Capacitors
Capacitors and capacitance  charge and unit of charge.
A capacitor is a device used to store electrical energy.
The plates of a capacitor is charged and there is an electric field between them. The capacitor will be discharged if the plates are connected together through a resistor.
Charge of a Capacitor
The charge of a capacitor can be expressed as
Q = I t (1)
where
Q = charge of capacitor (coulomb, C, mC)
I = current (amp, A)
t = time (s)
The quantity of charge (number of electrons) is measured in the unit Coulomb  C  where
1 coulomb = 6.24 10 ^{ 18 } electrons
The smallest charge that exists is the charge carried by an electron, equal to 1.602 10 ^{ 19 } coulomb .
Example  Quantity of Electricity Transferred
If a current of 5 amp flows for 2 minutes, the quantity of electricity  coulombs  can be calculated as
Q = (5 A) (2 min) (60 s/min)
= 600 C
or, in electrons:
(600 C) ( 6.24 10 ^{ 18 } electrons / C)
= 3.744 10 ^{ 21 } electrons
Electric Field Strength (Dielectric Strength)
If two charged plates are separated with an insulating medium  a dielectric  the electric field strength (potential gradient) between the two plates can be expressed as
E = U / d (2)
where
E = electric field strength (volts/m)
U = eletrical potential (volt)
d = thickness of dielectric, distance between plates (m)
Example  Electric Field Strength
The voltage between two plates is 230 V and the distance between them is 5 mm . The electric field strength can be calculated as
E = (230 V) / ((5 mm) (10 ^{ 3 } m/mm))
= 46000 volts/m
= 46 kV/m
Electric Flux Density
Electric flux density is the ratio between the charge of the capacitor and the surface area of the capacitor plates:
D = Q / A (3)
where
D = electric flux density (coulomb/m ^{ 2 } )
A = surface area of the capacitor (m ^{ 2 } )
Charge and Applied Voltage
Charge in a capacitor is proportional to the applied voltage and can be expressed as
Q = C U (4)
where
C = constant of proportionality or capacitance (farad, F, µF )
A farad is an enormous capacitance so it is common to deal with microfarads (μF), nanofarads (nF) or picofarads (pF).
Capacitance
From (4) the capacitance can be expressed as
C = Q / U (5)
One farad is defined as the capacitance of a capacitor when there is a potential difference across the plates of one volt when holding a charge of one coulomb.
It is common to use µF (10 ^{ 6 } F) .
Example  Voltage over a Capacitor
A 5 µF capacitor is charged with 10 mC . The voltage across the capacitor can be calculated by modifying (4) to
U = Q / C
= (10 mC) (10 ^{ 3 } C/mC) / ((5 µF) (10 ^{ 6 } F/µF)
= 2000 V
= 2 kV
Absolute Permittivity
The ratio of electric flux density to electric field is called absolute permittivity  ε  of a dielectric and can be expressed as
ε = D / E (6)
where
ε = absolute permittivity (F/m, farad/m)
The absolute permittivity of free space or vacuum  also called the electric constant  ε _{ 0 }  is 8.85 10 ^{ 12 } F/m .
Relative Permittivity
Relative permittivity  also called the dielectric constant ε _{ r }  is the ratio between the flux density of the field in an actual dielectric  ε  and the flux density of the field in absolute vacuum  ε _{ 0 } .
ε _{ r } = ε / ε _{ 0 } (7a)
The actual permittivity can be calculated by transforming (7a) to
ε = ε _{ r } ε _{ 0 }(7b)
Parallel Plate Capacitor
The capacitance of a plate capacitor  as shown in the figure above  is proportional with the area A of the plate. The capacitance can be expressed as
C = ε _{ r } ε _{ 0 } A / d (8)
where
A = area of plate (m ^{ 2 } )
d = thickness of dielectric, distance between plates (m)
For a plate capacitor with multiple plates the capacitance can be expressed as
C = ε _{ r } ε _{ 0 } A (n  1) / d (8b)
where
n = number of plates
Example  Capacitance of a Plate Capacitor
The capacitance of a plate capacitor with area 5 cm ^{ 2 } , 10 plates and distance 0.1 mm between the plates  with ceramic dielectric with relative permittivity 30 between the plates  can be calculated as
C = ( 8.85 10 ^{ 12 } F/m ) (30) (5 cm ^{ 2 } ) (10 ^{ 4 } m ^{ 2 } /cm ^{ 2 } ) (10  1) / ((0.1 mm) (10 ^{ 3 } m/mm))
= 11 10 ^{ 9 } F
= 11 pF
Typical commonly used Capacitors
Typical capacitors are
 variable air capacitors
 mica capacitors
 paper capacitors
 ceramic capacitors
 plastic capacitors
 titanium oxide capacitors
 electrolytic capacitors
Capacitor as Frequencydependent Resistor
Since a capacitor looks like a short circuit at higher AC frequencies  capacitors can be considered as simply frequencydependent resistors that allow you to make frequencydependent voltage di
viders.
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