Capacitance

Figure 1. Drawing of a capacitor with the capacitance, 400 microfarads, marked on the side.[1]

Capacitance is the ability of an object or material to store an electric charge. Specifically, it is a measure of an isolated conductor's ability to store charge at a given voltage difference.[2] In this sense, an object's capacitance is the ratio between its charge at a particular voltage difference and that voltage difference. Functionally, this leads to capacitance also being a measure of how much energy a capacitor can store.

Often a capacitance is thought of as being the physical property of a capacitor that has two conducting plates close to each other. The capacitance is described mathematically as:

[math] C = \frac{q}{V} [/math]
  • [math]C[/math] is the capacitance, measured in farads
  • [math]q[/math] is the charge that is on the positive plate of the capacitor, measured in coulombs
  • [math]V[/math] is the voltage of the conductor, measured in volts


Capacitance is measured in farads (F), with 1 farad representing 1 coulomb per volt. This means that if an isolated conductor had a capacitance of 1 farad and was charged with 1 coulomb, it would have a voltage of 1 volt on its surface. There is also an alternate way to determine the capacitance of a capacitor if its dimensions are known. If the area of the plates of the capacitor can be determined, the capacitance can be calculated from the expression:[3]

[math]C = \frac{\varepsilon_{0} \varepsilon_{r} A} {d}[/math]
  • [math]C[/math] is the capacitance, measured in farads (F)
  • [math]\varepsilon_{0}[/math] is a constant called the permittivity of free space = 8.854188x10-12 F/m [4]
  • [math]\varepsilon_{r}[/math] is the relative permittivity of the material between the plates
  • [math]A[/math] is the surface area of the plates of the capacitor, measured in square metres (m2)
  • [math]d[/math] is the distance between the plates, measured in metres (m)


The equation shows that the capacitance is influenced by the dimensions of the capacitor.

For Further Reading

References

  1. "Electrolytic Capacitor, Radial, 16x30 (Coloured)" Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Electrolytic_Capacitor,_Radial,_16x30_(Coloured).svg#/media/File:Electrolytic_Capacitor,_Radial,_16x30_(Coloured).svg
  2. P. Tipler and G. Mosca, "Electrostatic Energy and Capacitance," in Physics for Scientists and Engineers Volume 2, 5th ed. Freeman, ch. 24, pp. 752-755
  3. R. Kotz and M. Carlen, "Principles and applications of electrochemical capacitors," Electrochim. Acta, vol. 45, no. 15-16, pp. 2483-2498, May 2000.
  4. A. D. McNaught and A. Wilkinson. (2012, September 8). Permmittivity of vacuum [Online]. Available: http://goldbook.iupac.org/P04508.html

Authors and Editors

Bethel Afework, Gokul Dharan, Kailyn Stenhouse, Jason Donev
Last updated: July 21, 2018
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