Henry
SI derived unit · quantity: inductance
01 · Definition
The henry is the inductance of a circuit in which a current changing at one ampere per second induces a voltage of one volt. An equivalent definition: the inductance in which a current of one ampere creates a flux linkage of one weber.
Inductance is the inertia of current. As mass resists a change of speed, inductance resists a change of current: it cannot be started instantly, nor stopped. Hence the spark in a switch — at the break the current keeps going for a moment through the air.
Break a circuit with a coil in it and the current will try to continue through the air: an arc will flash at the contacts. That is why a suppression diode sits beside every relay and motor: it lets the current close on itself and die away without a spark.
Double the number of turns and you get four times the inductance: the turns both create the flux and link with it. A ferrite or steel core adds a further factor of thousands, but only up to saturation — beyond it the inductance collapses back towards the value of an empty coil.
02 · Conversion
Enter an inductance — the sheet will break it down by units
Real parts live in micro- and millihenries. In the CGSM system inductance, like capacitance in CGSE, had the dimension of length: the abhenry was simply called a centimetre. Hence the old engineering habit of speaking of a coil in centimetres — that is not about its size but about its inductance.
Paired with a capacitor, inductance sets the frequency of a resonant circuit — the very one that tuned radios to a station for a century. It was the capacitor that had to be turned: a variable capacitance is easier to build than a variable inductance.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| H | henry, an SI unit | 1 | henry, an SI unit |
| mH | millihenry | 1000 | millihenry |
| µH | microhenry | 1000000 | microhenry |
| nH | nanohenry | 1000000000 | nanohenry |
| pH | picohenry | 1000000000000 | picohenry |
| Wb/A | weber per ampere — the very same thing | 1 | weber per ampere — the very same thing |
| V·s/A | volt-second per ampere | 1 | volt-second per ampere |
| Ω·s | ohm-second: the working notation before the name was adopted | 1 | ohm-second: the working notation before the name was adopted |
| abH | abhenry, CGSM: also called the centimetre of inductance | 1000000000 | abhenry, CGSM: also called the centimetre of inductance |
| stH | stathenry, CGSE | 0 | stathenry, CGSE |
The second line is the definition through the weber: a henry is a weber per ampere. The third is the energy stored in the field of the winding.
03 · Orders of magnitude
from a board trace to an energy storemillihenries: relay windings, coupling transformers
04 · Measuring instruments
What inductance is measured with
It applies a sine wave and separates the reactive part of the impedance from the active one by the phase shift. The result depends on frequency and on the bias current: a ferrite coil will read differently at a kilohertz and at a megahertz, so the mode is stated together with the value.
It balances an unknown inductance against a reference capacitor and resistors: the coil is compared not with another coil but with a capacitance, which is easier to make accurately. The classical laboratory method, with an uncertainty of hundredths of a per cent.
The coil is connected with a known capacitor and the frequency at which the circuit rings is sought. The inductance follows from Thomson\u2019s formula — the most accessible method, needing only a generator and an oscilloscope, and the only practical one for nanohenries.
A single-layer winding on a cylinder of fused quartz, its dimensions measured to the micrometre: its inductance is computed from the geometry and the magnetic constant, without being measured at all. That is exactly how the unit was fixed before the move to quantum standards.
05 · Writing rules
Capital H — and not «henrys»
The capital H denotes the unit, the lower-case h the hour, which is outside the SI. In English the plural is henries; the name takes no capital in running text although it comes from a surname. An H next to an italic L in one formula is not to be confused: the quantity is set sloping, the unit upright.
The symbol of the quantity is an italic L, of the unit an upright H; the Russian symbol is Гн. The capital H in formulas is already taken by magnetic field strength, so in one expression the two are told apart by the typeface: the quantity leans, the unit stands straight.
06 · Neighbouring units
The henry is the reverse side of the farad: one quantity resists a change of current, the other a change of voltage. Together they set the frequency of a circuit; separately they smooth ripple — the coil in the current path, the capacitor across it.
The mutual inductance of two windings is denoted M and measured in the same henries. In a transformer it is less than the product of the self-inductances: the difference is precisely the part of the flux that missed the second winding.
flux per single ampere
inductance
the paired quantity of a circuit
Of the Simetrium passports neighbours of the henry weber and ampere from the definition, farad as the paired quantity of a tuned circuit, ohm from the time constant and hertz, in which the resonant frequency is expressed.
The henry closes the magnetic family: a weber divided by an ampere. With the ohm it gives seconds, with the farad a resonant frequency. Inductance and capacitance are mirror images: one resists a change of current, the other a change of voltage.
07 · Historical section
A discovery published second
Joseph Henry wound an iron arc with insulated wire — he made the insulation from silk ribbon bought off his wife\u2019s dress — and obtained a magnet that held a weight of a tonne. The schoolteacher from Albany went on to become the first secretary of the Smithsonian.
In 1832 Joseph Henry noticed a spark on breaking a circuit with an electromagnet and understood that the coil induces a voltage in itself. He described the effect in his laboratory notebook earlier than Faraday but published later — and the primacy on induction stayed with the Englishman.
The International Electrical Congress in Chicago gave the unit of inductance the name Henry — along with several other practical units. By then he had been dead for fifteen years, and the name went to the man who had lost the race for priority but not the respect of his colleagues.
The first name for the unit of inductance was the quadrant: ten million metres, a quarter of the Earth\u2019s meridian. It was replaced by the henry at the same congress that adopted the ohm and the volt.
The Ninth General Conference brought the henry into the system of practical units together with the weber and the tesla. The centimetre of inductance from the CGSM system, equal to a nanohenry, stayed in the handbooks for another two decades.
A unit that is computed, not measured
Until 2019 the henry was realised by calculation. The magnetic constant was fixed exactly, four pi times ten to the minus seventh henry per metre, and the inductance of a single-layer winding followed from its geometry alone. Since the redefinition the constant is measured, and the standard rests on the quantum Hall effect instead.
The magnetic constant µ₀ = 1.256 637·10⁻⁶ H/m is a henry per metre: the inductance of empty space. Until 2019 it was the exact number 4π·10⁻⁷; now it is measured, and its last digits are still being refined.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI units that neither engineering nor daily life can do without. Each gets its own sheet: definition, conversion, instruments, writing rules. In 2 languages.
SI derived units with names of their own
the henry sheet is openSI base units
in terracotta — the four units the henry is built fromInductance in other notations
Passport language
2 languages. The symbol H is international, but the way a value is written on a schematic differs: 100µ, 100uH and 0.1mH all mean the same thing, and in translation the sheet brings them to a common form.