Farad
SI derived unit · quantity: electrical capacitance
01 · Definition
One farad is the capacitance on which a charge of one coulomb creates a voltage of one volt. The unit came out so enormous that it is almost never used whole: capacitors in circuits are measured in picofarads and microfarads, and the farad entered everyday use only with supercapacitors. The capacitance of a sphere the size of the Earth is seven hundred microfarads.
The Leyden jar was the first capacitor in history, 1745. Its capacitance is about a nanofarad: a glass bottle with foil inside and out held a charge that knocked whole rows of monks off their feet.
A substance placed between the plates becomes polarised, its own field partly cancels the external one, the voltage for the same charge falls — and so the capacitance rises. Paper gives a factor of about three, mica six, water eighty, barium titanate in ceramics up to several thousand. The price of a high permittivity is instability: class Y5V ceramic loses up to eighty per cent of its capacitance at the edges of the working temperature range and sags noticeably under voltage, which is why precise circuits use film with its modest three.
02 · Conversion
Enter a capacitance and the passport will break it down by unit
Real parts live in pico- and microfarads, so the prefixes here work at full stretch. In old schematics and handbooks one meets centimetres of capacitance — a CGSE unit equal to about one picofarad.
Capacitor markings are three-digit and always in picofarads: the first two figures are the value, the third is the number of zeros. The code 104 means ten with four zeros, that is a hundred thousand picofarads, which are also a hundred nanofarads or nought point one microfarad — three ways of writing one quantity, met in different schools of draughtsmanship. The letter beside it gives the tolerance: K is ten per cent, J five, M twenty.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| F | farad, the SI unit | 1 | the unit of this sheet |
| mF | millifarad | 1000 | a rare prefix: thousands of microfarads are written instead |
| µF | microfarad | 1000000 | the most settled prefix in schematics |
| nF | nanofarad | 10⁹ | the European notation; in America the same 0.1 µF |
| pF | picofarad | 10¹² | below this begins the capacitance of the conductors themselves |
| cm | centimetre, CGSE | 8.988·10¹¹ | in the electrostatic system capacitance was measured by length |
| R, m | radius of a sphere | 8.988·10⁹ | for a farad the radius would come to nine million kilometres |
| cm | centimetre, CGSE | 8.988·10¹¹ | the capacitance of a sphere equals its radius |
| abF | abfarad, CGSM | 10⁻⁹ | a billion farads in a single unit |
| jar | the “jar” | 9.009·10⁸ | they counted how many Leyden jars made up a battery |
| µµF | micromicrofarad | 10¹² | a double prefix instead of pico |
| F | farad | 1 | the unit of this sheet |
The farad is the ratio of the coulomb to the volt, so it stands between them. With the ohm it gives seconds, with the henry the resonant frequency of a circuit
03 · Orders of magnitude
from a transistor to a planetOne farad: a supercapacitor the size of a glass
04 · Measuring instruments
What capacitance is measured with
It applies a sinusoid of known frequency to the part and works out the capacitance and the losses from the amplitude and phase shift of the current. The result depends on the measuring frequency: an electrolytic at a hundred hertz and at ten kilohertz will show different values, and the frequency is always stated in the data sheet.
A bridge circuit with a reference capacitor in one arm: capacitance and loss tangent are balanced at the same time. It is the chief instrument of high-voltage insulation — from the growth of losses in a cable or a transformer the ageing of the dielectric is judged long before breakdown.
Capacitance is found by timing how long it takes to reach sixty-three per cent of the voltage through a known resistance. That is how the built-in function in microcontrollers works, and every home-made meter too; for supercapacitors it is the only way, because bridge instruments are not designed for such values.
Four parallel cylinders whose capacitance per unit length depends on a single measured quantity — the overlap length. The theorem, found in 1956, made it possible to calculate capacitance from geometry and for decades tied electrical standards to the metre.
05 · Writing rules
µF, nF, pF — and no “µµF”
Double prefixes are forbidden in the SI: a picofarad is written pF, not “µµF” and not “mmF”, though both turn up in old schematics. The symbol F is a capital; °F beside it is the degree Fahrenheit, a different quantity. In capacitor markings “104” means 10·10⁴ pF, that is 100 nF.
Electrolytic capacitors are polarised, and the voltage in the marking is a limit, not a working point: a capacitor rated 16 V lives for years in a 12 V circuit and for months in a 15 V one. Amateur habit has preserved two abolished prefixes: “µµF” and “mmF” meant the picofarad. The historical statfarad of the CGSE system equals the centimetre: in electrostatic units capacitance was measured by length.
06 · Neighbouring units
The farad stands between charge and voltage, and paired with the henry it sets the frequency of a tuned circuit — the very circuit that tunes a radio to a station.
charge on the plate
coulomb times volt
the paired quantity in a tuned circuit
The square of the voltage in the energy formula means that doubling the voltage stores four times as much — which is why supercapacitor makers fight for every extra volt rather than for farads. From the Simetrium passports, the farad is adjoined by the Simetrium passports the farad is adjoined by coulomb and volt from the definition, henry as the paired quantity of a tuned circuit, ohm from the time constant and joule of the stored energy.
07 · Historical section
What capacitance was reckoned in before the farad
Pieter van Musschenbroek took a shock so violent that, by his own account, he would not repeat the experiment for the crown of France. The Leyden jar held about a nanofarad — and that was enough to knock a man off his feet.
Faraday had no systematic education and no command of mathematics, yet it was his experiments that gave electrical engineering the field, induction and electrolysis alike. The unit of capacitance was named after him.
The congress of electricians defined the farad through the coulomb and the volt, together with the volt, the ampere and the ohm. Practice moved to microfarads at once: in those years no man-made object had a capacitance of a whole farad.
The patent for the double-layer capacitor was filed by General Electric, but it was the Japanese firm NEC that brought it to market, releasing a “supercapacitor” for tape-recorder memory in 1978. Today a three-thousand-farad supercapacitor fits in the palm of a hand.
The unit was chosen so badly that for almost two hundred years nobody used it
Capacitance is the only electrical quantity whose standard can be built out of pure geometry. The Thompson–Lampard theorem of 1956 states that in a system of four parallel cylindrical electrodes the capacitance per unit length depends on the electric constant and on nothing else: neither on the diameter of the rods nor on the distances between them. It is enough to measure the overlap length with a movable screen — and the capacitance is known by calculation. Such a calculable capacitor gave about two picofarads per metre and served as the basis of national capacitance standards, and through them of ohm standards, since resistance is obtained from capacitance and frequency. The quantum Hall effect broke that chain in 1990 by making the ohm primary; calculable capacitors, however, remained in laboratories as an independent check — the discrepancy between the two routes still serves as one of the tests of the consistency of electrical standards.
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SI derived units with names of their own
the farad passport is openSI base units
in terracotta — the four units the farad is built fromCapacitance in other systems
Passport language
20 languages. The symbol F is international, but the way a value is written is not: a hundred nanofarads in European schematics, nought point one microfarad in American ones — the passport brings the notation to local practice.