
3243:
3232:complex number
3189:
3183:
3180:
3177:
3174:
3171:
3168:
3166:
3164:
3161:
3160:
3157:
3154:
3151:
3148:
3145:
3142:
3140:
3138:
3135:
3134:
3123:
3122:
3119:imaginary unit
3101:
3098:
3093:
3090:
3080:
3077:complex number
3071:indicates the
3056:
3052:
3039:
3021:
3011:
2999:
2989:
2973:
2963:
2958:
2949:
2943:
2919:
2892:
2885:
2876:
2871:
2864:
2855:
2852:
2850:
2847:
2846:
2837:
2830:
2825:
2822:
2820:
2817:
2816:
2812:
2806:
2803:
2800:
2797:
2794:
2791:
2788:
2784:
2780:
2775:
2771:
2766:
2762:
2755:
2751:
2745:
2742:
2740:
2737:
2734:
2731:
2728:
2727:
2723:
2717:
2714:
2711:
2707:
2703:
2698:
2694:
2689:
2685:
2678:
2674:
2668:
2665:
2663:
2660:
2657:
2654:
2651:
2650:
2592:absolute value
2557:
2554:
2552:
2549:
2548:
2547:
2504:
2498:
2494:
2488:
2484:
2477:
2471:
2468:
2465:
2462:
2457:
2424:
2421:
2419:
2386:
2381:
2378:
2373:
2367:
2364:
2361:
2358:
2355:
2352:
2347:
2322:
2319:
2306:
2286:
2255:
2248:
2247:
2205:
2198:
2197:
2196:
2195:
2194:
2186:
2183:
2180:
2179:
2176:
2172:
2171:
2168:
2157:
2156:
2153:
2139:
2138:
2135:
2121:
2120:
2117:
2113:
2112:
2109:
2089:
2088:Typical values
2086:
2059:Main article:
2056:
2053:
2030:Semiconductors
1967:
1963:
1959:
1956:
1953:
1885:
1859:
1853:
1850:
1845:
1842:
1839:
1837:
1835:
1832:
1831:
1828:
1823:
1820:
1815:
1812:
1809:
1807:
1805:
1802:
1801:
1767:Main article:
1764:
1761:
1708:
1705:
1702:
1643:Main article:
1640:
1637:
1599:
1596:
1553:
1552:
1549:
1489:
1486:
1466:
1462:
1456:
1452:
1327:
1322:
1319:
1314:
1309:
1306:
1301:
1298:
1294:
1289:
1286:
1281:
1278:
1167:
1166:
1153:
1147:
1139:
1133:
1125:
1122:
1116:
1108:
1105:
1099:
1086:
1080:
1079:
1066:
1063:
1058:
1055:
1045:
1040:
1037:
1036:
1033:
1024:
1023:
1020:
1014:
1013:
1008:
1006:Common symbols
1005:
1002:
1001:
993:
992:
979:
976:
970:
962:
959:
953:
945:
939:
931:
919:
913:
912:
909:
900:
899:
896:
890:
889:
884:
882:Common symbols
881:
878:
877:
869:
868:
866:
865:
858:
851:
843:
840:
839:
836:
835:
830:
825:
820:
815:
810:
805:
800:
795:
790:
785:
780:
775:
770:
765:
760:
755:
750:
745:
740:
735:
730:
725:
720:
715:
710:
705:
700:
695:
690:
685:
680:
675:
670:
665:
660:
654:
651:
650:
647:
646:
643:
642:
637:
632:
627:
622:
620:Four-potential
617:
612:
607:
601:
596:
595:
592:
591:
588:
587:
582:
577:
572:
567:
562:
557:
552:
547:
542:
537:
535:Electric motor
532:
527:
522:
516:
511:
510:
507:
506:
503:
502:
497:
492:
490:Series circuit
487:
482:
477:
472:
467:
462:
460:Kirchhoff laws
457:
452:
447:
442:
437:
432:
427:
425:Direct current
422:
417:
412:
406:
401:
400:
397:
396:
393:
392:
387:
382:
380:Maxwell tensor
377:
372:
367:
362:
357:
352:
350:Larmor formula
347:
342:
337:
332:
327:
322:
317:
312:
307:
302:
300:Bremsstrahlung
296:
291:
290:
287:
286:
283:
282:
277:
272:
267:
262:
257:
252:
250:Magnetic field
247:
242:
237:
232:
226:
223:Magnetostatics
221:
220:
217:
216:
213:
212:
207:
202:
197:
192:
187:
182:
177:
172:
167:
162:
157:
155:Electric field
152:
147:
142:
137:
132:
127:
125:Charge density
121:
118:Electrostatics
116:
115:
112:
111:
110:
109:
104:
99:
94:
89:
84:
79:
71:
70:
62:
61:
55:
54:
53:Articles about
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5151:
5140:
5137:
5135:
5132:
5130:
5127:
5126:
5124:
5113:
5109:
5105:
5101:
5097:
5093:
5092:
5088:
5081:
5077:
5072:
5067:
5063:
5056:
5053:
5048:
5041:
5038:
5033:
5029:
5025:
5021:
5017:
5013:
5008:
5003:
4999:
4995:
4988:
4985:
4972:
4965:
4959:
4956:
4940:
4933:
4927:
4924:
4919:
4913:
4909:
4902:
4899:
4894:
4888:
4883:
4882:
4876:
4869:
4866:
4861:
4857:
4852:
4847:
4843:
4839:
4835:
4831:
4827:
4823:
4816:
4813:
4808:
4802:
4798:
4797:
4789:
4787:
4783:
4778:
4772:
4768:
4767:
4759:
4757:
4753:
4747:
4740:
4736:
4730:
4727:
4723:
4706:
4703:
4639:
4626:
4623:
4601:
4598:
4584:
4581:
4575:
4571:
4568:
4566:
4563:
4561:
4558:
4556:
4553:
4551:
4548:
4546:
4543:
4541:
4538:
4536:
4533:
4530:
4527:
4525:
4522:
4519:
4516:
4514:
4511:
4509:
4506:
4501:
4498:
4497:
4496:
4493:
4492:
4488:
4482:
4477:
4472:
4470:
4468:
4464:
4460:
4456:
4448:
4444:
4443:liquid helium
4436:
4432:
4431:joule heating
4426:
4419:
4414:
4409:
4401:
4399:
4397:
4393:
4389:
4388:
4383:
4382:
4377:
4371:
4367:
4366:Photoresistor
4359:
4357:
4355:
4354:strain gauges
4351:
4346:
4342:
4338:
4332:
4324:
4322:
4305:is typically
4292:
4283:
4267:
4263:
4242:
4222:
4202:
4180:
4176:
4153:
4149:
4126:
4122:
4113:
4097:
4069:
4065:
4061:
4058:
4052:
4049:
4046:
4038:
4034:
4030:
4024:
4018:
4010:
4001:
3999:
3995:
3991:
3987:
3983:
3979:
3978:Joule heating
3975:
3970:
3968:
3964:
3958:
3956:
3949:
3941:
3936:
3934:
3924:
3904:
3899:
3895:
3891:
3888:
3879:
3877:
3876:incandescence
3874:(also called
3873:
3869:
3865:
3862:(also called
3861:
3857:
3852:
3850:
3846:
3842:
3837:
3835:
3831:
3830:ohmic heating
3827:
3823:
3822:
3821:Joule heating
3812:
3808:
3804:
3803:Joule heating
3799:
3794:
3793:Joule heating
3786:
3784:
3782:
3778:
3774:
3770:
3766:
3762:
3758:
3750:
3748:
3744:
3723:
3719:
3715:
3712:
3709:
3686:
3682:
3678:
3675:
3672:
3653:
3651:
3615:
3611:
3585:
3579:
3576:
3573:
3570:
3564:
3558:
3555:
3552:
3549:
3539:
3538:complex angle
3534:
3517:
3513:
3509:
3506:
3503:
3476:
3462:
3458:
3454:
3449:
3445:
3433:
3430:
3424:
3421:
3415:
3401:
3397:
3393:
3388:
3384:
3376:
3371:
3369:
3364:
3357:
3343:
3339:
3335:
3330:
3326:
3314:
3311:
3305:
3302:
3296:
3282:
3278:
3274:
3269:
3265:
3257:
3252:
3250:
3245:
3233:
3229:
3221:
3204:
3187:
3181:
3178:
3175:
3172:
3169:
3167:
3162:
3155:
3152:
3149:
3146:
3143:
3141:
3136:
3120:
3099:
3096:
3091:
3088:
3081:
3078:
3074:
3040:
3037:
3033:
3022:
3012:
2997:
2990:
2987:
2971:
2964:
2957:
2948:
2944:
2939:
2935:
2928:
2924:
2920:
2914:
2913:
2912:
2909:
2890:
2883:
2874:
2869:
2862:
2853:
2848:
2835:
2828:
2823:
2818:
2810:
2801:
2798:
2795:
2792:
2786:
2782:
2778:
2773:
2769:
2764:
2760:
2743:
2735:
2729:
2721:
2715:
2712:
2709:
2705:
2701:
2696:
2692:
2687:
2683:
2666:
2658:
2652:
2640:
2638:
2634:
2630:
2626:
2622:
2613:
2609:
2605:
2604:complex phase
2601:
2597:
2593:
2589:
2585:
2581:
2577:
2572:
2567:
2563:
2555:
2550:
2545:
2541:
2537:
2536:IMPATT diodes
2533:
2529:
2528:tunnel diodes
2525:
2524:
2519:
2515:
2502:
2496:
2486:
2475:
2455:
2446:
2441:
2439:
2435:
2431:
2425:
2420:
2417:
2413:
2409:
2405:
2401:
2397:
2384:
2379:
2376:
2371:
2345:
2335:
2333:
2332:DC resistance
2329:
2323:
2318:
2316:
2314:
2308:
2304:
2302:
2298:
2294:
2290:
2284:
2282:
2278:
2267:
2263:
2259:
2252:
2243:
2240:
2236:
2232:
2228:
2224:
2221:
2217:
2213:
2209:
2202:
2192:
2184:
2178:1000â100,000
2177:
2174:
2173:
2169:
2166:
2162:
2159:
2158:
2154:
2151:
2150:
2144:
2141:
2140:
2136:
2133:
2129:
2123:
2122:
2118:
2115:
2114:
2106:
2099:
2095:
2087:
2085:
2083:
2079:
2072:
2067:
2062:
2054:
2052:
2050:
2045:
2043:
2039:
2035:
2031:
2026:
2021:
2019:
2015:
2011:
2007:
2003:
1999:
1995:
1991:
1986:
1984:
1979:
1965:
1961:
1957:
1954:
1951:
1943:
1939:
1936:(also called
1935:
1931:
1923:
1919:
1915:
1907:
1906:square metres
1899:
1883:
1874:
1857:
1851:
1848:
1843:
1840:
1838:
1833:
1826:
1821:
1818:
1813:
1810:
1808:
1803:
1791:
1775:
1770:
1762:
1760:
1758:
1754:
1750:
1746:
1740:
1738:
1734:
1730:
1726:
1722:
1706:
1703:
1700:
1680:
1676:
1672:
1668:
1664:
1660:
1656:
1651:
1646:
1636:
1633:
1629:
1625:
1617:
1613:
1609:
1604:
1597:
1595:
1593:
1588:
1586:
1582:
1578:
1574:
1570:
1566:
1562:
1557:
1550:
1547:
1546:
1545:
1542:
1539:
1535:
1530:
1528:
1527:pressure drop
1524:
1520:
1516:
1508:
1504:
1499:
1494:
1487:
1485:
1483:
1464:
1454:
1439:
1435:
1424:
1420:
1416:
1386:
1382:
1378:
1373:
1371:
1367:
1363:
1359:
1338:
1325:
1320:
1317:
1312:
1307:
1304:
1299:
1296:
1292:
1287:
1284:
1279:
1276:
1261:
1258:across it to
1254:
1245:
1243:
1239:
1235:
1231:
1227:
1223:
1218:
1212:
1207:
1202:
1198:
1194:
1190:
1182:
1178:
1174:
1151:
1137:
1123:
1120:
1106:
1103:
1087:
1085:
1081:
1064:
1061:
1056:
1053:
1046:
1038:
1034:
1032:
1025:
1021:
1019:
1015:
1009:
1003:
998:
977:
974:
960:
957:
943:
920:
918:
914:
910:
908:
901:
897:
895:
891:
885:
879:
874:
864:
859:
857:
852:
850:
845:
844:
842:
841:
834:
831:
829:
826:
824:
821:
819:
816:
814:
811:
809:
806:
804:
801:
799:
796:
794:
791:
789:
786:
784:
781:
779:
776:
774:
771:
769:
766:
764:
761:
759:
756:
754:
751:
749:
746:
744:
741:
739:
736:
734:
731:
729:
726:
724:
721:
719:
716:
714:
711:
709:
706:
704:
701:
699:
696:
694:
691:
689:
686:
684:
681:
679:
676:
674:
671:
669:
666:
664:
661:
659:
656:
655:
649:
648:
641:
638:
636:
633:
631:
628:
626:
623:
621:
618:
616:
613:
611:
608:
606:
603:
602:
599:
594:
593:
586:
583:
581:
578:
576:
573:
571:
568:
566:
563:
561:
558:
556:
553:
551:
548:
546:
543:
541:
538:
536:
533:
531:
528:
526:
523:
521:
518:
517:
514:
509:
508:
501:
498:
496:
493:
491:
488:
486:
483:
481:
478:
476:
473:
471:
468:
466:
463:
461:
458:
456:
455:Joule heating
453:
451:
448:
446:
443:
441:
438:
436:
433:
431:
428:
426:
423:
421:
418:
416:
413:
411:
408:
407:
404:
399:
398:
391:
388:
386:
383:
381:
378:
376:
373:
371:
370:Lorentz force
368:
366:
363:
361:
358:
356:
353:
351:
348:
346:
343:
341:
338:
336:
333:
331:
328:
326:
323:
321:
318:
316:
313:
311:
308:
306:
303:
301:
298:
297:
294:
289:
288:
281:
278:
276:
273:
271:
270:Magnetization
268:
266:
263:
261:
258:
256:
255:Magnetic flux
253:
251:
248:
246:
243:
241:
238:
236:
233:
231:
228:
227:
224:
219:
218:
211:
208:
206:
203:
201:
198:
196:
193:
191:
188:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
161:
160:Electric flux
158:
156:
153:
151:
148:
146:
143:
141:
138:
136:
133:
131:
128:
126:
123:
122:
119:
114:
113:
108:
105:
103:
100:
98:
97:Computational
95:
93:
90:
88:
85:
83:
80:
78:
75:
74:
73:
72:
68:
64:
63:
60:
56:
52:
51:
48:
44:
37:
33:
19:
5111:
5100:the original
5061:
5055:
5046:
5040:
4997:
4993:
4987:
4975:. Retrieved
4958:
4946:. Retrieved
4939:the original
4926:
4907:
4901:
4880:
4868:
4825:
4821:
4815:
4795:
4765:
4729:
4705:
4625:
4600:
4583:
4570:Voltage drop
4465:, including
4424:
4417:
4411:
4391:
4385:
4379:
4373:
4334:
4331:Strain gauge
4284:
4111:
4002:
3974:thermometers
3971:
3959:
3951:
3880:
3863:
3853:
3838:
3833:
3829:
3819:
3816:
3754:
3742:
3654:
3535:
3205:
3124:
2955:
2946:
2937:
2933:
2926:
2922:
2910:
2641:
2617:
2521:
2442:
2437:
2433:
2429:
2428:Also called
2426:
2403:
2336:
2331:
2327:
2326:Also called
2324:
2309:
2299:, and their
2296:
2292:
2274:
2241:
2239:tangent line
2234:
2230:
2226:
2215:
2211:
2164:
2146:
2131:
2075:
2046:
2022:
2001:
1997:
1987:
1980:
1937:
1920:measured in
1875:
1792:
1780:
1748:
1744:
1741:
1724:
1684:
1678:
1671:voltage drop
1632:conductivity
1621:
1589:
1558:
1554:
1543:
1534:voltage drop
1531:
1523:voltage drop
1512:
1488:Introduction
1481:
1418:
1414:
1374:
1369:
1339:
1246:
1219:
1184:
1183:quantity is
1172:
1170:
1018:SI unit
894:SI unit
615:Four-current
550:Linear motor
479:
435:Electrolysis
315:Eddy current
275:Permeability
195:Polarization
190:Permittivity
47:
32:Conductivity
5134:Electricity
5112:wolfram.com
4948:13 December
4710:100 kΩ
4678:500 mA
4662:500 mA
4618:+40 °C
4610:â40 °C
4447:niobiumâtin
4435:dissipation
4350:compression
4343:(a form of
4319:10 Kâ1
4311:10 Kâ1
3845:power lines
3769:Drude model
3761:skin effect
3632:also), and
3234:identities
3228:susceptance
2551:AC circuits
2542:tubes, and
2532:Gunn diodes
2434:incremental
2175:Human body
2055:Measurement
2038:electrolyte
1998:geometrical
1994:skin effect
1942:reciprocals
1585:resistivity
1377:transformer
1372:materials.
1022:siemens (S)
585:Transformer
415:Capacitance
340:Faraday law
135:Coulomb law
77:Electricity
5123:Categories
5062:Volume 215
5007:1712.05938
4977:2 November
4748:References
4718:500 Ω
4698:900 Ω
4696:mains) is
4694:230 V
4686:240 Ω
4670:120 V
4654:120 V
4635:120 V
4614:0.1 Ω
4606:0.9 Ω
4378:, exhibit
3994:hysteretic
3967:thermistor
3858:and other
3640:reduce to
3610:capacitors
3036:admittance
2578:(top) and
2566:Admittance
2297:non-linear
2189:See also:
2163:filament (
2143:AA battery
2108:Component
2092:See also:
1624:conductors
1438:derivative
1181:reciprocal
652:Scientists
500:Waveguides
480:Resistance
450:Inductance
230:AmpĂšre law
5080:247959452
5000:: 83â88.
4714:1 kΩ
4690:60 W
4646:60 W
4631:60 W
4576:Footnotes
4451:77 K
4293:α
4264:α
4243:α
4223:α
4203:α
4098:α
4062:−
4053:α
3990:nonlinear
3984:, or for
3614:inductors
3580:
3574:−
3559:
3550:θ
3431:−
3312:−
3220:reactance
3097:−
3092:≡
3073:real part
3032:impedance
2998:φ
2972:ω
2802:φ
2793:ω
2779:⋅
2761:
2713:ω
2702:⋅
2684:
2629:capacitor
2608:impedance
2596:impedance
2588:sinusoids
2584:amplitude
2576:capacitor
2540:magnetron
2518:monotonic
2293:non-ohmic
2289:Ohm's law
2281:batteries
2266:monotonic
2214:at point
2170:200â1000
2125:1 km
2002:effective
1966:σ
1952:ρ
1932:) is the
1916:) is the
1884:ℓ
1852:ℓ
1844:σ
1819:ℓ
1814:ρ
1749:non-ohmic
1745:nonlinear
1729:resistors
1721:Ohm's law
1704:∝
1659:resistors
1645:Ohm's law
1639:Ohm's law
1573:insulator
1561:electrons
1366:Ohm's law
1358:constants
1121:−
1104:−
1084:Dimension
975:−
958:−
917:Dimension
808:Steinmetz
738:Kirchhoff
723:Jefimenko
718:Hopkinson
703:Helmholtz
698:Heaviside
560:Permeance
445:Impedance
185:Insulator
180:Gauss law
130:Conductor
107:Phenomena
102:Textbooks
82:Magnetism
5032:51912472
4877:(1992).
4860:26358546
4540:RKM code
4535:Resistor
4473:See also
4439:4 K
3986:feedback
3783:, etc.)
2918:is time;
2633:inductor
2625:resistor
2580:inductor
2416:gyrators
2287:satisfy
2225:of line
2147:typical
2078:ohmmeter
2071:ohmmeter
2061:Ohmmeter
1665:, and a
1628:resistor
1616:ohmmeter
1608:resistor
1551:material
1519:resistor
1193:friction
1035:kgâ
mâ
sâ
A
911:kgâ
mâ
sâ
A
833:Wiechert
788:Poynting
678:Einstein
525:DC motor
520:AC motor
355:Lenz law
140:Electret
5012:Bibcode
4881:Physics
4830:Bibcode
4682:
4666:
4658:
4642:
4341:tension
3921:is the
3824:(after
3117:is the
2984:is the
2911:where:
2606:of the
2430:dynamic
2412:op-amps
2408:Passive
2328:chordal
2220:inverse
2218:is the
2165:typical
2132:typical
2014:busbars
1922:siemens
1675:current
1667:battery
1606:A 75 Ω
1538:voltage
1513:In the
1410:
1398:
1385:battery
1260:current
1253:voltage
1211:siemens
898:ohm (Ω)
818:Thomson
793:Ritchie
783:Poisson
768:Neumann
763:Maxwell
758:Lorentz
753:Liénard
683:Faraday
668:Coulomb
495:Voltage
470:Ohm law
92:History
5078:
5030:
4914:
4889:
4858:
4822:Nature
4803:
4773:
4345:stress
4337:strain
4090:where
3917:where
3690:
3670:
3608:. For
3592:
3547:
3521:
3501:
3474:
3468:
3442:
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3413:
3407:
3381:
3355:
3349:
3323:
3318:
3294:
3288:
3262:
3222:, and
3206:where
3185:
3103:
2887:
2881:
2866:
2860:
2839:
2833:
2621:phases
2277:diodes
2025:teflon
2016:in an
1898:metres
1876:where
1753:diodes
1731:. The
1577:rubber
1565:copper
1362:strain
1226:rubber
1195:. The
1179:. Its
803:Singer
798:Savart
778:Ărsted
743:Larmor
733:Kelvin
688:Fizeau
658:AmpĂšre
580:Stator
87:Optics
5076:S2CID
5028:S2CID
5002:arXiv
4967:(PDF)
4942:(PDF)
4935:(PDF)
4856:S2CID
4612:, to
4453:with
4441:with
3982:fuses
3923:power
3079:; and
3075:of a
2445:slope
2436:, or
2400:chord
2223:slope
2137:0.03
2119:0.02
2049:below
2008:. At
1914:sigma
1908:(m),
1900:(m),
1737:slope
1725:ohmic
1679:ohmic
1663:diode
1592:below
1575:like
1569:steel
1434:curve
1423:chord
1381:diode
1370:ohmic
1224:like
828:Weber
823:Volta
813:Tesla
728:Joule
713:Hertz
708:Henry
693:Gauss
575:Rotor
4979:2014
4950:2011
4912:ISBN
4887:ISBN
4801:ISBN
4771:ISBN
4733:See
4422:and
4390:(or
4368:and
3992:and
3644:and
3636:and
3620:and
3612:and
3536:The
3034:and
3026:and
3016:and
2953:and
2931:and
2564:and
2303:are
2279:and
2256:The
2206:The
2155:0.1
2096:and
1755:and
1661:, a
1653:The
1532:The
1496:The
1391:and
1356:are
1352:and
1344:and
1171:The
748:Lenz
673:Davy
663:Biot
5066:doi
5020:doi
4846:hdl
4838:doi
4826:111
4616:at
4608:at
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4427:â 0
4420:= 0
4313:to
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3878:).
3843:in
3832:or
3745:= 0
3740:or
3577:arg
3556:arg
3226:is
3218:is
2631:or
2594:of
2330:or
2305:not
2295:or
2285:not
2283:do
2233:at
2069:An
1930:rho
1747:or
1417:or
1383:or
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1201:ohm
1027:In
903:In
773:Ohm
5125::
5110:.
5074:,
5026:.
5018:.
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4969:.
4854:.
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4755:^
4684:=
4660:=
4629:A
4469:.
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4315:+6
4307:+3
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4000:.
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3182:B
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2366:c
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2242:C
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1958:1
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1691:V
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1465:I
1461:d
1455:V
1451:d
1432:V
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1401:V
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1321:R
1318:1
1313:=
1308:V
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1300:=
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1280:=
1277:R
1267:G
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1249:R
1215:â§
1206:Ω
1203:(
1152:2
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