The farad (symbol: F) is the SI derived unit of electrical capacitance. It is named after the English physicist Michael Faraday.

Definition

One farad is defined as the capacitance of a capacitor across which, when charged with one coulomb of electricity, there is a potential difference of one volt.[1] Conversely, it is the capacitance which, when charged to a potential difference of one volt, carries a charge of one coulomb.[2] A coulomb is equal to the amount of charge (electrons) produced by a current of one ampere flowing for one second. For example, the voltage across the two terminals of a 47 nF capacitor will increase linearly by 1 V when a current of 47 nA flows through it for 1 s.

For most applications, the farad is an impractically large unit of capacitance, although capacitors measured in farads are now used, especially for backing up memory. The most commonly used SI prefixes for electrical and electronic applications are:

  • 1 millifarad (mF) = one thousandth (10−3) of a farad or 1000 μF
  • 1 microfarad (μF, or MFD in industrial use) = one millionth (10−6) of a farad, or 1000000 pF, or 1000 nF
  • 1 nanofarad (nF) = one billionth (10−9) of a farad, or 1000 pF
  • 1 picofarad (pF) = one trillionth (10−12) of a farad

Equalities

A farad has the base SI representation of: s4 × A2 × m−2 × kg−1

It can further be expressed as:

\mbox{F} = \,\mathrm{\frac{A \cdot s}{V} = \dfrac{\mbox{J}}{\mbox{V}^2} = \dfrac{\mbox{W} \cdot \mbox{s}}{\mbox{V}^2} = \dfrac{\mbox{C}}{\mbox{V}} = \dfrac{\mbox{C}^2}{\mbox{J}} = \dfrac{\mbox{C}^2}{\mbox{N} \cdot \mbox{m}} = \dfrac{\mbox{s}^2 \cdot \mbox{C}^2}{\mbox{m}^{2} \cdot \mbox{kg}} = \dfrac{\mbox{s}^4 \cdot \mbox{A}^2}{\mbox{m}^{2} \cdot \mbox{kg}} = \dfrac{\mbox{s}}{\Omega}}

where A=ampere, V=volt, C=coulomb, J=joule, m=metre, N=newton, s=second, W=watt, kg=kilogram, Ω=ohm.

History

The term “farad” was coined by Josiah Latimer Clark in the year of 1861, in honor of Michael Faraday, but it was for a unit of quantity of charge.

Explanation

Values of capacitors are usually specified in ranges of farads (F), millifarads (mF), microfarads (μF, or MFD in industrial use[3]), nanofarads (nF) or picofarads (pF).[4]

The size of commercially available capacitors ranges from around 100 fF (femtofarads, 10−15 F) to 5 kF (kilofarads, 103 F) supercapacitors. Designers of high-performance integrated circuits are concerned about parasitic capacitance measured in femtofarads, while makers of high-performance test equipment are able to detect changes in capacitance on the order of tens of attofarads (10−18).[5]

A picofarad is sometimes referred to as a “puff” or “pic”, as in “a ten-puff capacitor”.[6] If the Greek letter μ is not available, the notation uF is often used as a substitute for μF in electronics literature. A micro-microfarad (μμF, and confusingly often mmf or MMF), an obsolete unit sometimes found in older texts, is the equivalent of a picofarad. The millifarad is less used in practice, so that a capacitance of 4.7×10−3 F, for example, is sometimes written as 4700 µF; industrial parts at times use the abbreviation MFD instead of µF.[7]North American usage also avoids nanofarads: a capacitance of 1×10−9 F will frequently be indicated as 1000 pF; and a capacitance of 1×10−7 F as 0.1 μF.

The reciprocal of capacitance is called electrical elastance, the (non-standard, non-SI) unit of which is the daraf.[8]

A capacitor consists of two conducting surfaces, frequently referred to as plates, separated by an insulating layer usually referred to as a dielectric. The original capacitor was the Leyden jar developed in the 18th century. It is the accumulation of electric charge on the plates that results in capacitance. Modern capacitors are constructed using a range of manufacturing techniques and materials to provide the extraordinarily wide range of capacitance values used in electronics applications from femtofarads to farads, with maximum-voltage ratings ranging from a few volts to several kilovolts.

One picofarad is about the smallest value of capacitor available for general use in electronic design, since smaller capacitors would be dominated by the parasitic capacitances (stray capacitance) of other components, wiring or printed circuit boards. When capacitance values of 1 pF or lower are required, engineers sometimes create their own capacitors by twisting two short lengths of insulated wire together.[9][10]

The capacitance of the Earth’s ionosphere with respect to the ground is calculated to be about 1 F.[11]

CGS units

The abfarad (abbreviated abF) is an obsolete CGS unit of capacitance equal to 109 farads (1 gigafarad, GF). This very large unit is used in medical terminology only.

The statfarad (abbreviated statF) is a different and also rarely used CGS unit of capacitance that corresponds to approximately 1.1126 picofarads. It is equivalent to the capacitance of a capacitor with a charge of 1 statcoulomb across a potential difference of 1statvolt.