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A voltage source, V, drives an electric current, I , through resistor, R, the three quantities obeying Ohm's law: V = IR.

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.e. voltage drop or voltage) across the two points, and inversely proportional to the resistance between them, at a constant temperature. Image File history File links Question_book-3. ... Ohms acoustic law or simply Ohms law states that a musical sound is perceived by the ear as the sum of a number of pure harmonic tones. ... Image File history File links Ohms_law_voltage_source. ... Image File history File links Ohms_law_voltage_source. ... It has been suggested that this article or section be merged with Current source. ... This box:      Electric current is the flow (movement) of electric charge. ... Resistor symbols (American) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ... An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... This box:      Electric current is the flow (movement) of electric charge. ... This article is about proportionality, the mathematical relation. ... Potential difference is a quantity in physics related to the amount of energy that would be required to move an object from one place to another against various types of force. ... This article or section does not cite its references or sources. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ...

The mathematical equation that describes this relationship is:

where I is the current in amperes, V is the potential difference between two points of interest in volts, and R is a circuit parameter, measured in ohms (which is equivalent to volts per ampere), and is called the resistance. The potential difference is also known as the voltage drop, and is sometimes denoted by U, E or emf (electromotive force) instead of V.^[1] For other uses, see Ampere (disambiguation). ... Josephson junction array chip developed by NIST as a standard volt. ... A multimeter can be used to measure resistance in ohms. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... This article or section does not cite its references or sources. ... Electromotive force (emf) is the amount of energy gained per unit charge that passes through a device in the opposite direction to the electric field existing across that device. ...

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. 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; it could not exist until the ohm itself was defined (1861, 1864). Well before Georg Ohm's work, Henry Cavendish found experimentally (January 1781) that current varies in direct proportion to applied voltage, but he did not communicate his results to other scientists at the time.^[2] {{Infobox Scientist This guy was gay | name = Georg Simon Ohm | image = Ohm3. ... Year 1827 (MDCCCXXVII) was a common year starting on Monday (link will display the full calendar) of the Gregorian Calendar (or a common year starting on Wednesday of the 12-day slower Julian calendar). ... A multimeter can be used to measure resistance in ohms. ... For other persons named Henry Cavendish, see Henry Cavendish (disambiguation). ...

The resistance of most resistive devices (resistors) is constant over a large range of values of current and voltage. When a resistor is used under these conditions, the resistor is referred to as an ohmic device 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). An ideal resistor is a component with an electrical resistance that remains constant regardless of the applied voltage or current flowing through the device. ...

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. 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 section and the Relation to heat conduction section below. An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... Look up vector in Wiktionary, the free dictionary. ... A scalar may be: Look up scalar in Wiktionary, the free dictionary. ...

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.) 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.) An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ...

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

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Physicists often use the continuum form of Ohm's Law: Image File history File links Question_book-3. ...

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). While the notation above does not explicitly depict the variables, each are vectors and each are functions of three position variables. (Normally, and in some places below, the dot means the vector dot product. Here the dot just means multiplication.) 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). In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... Not to be confused with electrical conductance, a measure of an objects or circuits ability to conduct an electric current between two points, which is dependent on the electrical conductivity and the geometric dimensions of the conducting object. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ... 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. ...

The potential difference between two points is defined as

or, in the case where the electric field is independent of the choice of path (as it is in a circuit),

| ΔV | = EL

where L 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: Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ...

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. If the material is moving at velocity v relative to a magnetic field B, a term must be added as follows A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... For the indie-pop band, see The Magnetic Fields. ...

The analogy to the Lorentz force is obvious, and in fact Ohm's law can be derived from the Lorentz force and the assumption that there is a drag on the charge carriers proportional to their velocity. Lorentz force. ...

A perfect metal lattice would have no resistivity, but a real metal has crystallographic defects, impurities, multiple isotopes, and thermal motion of the atoms. Electrons scatter from all of these, resulting in resistance to their flow. 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. ... For other uses, see Isotope (disambiguation). ... In ordinary English, to scatter is to distribute randomly. ...

Ohm's law is sufficient to derive both Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL). Let us first examine only the right-hand side of the equation: Kirchhoffs circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. ... Kirchhoffs circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. ...

and calculate the line integral around a closed contour:

Applying Stokes's theorem, we can write over the surface bounded by the countour: Stokes theorem in differential geometry is a statement about the integration of differential forms which generalizes several theorems from vector calculus. ...

but, since E is the gradient of a scalar potential, yielding:

and gradients are irrotational, we have:

thereby proving KCL. Returning to the original formulation of Ohm's law:

and forming the closed line integrals again:

and recalling from Maxwell's equations that curl(H) = J:

we apply Stokes's theorem to obtain:

From our preceding derivation, we know that the right-hand side evaluates to zero:

thus proving that the net current flow through an open surface is zero, which restates KCL.

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 computers. Even though, today, computers running electronic computer-aided design and analysis programs do the bulk of the work predicting and optimizing the performance of electrical circuits (in particular, those circuits to be fabricated on silicon chips), 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 almost always considered ideal ohmic devices, i.e. they obey Ohm's Law. From the engineer's point of view, resistors (devices that "resist" the electric current) develop a voltage across their terminal conductors (e.g. 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. (That current must have been supplied by a circuit element functioning as a current source and it must be passed on to a circuit element that serves as a current sink.) Thus resistors act like current-to-voltage converters (just as springs act like displacement-to-force converters).

Similarly, a circuit may incorporate a resistor (of resistance R) designed to function as a voltage-to-current converter. In such a circuit, a desired voltage V is established across the resistor in order to force a current I exactly equal to 1/R times V through the resistor.

The DC resistance of a resistor is always a positive quantity, and the current through a resistor generates (waste) heat in the resistor as it does in one of Ohm's wires. Voltages can be either positive or negative, and are always measured with respect to a reference point. When we say that a point in a circuit has a certain voltage, it is understood that this voltage is really a voltage difference (a two-terminal measurement) and that there is an understood, or explicitly stated, reference point, often called ground or common. Currents can be either positive or negative, the sign of the current indicating the direction of current. Current in a wire consists of the slow drift of electrons due to the influence of a voltage established between two points on the wire.

Since the resistance of a resistor is always positive and the equation describing Ohm's law does not in itself constrain R to be positive (by being written as: |V|=|I| R), there is the potential for computing a negative value for R. Using measurements of voltage and current that are made correctly, the sign of a computed R is never negative. When a negative R is computed based on a measurement of the voltage drop across a resistor and a measurement of the current through the resistor, then one of the two measurements must have been made improperly. When circuits are analyzed, the direction of current between circuit elements may not be known or obvious. In this case, the direction of the current is assigned arbitrarily. Should a sign error (one that implies a negative resistance) arise during the analysis, the error is resolved by asserting that the initially assigned direction of current was incorrect, and that the actual direction of current is in the direction opposite to the initially assigned direction.

Various I vs. V graphs representing ohmic (blue line) and non-ohmic devices (red and yellow curves).

Non-ohmic and active components may actually have negative differential resistance, a subject discussed in its own article. The word 'differential' is key, though often omitted, because it describes the characteristics of an interesting portion of the I vs. V curve of the non-ohmic device. At no time is the 'static' resistance itself negative. Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... A VI curve with a negative differential resistance region Negative resistance or negative differential resistance (NDR) is a property of electrical circuit elements composed of certain materials in which, over certain voltage ranges, current is a decreasing function of voltage. ...

Certain powered circuit devices, constructed as two-terminal devices and tested as if they were a resistor (by applying a voltage across the two terminals while measuring the current), may exhibit actual negative resistance. Ohm's law is not intended to apply to such devices. Further the law of conservation of energy is not violated because there is an integrated source of power.

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 just too simple to encompass devices described by a more complicated I vs. V relationship.

The blue line in the I vs. V graph at right represents ohmic devices because current is directly (linearly) proportional to the applied voltage. The slope of the blue line is 1/R. The graph's red line represents a non-ohmic device such as a lamp filament because as more voltage is applied, heating the filament, the filament's resistance rises, forcing the (magnitude of the) slope to decrease. The graph's yellow line illustrates the I vs. V characteristics of a non-ohmic two-terminal circuit having semi-conductor components (such as paralleled and oppositely oriented diodes).

Hydraulic analogs

While the terms voltage, current and resistance are fairly intuitive terms, beginning students of electrical engineering might find the analog terms for water flow helpful. 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. Water flow rate, as in liters (or gallons) of water per minute, is the analog of current, as in coulombs per second. 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, i.e. the electrical current, passing through an electrical resistor is proportional to the difference in voltage measured across the resistor. For other uses, see Pascal. ... A pressure gauge reading in PSI (red scale) and kPa (black scale) 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 pressure or of stress based on avoirdupois units. ... The liter (spelled liter in American English and litre in Commonwealth English) is a unit of volume. ... The gallon (abbreviation: gal) is a unit of volume. ...

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. This article or section does not cite any references or sources. ...

Temperature effects

When the temperature of the conductor increases, the collisions between electrons and ions increase. 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: For other uses, see Temperature (disambiguation). ...

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. In the above expression, we have assumed that L and A remain unchanged within the temperature range. Electrical resistivity (also known as specific electrical resistance) is a measure of how strongly a material opposes the flow of electric current. ...

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. 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. An intrinsic semiconductor, also called an undoped semiconductor or i-type semiconductor, is a pure semiconductor without any significant dopant species present. ... In semiconductors and insulators, the conduction band is the range of electron energy, higher than that of the valence band, sufficient to make the electrons free to accelerate under the influence of an applied electric field and thus constitute an electric current. ... For the following two reasons the electron hole was introduced into calculations: If an electron is excited into higher state it leaves a hole in its old state. ... In solids, the valence band is the highest range of electron energies where electrons are normally present at zero temperature. ...

Extrinsic semiconductors have much more complex temperature behaviour. 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. An extrinsic semiconductor is a semiconductor that has been introduced to a doping agent, giving it different electrical properties than the intrinsic (pure) 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 strain), which means to mechanically stretch 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 (the other form of strain), 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. This article is about the deformation of materials. ... Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it. ... Typical foil strain gauge. ...

AC circuits

Ohm's law holds for linear circuits where the current and voltage are steady (DC). When the current and/or voltage are varying then effects other than ohmic resistance are at work. These effects are principally those of inductance and capacitance. When inductors and/or capacitors are involved in a circuit then the relationship between voltage and current becomes the solution to a differential equation and can be complex. Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ...

However, if the varying voltage and current are steady AC voltages and currents then a simplification can be made to the differential equations that takes the form of Ohm's law. This is done by defining reactance, X as being the relationship of voltage and current in an inductor or capacitor as; City lights viewed in a motion blurred exposure. ... It has been suggested that Electric reactance be merged into this article or section. ...

where V and I are the RMS voltage and current respectively. In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ...

It can be shown that for an inductor,

and for a capacitor,

where j is the unit imaginary number and ω is the angular frequency of oscillation of the ac generator. In the general case, a circuit can be made up of many components and the total effect is partly resistive and partly reactive. To deal with this a further quantity is defined, namely impedance, Z. In general, Z is a complex number where the real part represents resistance and the imaginery part represents reactance so that, It has been suggested that this article or section be merged into Angular velocity. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... In mathematics, a complex number is a number which is often formally defined to consist of an ordered pair of real numbers , often written: In mathematics, the adjective complex means that the underlying number field is complex numbers, for example complex analysis, complex matrix, complex polynomial and complex Lie algebra. ...

We can now write,

where V and I are the oscillating phasor voltage and current respectively and Z is the complex impedance. See wikibooks book on Phasors A phasor is a constant complex number representing the complex amplitude (magnitude and phase) of a sinusoidal function of time. ...

While this has the form of Ohm's law, with Z taking the place of R, it is important to understand that it is not the same as Ohm's law. For one thing, when Z is purely imaginery, then there is no net energy delivered by the generator and no heat dissipated in the circuit. This is because inductors and capacitors store energy during part of the ac cycle but then return it to the circuit in another part. When Z is complex, only the real part is responsible for dissipating heat.

Another difference is that in a purely ohmic cicuit the voltage and current are proportional at any instant of time. In the general case of an ac circuit this is no longer true. It is only the rms average values that have this simple relationship.

A final difference is that in a purely ohmic circuit (ie resistance only, no reactance) the relationship between voltage and current is independant of the frequency (but see also skin effect). In the general ac circuit, Z will vary strongly with frequency and hence also the relationship between voltage and current. The skin effect is the tendency of an alternating electric current (AC) to distribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core. ...

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. 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.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.e. charge) variables. The basis of Fourier's work was his clear conception and definition of thermal conductivity. 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. Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... For other uses, see Temperature (disambiguation). ... flux in science and mathematics. ... This article does not cite any references or sources. ... This box:      Electric current is the flow (movement) of electric charge. ... K value redirects here. ...

See also

Electronics Portal

• Poiseuille's law
• Scientific laws named after people
• Ohm's acoustic law
• Hydraulic analogy
• Hopkinson's Law ("Ohm's Law for magnetics")
• Mesh analysis

Image File history File links Nuvola_apps_ksim. ... The Poiseuilles law (or the Hagen-Poiseuille law also named after Gotthilf Heinrich Ludwig Hagen (1797-1884) for his experiments in 1839) is the physical law concerning the voluminal laminar stationary flow ΦV of incompressible uniform viscous liquid (so called Newtonian fluid) through a cylindrical tube with the constant... This is a list of scientific laws named after people (eponymous laws). ... Ohms acoustic law or simply Ohms law states that a musical sound is perceived by the ear as the sum of a number of pure harmonic tones. ... Since electric current is invisible and the processes at play in electronics are often difficult to understand in an intuitive way, it is common to teach electronics using analogies to more common sense objects and processes. ... 1 Meshes and Mesh Currents For planar networks the meshes are the “windows” formed when the network is drawn with no branches crossing. ...

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.
• An interactive and downloadable Ohm's Law calculator.

References