Ohm's law: Difference between revisions

Revision as of 04:39, 24 February 2006

Revision as of 23:39, 24 February 2006

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The equation contains the proportionality constant ''R'', which is the [[electrical resistance]] of the device.

The unit of resistance is the ohm. The ohm is a unit of measure derived from more basic units of measure. An ohm is equal to a volt per ampere, or a (volt sec) /coulomb. The inverse of resistance, 1/R, is conductivity or [[electrical conductance]], and its [[SI]] unit is the [[Siemens (unit)|siemens]].

A conduction path in an electrical circuit comprises one or more conductors (i.e. wires having minimal resistance) and/or one or more electrical devices, collectively called circuit elements. Conductors and devices are electrically connected in a way that achieves a desired electrical objective. Devices in electrical circuits that introduce electrical resistance in a conduction path are called resistors. There are many circuit elements whose primary electrical function is distinctly different from that of resistors, yet they also have significant, and often an undesired amount of, electrical resistance (e.g. inductors). Resistive circuit elements are one route by which electric power is lost in an electrical circuit. Usually the power loss is in the form of generating heat or radiating electromagnetic energy.

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\mathbf{J} = \sigma \cdot \mathbf{E}

</math>

where '''J''' is the [[current density]] (current per unit area), &sigma;σ is the [[conductivity]] (which can be a [[tensor]] in anisotropic materials) and '''E''' is the [[electric field]]. <!-- Jpkotta:I'm not sure about the following statement: This is the form Ohm originally stated.--> The common form <math>V = I \cdot R</math> used in circuit design is the macroscopic, averaged-out version.

The equation above 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

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Many engineers use Ohm's Law every working day. One can not be a functioning electrical engineer without understanding this law intimately. Virtually all electronic circuits have resistive elements which are much more often than not considered ideal ohmic devices, i.e. they obey Ohm's Law. From the engineer's point of view, resistors (devices that "resist" the flow of electrical current) develop a voltage across their terminal conductors (e.g. the two wires emerging from the device) proportional to the amount of current flowing through the device.

More specifically, the voltage measured across a resistor at a given instant is strictly proportional to the current passing 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. Thus resistors act like current to voltage convertorsconverters (just as springs act like displacement to force convertorsconverters). Similarly, resistors act like voltage to current convertorsconverters when a desired voltage is established across the resistor because a current '''I''' equal to 1/'''R''' times '''V''' must be flowing through the resistor. 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.

The DC resistance of a resistor is always a positive quantity, and the current flowing through a resistor generates heat in the resistor. 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 cirucit 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. Currents can be either positive or negative, the sign of the current indicating the direction of current flow. Current flow in a wire consists of the slow drift of electrons due to the influence of a voltage established between two points on the wire.

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R = \frac{L}{A} \cdot \rho = \frac{L}{A} \cdot \rho_0 (\alpha (T - T_0) + 1)

</math>

where &rho;ρ is the resistivity, ''L'' is the length of the conductor, ''A'' is its cross-sectional area, ''T'' is its temperature, <math>T_0</math> is a reference temperature (usually room temperature), and <math>\rho_0</math> and <math>\alpha</math> 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.

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[[Intrinsic semiconductor]]s exhibit the opposite temperature behavior, becoming better conductors as the temperature increases. This occurs because the electrons are bumped to the [[conduction band|conduction energy band]] by the thermal energy, where they can flow freely and in doing so they leave behind [[hole]]s in the [[valence band]] which can also flow freely.

[[Extrinsic semiconductor]]s 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 and the number of electrons that have jumped right over the energy gap is negligablenegligible 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 ==

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Z(d) = Z_0 \frac{Z_L + j Z_0 \tan(\beta d)}{Z_0 + j Z_L \tan(\beta d)}

</math>,

where ''d'' is the distance from the load impedance <math>Z_L</math> measured in wavelengths, &beta;β is the [[wavenumber]] of the line, and <math>Z_0</math> is the [[characteristic impedance]] of the line.

== Relation to [[heat conduction]] ==