CAPACITANCE - CHARGE

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CAPACITANCE

 As these figures and formulas indicate, capacitance is a measure of the ability of two surfaces to store an electric charge. Separated and isolated by a dielectric (insulator), a net positive charge is accumulated on one surface and a net negative charge is stored on the other surface.

In an ideal capacitor, charge would be stored indefinitely; however, real world capacitors gradually lose their charge due to leakage currents through the non-ideal dielectric.

Additionally, an inductive component is present due to metal leads (if present) and characteristics of the plate surfaces. This inductance, in combination with the capacitance, creates a resonant frequency where the capacitor looks like a pure resistance.

 

Series Capacitors

1 =  1  +  1 + · · · +  1
      Cs   C1    C2           Cn      
Parallel Capacitors
Cp = C1 + C2 + · · · + Cn

Parallel Plates

C =

 e0er A
    D    


W = ˝ C v2
i (t) = C dv(t)
             dt
v (t) =+ v0

XC =

   1
2
p f C

Coaxial Cable

C =

2 p e0er x
  ln [ b/a ]

A = Area of plates
C = Capacitance (F)
D = Distance between plates (m)
a = Inner radius (m)
b = Outer radius (m)
q = Charge (Coulombs)
x = Length (m)
W = Energy (J)
er = Relative permittivity
e0 = 8.85 x 10-12 F/m
D.F. = Dissipation Factor = 1/q

 C = 

 q
 V

D.F. =

 1
 q

Equivalent Capacitor (total model)

CAPACITANCE CONVERSIONS

Standard unit = Farad (F)
 

  abfarad farad microfarad statfarad
1 abF = 1 109 1015 8.987*1020
1 F = 10-9 1 106 8.987*1011
1 mF = 10-15 10-6 1 105
1 statF = 1.113*10-21 1.113*10-12 1.113*10-6 1
 

CHARGE CONVERSIONS

 

Standard unit = Coulomb (C)

 
  abcoulomb amp·hour coulomb statcoulomb
1 abC = 1 2.778 * 10-3 10 2.998 * 1010
1 A·h = 360 1 3600 1.079 * 1013
1 C = 0.1 2.778 * 10-4 1 2.998 * 109
1 statC = 3.336 * 10-11 9.266 * 10-14 3.336 * 10-10 1