Capacitors

Summary

• A capacitor is…
  • a device for storing separated electric charges.
  • a pair of oppositely charged conductors (called plates even if they aren't flat) separated by an insulator (called a dielectric).
• The capacitance (C) of an electrostatic system is, by definition, the ratio of the quantity of charge separated (Q) to the potential difference applied (V).

  C =	Q
  	V

• The SI unit of capacitance is the farad [F], which is equivalent to the coulomb per volt [C/V].
  • One farad is generally considered a large capacitance.
• The energy stored in a capacitor can be calculated using one of the following equations…

  Uc = ½QV = ½CV2 = ½	Q2
  	C

• The capacitance of a parallel plate capacitor is.
  • directly proportional to the area (A) of one plate
  • inversely proportional to the separation (d) between the plates
  • directly proportional to the dielectric constant (κ the Greek letter kappa) of the material between the plates

  C =	κε0A
  	d

• The capacitance of a cylindrical capacitor is given by

  C =	2πκε0ℓ
  	ln(r2/r1)

  where

  ℓ =	length
  b =	outer radius
  a =	inner radius

• The capacitance of a spherical capacitor is given by

  C =	4πκε0
  	(1/r1) − (1/r2)

  where

  b =	outer radius
  a =	inner radius

• The self capacitance of a spherical conductor is given by

  C = 4πε₀R

  where

  R =

  radius