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Ohm's law
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This article is about the law related to electricity. For other uses, see Ohm's acoustic law.

V, I, and R, the parameters of Ohm's law.
Ohm's law states that the current through a conductor between two points is directlyproportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance,[1] one arrives at the usual mathematical equation that describes this relationship:[2]

where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.[3]
The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly more complex equation than the one above (see History section below) to explain his experimental results. The above equation is the modern form of Ohm's law.
In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:

where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ is a material dependent parameter called the conductivity. This reformulation of Ohm's law is due to Gustav Kirchhoff
Ohm's law is an empirical law, a generalization from many experiments that have shown that current is approximately proportional to electric field for most materials. It is less fundamental than Maxwell's equations and is not always obeyed. Any given material will break down under a strong-enough electric field, and some materials of interest in electrical engineering are "non-ohmic" under weak fields.[11][12]
Ohm's law has been observed on a wide range of length scales. In the early 20th century, it was thought that Ohm's law would fail at theatomic scale, but experiments have not borne out this expectation. As of 2012, researchers have demonstrated that Ohm's law works for silicon wires as small as four atoms wide, and one atom high.[
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Circuit analysis

Ohm's law triangle
In circuit analysis, three equivalent expressions of Ohm's law are used interchangeably:

Each equation is quoted by some sources as the defining relationship of Ohm's law,[2][19][20] or all three are quoted,[21] or derived from a proportional form,[22] or even just the two that do not correspond to Ohm's original statement may sometimes be given.[23][24]
The interchangeability of the equation may be represented by a triangle, where V (voltage) is placed on the top section, the I (current) is placed to the left section, and the R (resistance) is placed to the right. The line that divides the left and right sections indicate multiplication, and the divider between the top and bottom sections indicates division (hence the division bar).
Resistive circuits
Resistors are circuit elements that impede the passage of electric charge in agreement with Ohm's law, and are designed to have a specific resistance value R. In a schematic diagram the resistor is shown as a zig-zag symbol. An element (resistor or conductor) that behaves according to Ohm's law over some operating range is referred to as an ohmic device (or an ohmic resistor) because Ohm's law and a single value for the resistance suffice to describe the behavior of the device over that range.
Ohm's law holds for circuits containing only resistive elements (no capacitances or inductances) for all forms of driving voltage or current, regardless of whether the driving voltage or current is constant (DC) or time-varying such as AC. At any instant of time Ohm's law is valid for such circuits.
Resistors which are in series or in parallel may be grouped together into a single "equivalent resistance" in order to apply Ohm's law in analyzing the circuit. This application of Ohm's law is illustrated with examples in "How To Analyze Resistive Circuits Using Ohm's Law" on wikiHow.
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Other versions
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 resistance 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 microscopic 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 V, I, and R scalar variables of Ohm's law, but which are each functions of position within the conductor. Physicists often use this continuum form of Ohm's Law:[31]

where "E" is the electric field vector with units of volts per meter (analogous to "V" of Ohm's law which has units of volts), "J" is thecurrent density vector with units of amperes per unit area (analogous to "I" of Ohm's law which has units of amperes), and "ρ" (Greek "rho") is the resistivity with units of ohm·meters (analogous to "R" of Ohm's law which has units of ohms). The above equation is sometimes written[32] as J = E where "σ" (Greek "sigma") is the conductivity which is the reciprocal of ρ.

Current flowing through a uniform cylindrical conductor (such as a round wire) with a uniform field applied.
The potential difference between two points is defined as:[33]

with the element of path along the integration of electric field vector E. If the applied E field is uniform and oriented along the length of the conductor as shown in the figure, then defining the voltage V in the usual convention of being opposite in direction to the field (see figure), and with the understanding that the voltage V is measured differentially across the length of the conductor allowing us to drop the Δ symbol, the above vector equation reduces to the scalar equation:

Since the E field is uniform in the direction of wire length, for a conductor having uniformly consistent resistivity ρ, the current density Jwill also be uniform in any cross-sectional area and oriented in the direction of wire length, so we may write:[34]

Substituting the above 2 results (for E and J respectively) into the continuum form shown at the beginning of this section:

The electrical resistance of a uniform conductor is given in terms of resistivity by:[34]

where l is the length of the conductor in SI units of meters, a is the cross-sectional area (for a round wire a = πr2 if r is radius) in units of meters squared, and ρ is the resistivity in units of ohm·meters.
After substitution of R from the above equation into the equation preceding it, the continuum form of Ohm's law for a uniform field (and uniform current density) oriented along the length of the conductor reduces to the more familiar form:

A perfect crystal lattice, with low enough thermal motion and no deviations from periodic structure, would have no resistivity,[35] 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.
The more complex generalized forms of Ohm's law are important to condensed matter physics, which studies the properties of matterand, in particular, its electronic structure. In broad terms, they fall under the topic of constitutive equations and the theory of transport coefficients.
Magnetic effects
If an external B-field is present and the conductor is not at rest but moving at velocity v, then an extra term must be added to account for the current induced by the Lorentz force on the charge carriers.

In the rest frame of the moving conductor this term drops out because v= 0. There is no contradiction because the electric field in the rest frame differs from the E-field in the lab frame: E ' = E + v×B. Electric and magnetic fields are relative, see Lorentz transform.
If the current J is alternating because the applied voltage or E-field varies in time, then reactance must be added to resistance to account for self-inductance, see electrical impedance. The reactance may be strong if the frequency is high or the conductor is coiled.
See Hall effect for some other implication of a magnetic field.

Ohm's Law defines the relationships between (P) power, (E) voltage, (I) current, and (R) resistance. One ohm is the resistance value through which one volt will maintain a current of one ampere.

( I ) Current is what flows on a wire or conductor like water flowing down a river. Current flows from negative to positive on the surface of a conductor. Current is measured in (A) amperes or amps.

( E ) Voltage is the difference in electrical potential between two points in a circuit. It's the push or pressure behind current flow through a circuit, and is measured in (V) volts.

( R ) Resistance determines how much current will flow through a component.Resistors are used to control voltage and current levels. A very high resistance allows a small amount of current to flow. A very low resistance allows a large amount of current to flow. Resistance is measured in ohms.

( P ) Power is the amount of current times the voltage level at a given point measured in wattage or watts.