Editing Capacitance (section)

==Self capacitance==
In discussing electrical circuits, the term ''capacitance'' is usually a shorthand for the mutual capacitance between two adjacent conductors, such as the two plates of a capacitor. However, every isolated conductor also exhibits capacitance, here called ''self capacitance''. It is measured by the amount of electric charge that must be added to an isolated conductor to raise its [[electric potential]] by one unit of measurement, e.g., one [[volt]].<ref>{{cite book|author=William D. Greason| title=Electrostatic discharge in electronics|url=https://books.google.com/books?id=404fAQAAIAAJ|year=1992|publisher=Research Studies Press|isbn=978-0-86380-136-5 |page=48}}</ref> The reference point for this potential is a theoretical hollow conducting sphere, of infinite radius, with the conductor centered inside this sphere.

Self capacitance of a conductor is defined by the ratio of charge and electric potential:
<math display="block">C = \frac{q}{V},</math>
where
*<math display="inline">q</math> is the charge held,
*<big><math display="inline">V = \frac{1}{4\pi\varepsilon_0}\int \frac{\sigma}{r}\,dS</math></big> is the electric potential,
*<math display="inline">\sigma</math> is the surface charge density,
*<math display="inline">dS</math> is an infinitesimal element of area on the surface of the conductor, over which the surface charge density is integrated,
*<math display="inline">r</math> is the length from <math display="inline">dS</math> to a fixed point ''M'' on the conductor,
*<math>\varepsilon_0</math> is the [[vacuum permittivity]].

Using this method, the self capacitance of a conducting sphere of radius <math display="inline">R</math> in free space (i.e. far away from any other charge distributions) is:<ref name=NSW>{{cite web|archive-url= https://web.archive.org/web/20090226225105/http://www.phys.unsw.edu.au/COURSES/FIRST_YEAR/pdf%20files/5Capacitanceanddielectr.pdf|archive-date=2009-02-26|url=http://www.phys.unsw.edu.au/COURSES/FIRST_YEAR/pdf%20files/5Capacitanceanddielectr.pdf|title=Lecture notes: Capacitance and Dieletrics|publisher=University of New South Wales}}</ref>
<math display="block">C = 4 \pi \varepsilon_0 R.</math>

Example values of self capacitance are:
*for the top "plate" of a [[van de Graaff generator]], typically a sphere 20&nbsp;cm in radius: 22.24 pF,
*the planet [[Earth]]: about 710 μF.<ref>{{cite book | last1 = Tipler | first1 = Paul | last2 = Mosca | first2 = Gene | title = Physics for Scientists and Engineers | publisher = Macmillan | year = 2004 | edition = 5th | page = 752 | isbn = 978-0-7167-0810-0 }}</ref>

The inter-winding capacitance of a [[electromagnetic coil|coil]] is sometimes called self capacitance,<ref>{{cite journal| title=Self capacitance of inductors|doi=10.1109/63.602562 |last1=Massarini |first1=A. |last2=Kazimierczuk |first2=M. K. |year=1997 |volume=12 |issue=4 |pages=671–676 |journal=IEEE Transactions on Power Electronics |postscript=: example of the use of the term 'self capacitance'.|bibcode=1997ITPE...12..671M |citeseerx=10.1.1.205.7356 }}</ref> but this is a different phenomenon. It is actually mutual capacitance between the individual turns of the coil and is a form of stray or [[parasitic capacitance]]. This self capacitance is an important consideration at high frequencies: it changes the [[Electrical impedance|impedance]] of the coil and gives rise to parallel [[Electrical resonance|resonance]]. In many applications this is an undesirable effect and sets an upper frequency limit for the correct operation of the circuit.{{citation needed|date=May 2017}}