Henry (unit)

{{short description|SI unit of inductance}} {{Infobox Unit | name = henry | image = 150px | caption = An inductor composed of an enameled wire wound around a magnetic core used to confine and guide the induced magnetic field. | standard = SI | quantity = inductance | symbol = H | dimension = M¹·L²·T⁻³·I⁻² | namedafter = Joseph Henry | units1 = SI base units | inunits1 = 1 kg⋅m²⋅s⁻²⋅A⁻² }}

The '''henry''' (symbol: '''H''') is the unit of electrical inductance in the International System of Units (SI), defined as 1 kg⋅m²⋅s⁻²⋅A⁻².<ref>{{cite web | title=How Many? A Dictionary of Units of Measurement | last=Rowlett | first=Russ | url=http://www.unc.edu/~rowlett/units/dictH.html | publisher=University of North Carolina at Chapel Hill | access-date=2011-08-29 | archive-date=2016-08-29 | archive-url=https://web.archive.org/web/20160829224528/https://www.unc.edu/~rowlett/units/dictH.html | url-status=dead }}</ref><ref name=SI9>{{SIbrochure9th|page=138}}</ref> If a current of 1 ampere flowing through a coil produces flux linkage of 1 weber, that coil has a self-inductance of 1 henry.‌ The unit is named after Joseph Henry (1797–1878), the American scientist who discovered electromagnetic induction independently of and at about the same time as Michael Faraday (1791–1867) in England.<ref>{{cite web | title = A Princeton Companion | url = http://etcweb.princeton.edu/CampusWWW/Companion/henry_joseph.html | author = Herbert S. Bailey Jr. | access-date = 2011-08-29 | archive-date = 2011-08-12 | archive-url = https://web.archive.org/web/20110812130355/http://etcweb.princeton.edu/CampusWWW/Companion/henry_joseph.html | url-status = dead }}</ref>

==Definition== The inductance of an electric circuit is one henry when an electric current that is changing at one ampere per second results in an electromotive force of one volt across the inductor: <math display=block>V(t)= L \frac{\mathrm{d}I}{\mathrm{d}t}\,,</math> where {{math|''V''(''t'')}} is the resulting voltage across the circuit, {{math|''I''(''t'')}} is the current through the circuit, and {{mvar|L}} is the inductance of the circuit.

The henry is a derived unit based on four of the seven base units of the International System of Units: kilogram (kg), metre (m), second (s), and ampere (A). Expressed in combinations of SI units, the henry is:<ref name=SI9 /> <math display=block>\begin{alignat}{6} \mathrm{H} &= \dfrac{\mathrm{kg} {\cdot} \mathrm{m}^2}{\mathrm{s}^{2} {\cdot} \mathrm{A}^2} &&= \dfrac{\mathrm{N} {\cdot} \mathrm{m}}{\mathrm{A}^2} &&= \dfrac{\mathrm{J}}{\mathrm{A}^2} &&= \dfrac{\mathrm{kg} {\cdot} \mathrm{m}^2}{\mathrm{C}^2} &&= \dfrac{\mathrm{s}^2}{\mathrm{F}} \\ &= \dfrac{\mathrm{T} {\cdot} \mathrm{m}^2}{\mathrm{A}} &&= \dfrac{\mathrm{Wb}}{\mathrm{A}} &&= \dfrac{\mathrm{V} {\cdot} \mathrm{s}}{\mathrm{A}} &&= \dfrac{\Omega}{\mathrm{rad}{\cdot} \mathrm{Hz}} &&= \dfrac{\Omega{\cdot}\mathrm{s}} { \mathrm{rad}} &&= \Omega{\cdot}\mathrm{s} \end{alignat}</math> where: {{nowrap|1=H = henry}}, {{nowrap|1=kg = kilogram}}, {{nowrap|1=m = metre}}, {{nowrap|1=s = second}}, {{nowrap|1=A = ampere}}, {{nowrap|1=N = newton}}, {{nowrap|1=C = coulomb}}, {{nowrap|1=J = joule}}, {{nowrap|1=T = tesla}}, {{nowrap|1=Wb = weber}}, {{nowrap|1=V = volt}}, {{nowrap|1=F = farad}}, {{nowrap|1=Ω = ohm}}, Hz = hertz, rad = radian (dimensionless quantity)

==Use== The International System of Units (SI) specifies that the symbol of a unit named for a person is written with an initial capital letter, while the name is not capitalized in sentence text, except when any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case.

The United States National Institute of Standards and Technology recommends users writing in English to use the plural as ''henries''.<ref name=Taylor>{{cite report |last1= Thompson |first1= Ambler |last2= Taylor |first2= Barry N. |date= 2008 |url= http://physics.nist.gov/cuu/pdf/sp811.pdf |title= NIST Special Publication 811: Guide for the Use of the International System of Units (SI) |edition= 2008 |type= Special Publication |publisher= National Institute of Standards and Technology |page= 31 |access-date= 2024-01-22}} </ref>

==Applications== The inductance of a coil depends on its size, the number of turns, and the permeability of the material within and surrounding the coil. Formulae can be used to calculate the inductance of many common arrangements of conductors, such as parallel wires, or a solenoid. A small air-core coil used for broadcast AM radio tuning might have an inductance of a few tens of microhenries (~10{{nbsp}}μH). A large motor winding with many turns around an iron core may have an inductance of hundreds of henries. The physical size of an inductance is also related to its current carrying and voltage withstand ratings.

==See also== * Inductor

==References== {{Reflist}}

{{SI units}}

Category:SI derived units Category:Units of electrical inductance