The Physics
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# 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…  U = 1 CV2 = 1 Q2 = 1 QV 2 2 C 2
• 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, and
• directly proportional to the dielectric constant (κ) of the material between the plates.
 C = κε0A d
• The capacitance of a cylindrical capacitor is given by  C = 2πκε0ℓ ln(b/a)
where  ℓ = length b = outer radius a = inner radius
• The capacitance of a spherical capacitor is given by  C = 4πκε0 (1/a) − (1/b)
where  b = outer radius a = inner radius
• The self capacitance of a spherical conductor is given by

C = 4πε0R

where  R = radius