Ohm
SI derived unit · quantity: electrical resistance
01 · Definition
One ohm is the resistance of a stretch on which a current of one ampere produces a drop of one volt. The quantity is settled from both sides: a copper wire of one square millimetre gives 17 milliohms per metre, a heating coil tens of ohms, a resistor on a board anything from units to megaohms, insulation gigaohms. Resistance depends on the material, the geometry and the temperature: in metals it grows with heat, in semiconductors it falls, and in a superconductor below the critical temperature it becomes exactly zero.
The resistance of a conductor is made of three things: the resistivity of the material, the length and the cross-sectional area. Twice as long is twice as much; twice as thick across is four times less, because area grows as the square. The range of values in nature is wider than for any other electrical quantity: between copper and quartz glass the difference is twenty-four orders of magnitude. Ohm’s law, meanwhile, does not always hold: it is true for metals at constant temperature, but not for a diode, an incandescent lamp or a gas discharge, where resistance depends on the current itself.
A straight line on the graph comes out only for a metal resistor at constant temperature. The filament of an incandescent lamp heats up with the current, its resistance grows tenfold and the curve bends down. A diode does not conduct at all until the voltage reaches a threshold, and then the current rises exponentially. A gas discharge behaves stranger still: it has a stretch of negative resistance where rising current comes with falling voltage, and that is exactly why a fluorescent lamp needs a ballast to limit the current.
02 · Conversion
Enter a resistance and the passport will turn it into conductance
The siemens is the reciprocal ohm, and the table turns the quantity over rather than multiplying it. The historical ohms differed from today’s by fractions of a per cent, but that was enough for telegraph calculations to disagree between countries.
Resistor values are coded in coloured bands, because there is nowhere to print digits on a part the size of a grain of rice, and bands read from any side. The first two give the significant figures, the third the multiplier, the fourth the tolerance. The values themselves are not taken in sequence but from the E24 series: twenty-four values per decade, chosen so that neighbours differ by about ten per cent and their tolerance bands overlap.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| Ω | ohm, the SI unit | 1 | the unit of this sheet |
| mΩ | milliohm | 1000 | where resistance is a nuisance |
| µΩ | microohm | 1000000 | measured with a four-wire connection |
| kΩ | kilohm | 0.001 | the most settled stretch of the scale |
| MΩ | megaohm | 10⁻⁶ | above this insulation begins |
| GΩ | gigaohm | 10⁻⁹ | no ordinary instrument measures this current |
| S | siemens, conductance | 1 | a reciprocal quantity, not another unit |
| statΩ | ohm of the CGSE system | 1.113·10⁻¹² | almost nine hundred gigaohms in a single unit |
| abΩ | abohm of the CGSM system | 10⁹ | a billion times smaller than the ohm |
| Ω (int.) | international ohm of 1908 | 0.9995 | a mercury column 106.3 cm long |
| Ω₉₀ | practical ohm of 1990 | 1 | differed by seventeen parts in a billion |
| h/e² | quantum resistance | 3.874·10⁻⁵ | an exact number since 2019 |
| Ω | ohm | 1 | the unit of this sheet |
The ohm and the siemens are reciprocals: one and the same physics written as resistance or as conductance
03 · Orders of magnitude
from a superconductor to an insulatorOne ohm: a metre of nichrome wire thinner than a match
04 · Measuring instruments
What resistance is measured with
It passes a current of its own through the part and measures the voltage drop. It works only on a circuit with the power off: any outside voltage upsets the reading or destroys the instrument. The meter also sees parallel branches of the circuit, so a resistor is more often unsoldered for testing.
Four arms and a galvanometer across the diagonal: the resistance being measured is balanced against a known one until the needle rests on zero. The accuracy depends only on the reference resistors and the sensitivity of the null indicator, not on the supply — hence parts per million in laboratory bridges.
The current is fed through one pair of wires and the voltage taken off another — and the resistance of the wires and contacts drops out of the result. Without this trick milliohms cannot be measured: the probes of a multimeter give about a tenth of an ohm by themselves.
A two-dimensional electron gas in a strong magnetic field at about one kelvin gives a resistance exactly equal to the von Klitzing constant divided by a whole number. The value depends on neither the material nor the shape of the sample — reproducibility reaches parts per billion.
05 · Writing rules
Ω is a Greek omega, not the letter O and not “Ohm”
Unicode gives the symbol its own position, U+03A9; the “Ω” from the Letterlike Symbols block is formally deprecated, though it looks the same. A kilohm is written kΩ, a megaohm MΩ. On schematics the decimal point is often replaced by the prefix itself: 4k7 means 4.7 kΩ.
A lower-case m is milli-, a capital M is mega-, and confusing a milliohm with a megaohm gives a difference of nine orders of magnitude. The Russian symbol is Ом, with a capital О.
06 · Neighbouring units
The ohm and the siemens describe one and the same property from two sides. In alternating current a reactive part is added to resistance, and the whole quantity is called impedance — measured in the very same ohms.
the reciprocal ohm
resistance
resistivity
The wave impedance of vacuum is not a property of any substance but a constant linking the electric and magnetic fields of a travelling wave. Among the Simetrium passports next to the ohm stand volt and ampere from Ohm’s law, siemens as the reciprocal quantity, watt and henry s the farad, which set the reactive part of impedance.
07 · Historical section
The law that was laughed at first
Ohm published his law in 1827 and was accused of charlatanry in return: his colleagues held that electricity does not obey simple proportions. Recognition came twenty years later.
The transatlantic cable forced engineers to agree on a measure of resistance. The committee of the British Association issued standard coils, but their value later proved to be a third over one per cent too low.
The international ohm was defined as the resistance of a column of mercury weighing 14.4521 grams and 106.3 centimetres long, at the melting point of ice. The unit could be reproduced in any laboratory that had pure mercury and accurate scales.
Klaus von Klitzing found that the Hall resistance of a two-dimensional gas takes strictly discrete values that do not depend on the sample. Ten years later a standard was built on that effect, and he received the Nobel Prize.
For forty years the ohm was a column of mercury — until steps were found in a two-dimensional gas
The international ohm was set by mercury in a glass tube of stated length, mass and temperature: reproducibility held to the fourth digit, and the tubes had to be recalibrated. In 1980 von Klitzing found that the resistance of a two-dimensional electron gas in a strong magnetic field settles onto plateaux that are multiples of h/e², with an accuracy no material could reach. Ten years later that became the practical standard, and in 2019 h and e were fixed as exact numbers — turning the quantum Hall resistance from a measured quantity into a defined one.
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 20 languages.
SI derived units with names of their own
the ohm passport is openSI base units
in terracotta — the four units the ohm is built fromResistance in other systems
Passport language
20 languages. The symbol Ω is international, but wire cross-sections are not: square millimetres in Europe and AWG gauge in North America — in translation the tables are brought to local practice.