Ohm's law applies to electrical circuits; it states that the current passing through a conductor between two points is directly proportional to the potential difference (i. An electrical network is an interconnection of Electrical elements such as Resistors Inductors Capacitors Transmission lines Voltage Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. This article is about proportionality the mathematical relation In Physics, the potential difference or pd between two points is the difference of the points' Scalar potential, equivalent to the line integral e. voltage drop or voltage) across the two points, and inversely proportional to the resistance between them. Voltage drop is the reduction in Voltage in an Electrical circuit between the source and load Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is

The mathematical equation that describes this relationship is:

V = IR

where V is the potential difference between two points of interest in volts, I is the current in amperes, and R is a circuit parameter, measured in ohms (which is equivalent to volts per ampere), and is called the resistance. The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second The ohm (symbol Ω) is the SI unit of Electrical impedance or in the Direct current case Electrical resistance, Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is The potential difference is also known as the voltage drop, and is sometimes denoted by U, E or emf (electromotive force) instead of V. Voltage drop is the reduction in Voltage in an Electrical circuit between the source and load Electromotive force ( emf, \mathcal{E} is a term used to characterize electrical devices such as Voltaic cells thermoelectric devices electrical ^[1]

The law was named after the physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current passing through simple electrical circuits containing various lengths of wire. Georg Simon Ohm' was a German physicist As a high school teacher Ohm began his research with the recently invented Electrochemical cell, invented by Italian Count Year 1827 ( MDCCCXXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Common He presented a slightly more complex equation than the one above to explain his experimental results. The above equation is the modern form of Ohm's law.

The resistance of most resistive devices (resistors) is constant over a large range of values of current and voltage. |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| | When a resistor is used under these conditions, the resistor is referred to as an ohmic device (or an ohmic resistor) because a single value for the resistance suffices to describe the resistive behavior of the device over the range. When sufficiently high voltages are applied to a resistor, forcing a high current to flow through it, the device is no longer ohmic because its resistance, when measured under such electrically stressed conditions, is different (typically greater) from the value measured under standard conditions (see temperature effects, below).

Ohm's law, in the form above, is an extremely useful equation in the field of electrical/electronic engineering because it describes how voltage, current and resisitance are interrelated on a macroscopic level, that is, commonly, as circuit elements in an electrical circuit. An electrical network is an interconnection of Electrical elements such as Resistors Inductors Capacitors Transmission lines Voltage Physicists who study the electrical properties of matter at the microsopic level use a closely related and more general vector equation, sometimes also referred to as Ohm's law, having variables that are closely related to the I, V and R scalar variables of Ohm's law, but are each functions of position within the conductor. See the Physics and Relation to heat conduction sections below. Ohm's law applies to Electrical circuits it states that the current through a conductor between two points is directly proportional to the Ohm's law applies to Electrical circuits it states that the current through a conductor between two points is directly proportional to the

Contents 1 Elementary description and use 2 Physics 3 How electrical and electronic engineers use Ohm's law 3.1 Hydraulic analogies 3.2 Sheet resistance 4 Temperature effects 5 Strain (mechanical) effects 6 Transients and ac circuits 7 Relation to heat conduction 8 History 9 See also 10 References 11 External links

Elementary description and use

Electrical circuits consist of electrical devices connected by wires (or other suitable conductors). (See the article electrical circuits for some basic combinations. An electrical network is an interconnection of Electrical elements such as Resistors Inductors Capacitors Transmission lines Voltage ) The above diagram shows one of the simplest electrical circuits that can be constructed. One electrical device is shown as a circle with + and - terminals, which represents a voltage source such as a battery. The other device is illustrated by a zig-zag symbol and has an R beside it. This symbol represents a resistor, and the R designates its resistance. The + or positive terminal of the voltage source is connected to one of the terminals of the resistor using a wire of negligible resistance, and through this wire a current I is shown to be passing, in a specified direction illustrated by the arrow. The other terminal of the resistor is connected to the - or negative terminal of the voltage source by a second wire. This configuration forms a complete circuit because all the current that leaves one terminal of the voltage source must return to the other terminal of the voltage source. (While not shown, because electrical engineers assume that it exists, there is an implied current I, and an arrow pointing to the left, associated with the second wire. )

Voltage is the electrical force that moves (negatively charged) electrons through wires and electrical devices, current is the rate of electron flow, and resistance is the property of a resistor (or other device that obeys Ohm's law) that limits current to an amount proportional to the applied voltage. So, for a given resistance R (ohms), and a given voltage V (volts) established across the resistance, Ohm's law provides the equation (I=V/R) for calculating the current through the resistor (or device).

The 'conductor' mentioned by Ohm's law is a circuit element across which the voltage is measured. Resistors are conductors that slow down the passage of electric charge. A resistor with a high value of resistance, say greater than 10 megohms, is a poor conductor, while a resistor with a low value, say less than 0. 1 ohm, is a good conductor. (Insulators are materials that, for most practical purposes, do not allow a current when a voltage is applied. )

In a circuit diagram like the one above, the various components may be joined by connectors, contacts, welds or solder joints of various kinds, but for simplicity these connections are usually not shown.

Physics

Physicists often use the continuum form of Ohm's Law:^[2]

where J is the current density (current per unit area, unlike the simpler I, units of amperes, of Ohm's law), σ is the conductivity (which can be a tensor in anisotropic materials) and E is the electric field (units of volts per meter, unlike the simpler V, units of volts, of Ohms's law). Current density is a measure of the Density of flow of a conserved charge. Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an Electric current. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can While the notation above does not explicitly depict the variables, each are vectors and each are functions of three position variables. That is, in the case of J, using cartesian coordinates, there are actually three separate equations, one for each component of the vector, each equation having three independent position variables. For example, the components of J in the x, y and z directions would be J_x(x,y,z), J_y(x,y,z) and J_z(x,y,z).

The potential difference between two points is defined as

with the differential in the displacement vector . In the case where the electric field is independent of the choice of path (as it is in a circuit),

where is the distance between points of interest. Since the current per unit area, J, is equal to I / A, Ohm's Law becomes:

The electrical resistance of a conductor is defined in terms of conductivity, length, and cross sectional area:

From this, it can be seen that Ohm's law takes on the more familiar, yet macroscopic and averaged version:

The continuum form of the equation is only valid in the reference frame of the conducting material. Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is See also Inertial frame A frame of reference in Physics, may refer to a Coordinate system or set of axes within which to If the material is moving at velocity v relative to a magnetic field B, a term must be added as follows:

See Lorentz force for more on this and Hall effect for some other implications of a magnetic field. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation The Hall effect refers to the Potential difference ( Hall voltage) on the opposite sides of an Electrical conductor through which there is an Electric This equation is not a modification to Ohm's law. Rather, it is analogous in circuit analysis terms to taking into account inductance as well as resistance.

A perfect crystal lattice, with no thermal motions or other deviations from periodic structure, would have no resistivity,^[3] but a real metal has crystallographic defects, impurities, multiple isotopes, and thermal motion of the atoms. Electrical resistivity (also known as specific electrical resistance) is a measure of how strongly a material opposes the flow of Electric current. Crystalline solids have a very regular atomic structure that is the local positions of atoms with respect to each other are repeated at the atomic scale Isotopes (Greek isos = "equal" tópos = "site place" are any of the different types of atoms ( Nuclides Electrons scatter from all of these, resulting in resistance to their flow.

How electrical and electronic engineers use Ohm's law

Ohm's law is one of the equations used in the analysis of electrical circuits, whether the analysis is done by engineers or by computers. Though computers running electronic computer-aided design and analysis programs do the bulk of the work predicting and optimizing the performance of electrical circuits, most electrical engineers still use Ohm's law every working day. Whether designing or debugging an electrical circuit, electrical engineers must have a working knowledge of the practical aspects of Ohm's law.

Virtually all electronic circuits have resistive elements, which are usually treated as ideal ohmic devices, that is, they obey Ohm's law. From the engineer's point of view, resistors (devices that "resist" the electric current) develop a voltage across their terminals (the two wires emerging from the device) proportional to the amount of current through the device.

More specifically, the voltage measured across a resistor at a given instant is strictly proportional to the current through the resistor at that instant. When a functioning electrical circuit drives a current I, measured in amperes, through a resistor of resistance R, the voltage that develops across the resistor is I R, the value of R serving as the proportionality factor.

The DC resistance of a resistor is always a positive quantity, and the current through a resistor generates heat in it. Voltages can be either positive or negative, depending on the ordering of the terminals and the direction of current flow. Currents can be either positive or negative, the sign of the current indicating the direction of current.

Ohm's law applies to conductors whose resistance is (substantially) independent of the applied voltage (or equivalently the injected current). That is, Ohm's law only applies to the linear portion of the I vs. V curve centered around the origin. The equation is too simple to encompass devices described by a more complicated I vs. V relationship.

Hydraulic analogies

A Hydraulic analogy is sometimes used to describe Ohm's Law. The electronic&ndash hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Heaviside) is the most widely used analogy for "electron fluid" Water pressure, measured by pascals (or PSI), is the analog of voltage because establishing a water pressure difference between two points along a (horizontal) pipe causes water to flow. The pound per square inch or more accurately pound-force per square inch (symbol psi or lbf/in² or lbf/in²) is a unit of Water flow rate, as in liters per second, is the analog of current, as in coulombs per second. The litre or liter (see spelling differences) is a unit of Volume. The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. Finally, flow restrictors — such as apertures placed in pipes between points where the water pressure is measured — are the analog of resistors. We say that the rate of water flow through an aperture restrictor is proportional to the difference in water pressure across the restrictor. Similarly, the rate of flow of electrical charge, that is, the electrical current, passing through an electrical resistor is proportional to the difference in voltage measured across the resistor.

Sheet resistance

Thin metal films, usually deposited on insulating substrates, are used for various purposes, the electrical current traveling parallel to the plane of the film. When describing the electrical resistivity of such devices, the term ohms-per-square is used. See sheet resistance. The sheet resistance is a measure of resistance of thin films that have a uniform thickness

Temperature effects

When the temperature of the conductor increases, the collisions between electrons and ions increase. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Thus as a substance heats up because of electricity flowing through it (or by any heating process), the resistance will usually increase. The exception is semiconductors. The resistance of an Ohmic substance depends on temperature in the following way:

where ρ is the resistivity :, L is the length of the conductor, A is its cross-sectional area, T is its temperature, T₀ is a reference temperature (usually room temperature), and ρ₀ and α are constants specific to the material of interest. Electrical resistivity (also known as specific electrical resistance) is a measure of how strongly a material opposes the flow of Electric current. In the above expression, we have assumed that L and A remain unchanged within the temperature range.

It is worth mentioning that temperature dependence does not make a substance non-ohmic, because at a given temperature, R does not vary with voltage or current (V / I = constant).

Intrinsic semiconductors exhibit the opposite temperature behavior, becoming better conductors as the temperature increases. An intrinsic semiconductor, also called an undoped semiconductor or i-type semiconductor, is a pure Semiconductor without any significant Dopant This occurs because the electrons are bumped to the conduction energy band by the thermal energy, where they can flow freely and in doing so they leave behind holes in the valence band which can also flow freely. In the Physics field of Semiconductors and insulators the conduction band is the range of Electron Energy, higher than that of the An electron hole is the conceptual and mathematical Opposite of an Electron, useful in the study of Physics and Chemistry. In Solids the valence band is the highest range of Electron energies where electrons are normally present at Absolute zero.

Extrinsic semiconductors have much more complex temperature behaviour. An extrinsic semiconductor is a Semiconductor that has been doped, that is into which a doping agent has been introduced giving it different electrical First the electrons (or holes) leave the donors (or acceptors) giving a decreasing resistance. Then there is a fairly flat phase in which the semiconductor is normally operated where almost all of the donors (or acceptors) have lost their electrons (or holes) but the number of electrons that have jumped right over the energy gap is negligible compared to the number of electrons (or holes) from the donors (or acceptors). Finally as the temperature increases further the carriers that jump the energy gap becomes the dominant figure and the material starts behaving like an intrinsic semiconductor.

Strain (mechanical) effects

Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon strain. By placing a conductor under tension (a form of 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. In Physics String Tension is the magnitude of the pulling force exerted by a string cable chain or similar object on another object Stress is a measure of the average amount of Force exerted per unit Area. 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 gauges for details about devices constructed to take advantage of this effect. A strain gauge (alternatively strain gage) is a device used to measure the strain of an object

Transients and ac circuits

Ohm's law holds for linear circuits where the current and voltage are steady (DC), and for instantaneous voltage and current in linear circuits with no reactive elements. Direct current ( DC) is the unidirectional flow of Electric charge. When the current and voltage are varying, effects other than resistance may be at work; these effects are principally those of inductance and capacitance. In Electrical circuits, any Electric current i produces a Magnetic field and hence generates a total Magnetic flux \Phi acting Capacitance is a measure of the amount of Electric charge stored (or separated for a given Electric potential. When such reactive elements, or transmission lines, are involved in a circuit, the relationship between voltage and current becomes the solution to a differential equation.

Equations for time-invariant AC circuits take the same form as Ohm's law, however, if the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials. A time-invariant system is one whose output does not depend explicitly on time An alternating current ( AC) is an Electric current whose direction reverses cyclically as opposed to Direct current, whose direction remains constant Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted This article is about Euler's formula in Complex analysis. For Euler's formula in algebraic topology and polyhedral combinatorics see Euler characteristic ^[4]

In this approach, a voltage or current waveform takes the form Ae^st, where t is time, s is a complex parameter, and A is a complex scalar. In any linear time-invariant system, all of the currents and voltages can be expressed with the same s parameter as the input to the system, allowing the time-varying complex exponential term to be canceled out and the system described algebraically in terms of the complex scalars in the current and voltage waveforms. LTI system theory or linear time-invariant system theory is a theory in the field of Electrical engineering, specifically in circuits Signal processing

The complex generalization of resistance is impedance, usually denoted Z; it can be shown that for an inductor,

and for a capacitor,

We can now write,

where V and I are the complex scalars in the voltage and current respectively and Z is the complex impedance.

While this has the form of Ohm's law, with Z taking the place of R, it is not the same as Ohm's law. When Z is complex, only the real part is responsible for dissipating heat.

In the general AC circuit, Z will vary strongly with the frequency parameter s, and so also will the relationship between voltage and current.

For the common sinusoidal case, the s parameter is taken to be jω, corresponding to a complex sinusoid Ae^jωt. The real parts of such complex current and voltage waveforms describe the actual sinusoidal currents and voltages in a circuit, which can be in different phases due to the different complex scalars.

Relation to heat conduction

Ohm's principle predicts the flow of electrical charge (i. e. current) in electrical conductors when subjected to the influence of voltage differences; Jean-Baptiste-Joseph Fourier's principle predicts the flow of heat in heat conductors when subjected to the influence of temperature differences. Jean Baptiste Joseph Fourier ( March 21, 1768 &ndash May 16, 1830) was a French Mathematician and Physicist In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature The same equation describes both phenomena, the equation's variables taking on different meanings in the two cases. Specifically, solving a heat conduction (Fourier) problem with temperature (the driving "force") and flux of heat (the rate of flow of the driven "quantity", i. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature In the various subfields of Physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks e. heat energy) variables also solves an analogous electrical conduction (Ohm) problem having electric potential (the driving "force") and electric current (the rate of flow of the driven "quantity", i. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. e. charge) variables. The basis of Fourier's work was his clear conception and definition of thermal conductivity. In Physics, thermal conductivity, k is the property of a material that indicates its ability to conduct Heat. He assumed that, all else being the same, the flux of heat is strictly proportional to the gradient of temperature. Although undoubtedly true for small temperature gradients, strictly proportional behavior will be lost when real materials (e. g. ones having a thermal conductivity that is a function of temperature) are subjected to large temperature gradients. A similar assumption is made in the statement of Ohm's law: other things being alike, the strength of the current at each point is proportional to the gradient of electric potential. The accuracy of the assumption that flow is proportional to the gradient is more readily tested, using modern measurement methods, for the electrical case than for the heat case.

History

In January 1781, before Georg Ohm's work, Henry Cavendish experimented with Leyden jars and glass tubes of varying diameter and length filled with salt solution. Henry Cavendish, FRS (10 October 1731 - 24 February 1810 was a British Scientist noted for his discovery of Hydrogen or what he called "inflammable The Leyden jar is a simple device that "stores" static electricity in large amounts He measured the current by noting how strong a shock he felt as he completed the circuit with his body. Cavendish wrote that the "velocity" (current) varied directly as the "degree of electrification" (voltage). He did not communicate his results to other scientists at the time,^[5] and his results were unknown until Maxwell published them in 1879. James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. ^[6]

Ohm did his work on resistance in the years 1825 and 1826, and published his results in 1827. Year 1827 ( MDCCCXXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Common ^[7] He drew considerable inspiration from Fourier's work on heat conduction in the theoretical explanation of his work. For experiments, he initially used voltaic piles, but later used a thermocouple as this provided a more stable voltage source in terms of internal resistance and constant potential difference. A voltaic pile is a set of individual Voltaic cells placed in series In Electrical engineering and industry thermocouples are a widely used type of temperature sensor and can also be used as a means to convert thermal Potential He used a galvanometer to measure current, and knew that the voltage between the thermocouple terminals was proportional to the junction temperature. He then added test wires of varying length, diameter, and material to complete the circuit. He found that his data could be modeled through the equation

,

where X was the reading from the galvanometer, l was the length of the test conductor, a depended only on the thermocouple junction temperature, and b was a constant of the entire setup. From this, Ohm determined his law of proportionality and published his results.

Ohm's law was probably the most important of the early quantitative descriptions of the physics of electricity. We consider it almost obvious today. When Ohm first published his work, this was not the case; critics reacted to his treatment of the subject with hostility. They called his work a "web of naked fancies"^[8] and the German Minister of Education proclaimed that Ohm was "a professor who preached such heresies was unworthy to teach science. " ^[9] The prevailing scientific philosophy in Germany at the time, led by Hegel, asserted that experiments need not be performed to develop an understanding of nature because nature is so well ordered, and that scientific truths may be deduced through reasoning alone. Also, Ohm's brother Martin, a mathematician, was battling the German educational system. These factors hindered the acceptance of Ohm's work, and his work did not become widely accepted until the 1840s. Fortunately, Ohm received recognition for his contributions to science well before he died.

In the 1850s, Ohm's law was known as such, and was widely considered proved, and alternatives such as "Barlow's law" discredited, in terms of real applications to telegraph system design, as discussed by Samuel F. B. Morse in 1855. Samuel Finley Breese Morse ( April 27, 1791 &ndash April 2, 1872) was an American painter of portraits and historic ^[10]

While the old term for electrical conductance, the mho, is still used, a new name, the siemens, was adopted in 1971, honoring Ernst Werner von Siemens. The siemens (symbol S is the SI derived unit of Electric conductance. The siemens (symbol S is the SI derived unit of Electric conductance. The siemens is preferred in formal papers.

In the 1920s, it was discovered that the current through an ideal resistor actually has statistical fluctuations, which depend on temperature, even when voltage and resistance are exactly constant; this fluctuation, now known as Johnson–Nyquist noise, is due to the discrete nature of charge. Johnson–Nyquist noise ( thermal noise, Johnson noise, or Nyquist noise) is the electronic noise generated by the thermal agitation This thermal effect implies that measurements of current and voltage that are taken over sufficiently short periods of time will yield ratios of V/I that fluctuate from the value of R implied by the time average or ensemble average of the measured current; Ohm's law remains correct for the average current, in the case of ordinary resistive materials. In Statistical mechanics, the ensemble average is defined as the Mean of a quantity that is a function of the micro-state of a system (the ensemble of possible

Ohm's work long preceded Maxwell's equations and any understanding of frequency-dependent effects in AC circuits. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric Modern developments in electromagnetic theory and circuit theory do not contradict Ohm's law when they are evaluated within the appropriate limits.

See also

• Poiseuille's law
• Scientific laws named after people
• Ohm's acoustic law
• Hydraulic analogy
• Hopkinson's Law ("Ohm's Law for magnetics")
• Mesh analysis
• Walking along the resistive film - building various resistive circuits by reproducing Ohm's experiment nowadays

References

External links

• Calculation of Ohm's law · The Magic Triangle
• Calculation of electric power, voltage, current and resistance
• Interactive calculator for Ohm's Law and other circuit parameters
• An interactive simulation of simple electric circuit.

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