Ohm

The ohm (symbol: Ω) is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.

Contents

Definition

The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere, the conductor not being the seat of any electromotive force.[1]

\Omega = \dfrac{\mbox{V}}{\mbox{A}} = \dfrac{\mbox{m}^2 \cdot \mbox{kg}}{\mbox{s} \cdot \mbox{C}^2} = \dfrac{\mbox{J}}{\mbox{s} \cdot \mbox{A}^2}=\dfrac{\mbox{kg}\cdot\mbox{m}^2}{\mbox{s}^3 \cdot \mbox{A}^2}= \dfrac{\mbox{J} \cdot \mbox{s}}{\mbox{C}^2}

In many cases the resistance of a conductor in ohms is approximately constant within a certain range of voltages, temperatures, and other parameters; one speaks of linear resistors. In other cases resistance varies (e.g., thermistors).

Commonly used multiples and submultiples in electrical and electronic usage are the milliohm, ohm, kilohm, megohm, and gigaohm.[2]

In alternating current circuits, electrical impedance is also measured in ohms.

Conversions

The SI unit of electrical conductance is the siemens, also known as the mho (ohm spelled backwards, symbol is ℧); it is the reciprocal of resistance in ohms.

Power as a function of resistance

The power dissipated by a linear resistor may be calculated from its resistance, and voltage or current. The formula is a combination of Ohm's law and Joule's laws:

P=V\cdot I =\frac{V^2}{R} = I^2\cdot R

where P is the power in watts, R the resistance in ohms, V the voltage across the resistor, and I the current through it.

This formula is applicable to devices whose resistance varies with current.

Use of the Ω symbol in electronic documents

Care should be taken when preparing documents (including HTML documents) that make use of the symbol Ω. Some document editing software will attempt to use the symbol typeface to render the character. Where the font is not supported, a W is displayed instead (a "10 W" resistor instead of a "10 Ω" resistor, for instance). As this represents the SI unit of power, not resistance, this can lead to confusion.

Unicode encodes an ohm symbol (U+2126 Ω , Ω) distinct from Greek omega among letterlike symbols, but it is only included for backwards compatibility and the Greek uppercase omega character (U+03A9 Ω (HTML: Ω Ω), Ω) is preferred.[3]. Many text editors allow the use of ALT 234 to produce the Ω symbol.

See also

References

  1. ^ BIPM SI Brochure: Appendix 1, p. 144
  2. ^ The NIST Guide to the SI: 9.3 Spelling unit names with prefixes reports that IEEE/ASTM SI 10-2002 IEEE/ASTM Standard for Use of the International System of Units (SI): The Modern Metric System states that there are three cases in which the final vowel of an SI prefix is commonly omitted: megohm, kilohm, and hectare. "In all other cases in which the unit name begins with a vowel, both the final vowel of the prefix and the vowel of the unit name are retained and both are pronounced."
  3. ^ Excerpts from The Unicode Standard, Version 4.0, accessed 11 October 2006

External links

Base units
Ampere · Candela · Kelvin · Kilogram · Metre · Mole · Second
Derived units
Becquerel · Coulomb · degree Celsius · Farad · Gray · Henry · Hertz · Joule · Katal · Lumen · Lux · Newton · Ohm · Pascal · Radian · Siemens · Sievert · Steradian · Tesla · Volt · Watt · Weber
Accepted for use
with SI
See also
Book:International System of Units  · Category:SI base units