# Capacitors

## Capacitors and capacitance - charge and unit of charge

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A capacitor is a device capable 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 (coulomb, C)

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 *

### Electric Field Strength

The charged plates are separated with a dielectric - an insulating medium. The electric field strength - the ratio between the potential difference or voltage and the thickness of the dielectric can be expressed as

E = V / d (2)

where

E = electric field strength (volt/m)

V = potential difference (volt)

d = thickness of dielectric (m)

### Electric Flux Density

Electric flux density is the ratio between the charge of the capacitor and the surface area of the capacitor plates and can be expressed as

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 on a capacitor is proportional to the applied voltage and can be expressed as

Q = C V (4)

where

C = constant of proportionality or capacitance (farad, F)

### Capacitance

From *(4)* the capacitance can be expressed as

C = Q / V (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)*.

### Absolute Permittivity

The ratio of electric flux density - *D* - to the electric field - *E* - is called absolute permittivity - *ε* - of a dielectric and can be expressed as

ε = D / E (6)

where

ε = absolute permittivity (F/m)

The absolute permittivity of free space or vacuum - also called the electric constant - *ε _{0}* =

*8.85 10*.

^{-12}F/m### Relative Permittivity

Relative permittivity - also called dielectric constant - is the ratio between the flux density of the field in an actual dielectric and the flux density of the field in absolute vacuum.

The actual permittivity can be calculated by multiplying the relative permittivity by *ε _{0}.*

ε = ε_{r}ε_{0 }(7)

### Energy Stored in Capacitors

The energy stored in a capacitor can be expressed as

W = 1/2 C V^{2}(8)

W = energy stored - or work done in establishing the electric field (joules, J)

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