In electrical circuits, the result that potential difference U and current I satisfy U = IR for resistance R; for alternating current circuits, U = IZ, where Z is impedance; stated by Georg Ohm in 1827.
Ohm's law states that, in an electrical circuit, the current passing through a conductor is directly proportional to the potential difference applied across them provided all physical conditions are kept constant.
In mathematical terms, this is written as:
,where I is the current, V is the potential difference, and R is a proportionality constant called the resistance.
The SI unit of current is the ampere;
Physics
Physicists often use the continuum form of Ohm's Law:
where J is the current density (current per unit area), σ is the conductivity (which can be a tensor in anisotropic materials) and E is the electric field.
The common form used in circuit design is the macroscopic, averaged-out 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
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.
A perfect metal lattice would have no resistivity, but a real metal has crystallographic defects, impurities, multiple isotopes, and thermal motion of the atoms.
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:
and calculate the line integral around a closed contour:
Applying Stokes's theorem, we can write over the surface bounded by the countour:
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.
Virtually all electronic circuits have resistive elements which are almost always considered ideal ohmic devices, i.e. 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.
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.
Similarly, resistors act like voltage to current converters 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 (waste) heat in the resistor as it does in one of Ohm's wires. 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 flow.
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. When a negative R is computed based on a measurement of the voltage drop across a resistor and a measurement of the current passing through the resistor, then one of the two measurements must have been made improperly. 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.
Non-ohmic and active components may actually have negative differential resistance, a subject discussed in its own article.
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 applies to conductors whose resistance is (substantially) independent of the applied voltage (or equivalently the injected current).
Hydraulic analogy
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. 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.
Temperature effects
When the temperature of the conductor increases, the collisions between electrons and atoms increase. 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.
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.
Extrinsic semiconductors have much more complex temperature behaviour.
Strain (mechanical) effects
Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon strain.
AC circuits
For an AC circuit Ohm's law can be written , where V and I are the oscillating phasor voltage and current respectively and Z is the complex impedance for the frequency of oscillation.
In a transmission line, the phasor form of Ohm's law above breaks down because of reflections. In a lossless transmission line, the ratio of voltage and current follows the complicated expression
,where d is the distance from the load impedance ZL measured in wavelengths, β is the wavenumber of the line, and Z0 is the characteristic impedance of the line.
Relation to heat conduction
Ohm's principle predicts the flow of electrical charge (i.e.
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