Electricity – Capacitance

Capacitance is the ability of a body to store an electrical charge.

Any object that can be electrically charged exhibits capacitance.

A common form of energy storage device is a parallel-plate capacitor. In a parallel plate capacitor, capacitance is directly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates.

Parallel-Plate Capacitor:

C= ε0 εr A / d

where

εr = the dielectric constant of the material between the plates (for a vacuum, εr = 1)

ε0 = the electric constant (8.85× 10-12)

A = area of one plate

d = separation between plates

Maximum Charge on a Capacitor:

If the charges on the plates are +q and −q, and V gives the voltage between the plates, then

Q= VC

where

Q = charge in Coulombs

V = electrical potential difference in volts

C = capacitance in farads

A 1 farad capacitor when charged with 1 coulomb of electrical charge will have a potential difference of 1 volt between its plates.

Electrical Energy Stored in a Capacitor:

For a flat-plate capacitor the energy stored is:

UE = ½ C V2

where

U = Potential Energy

Q = Coulombs

V = volts

C = capacitance in farads

Charge per unit Area:

σ = q/A

where q = charge and A = area

Energy Density:

U =½ ε0 E2

where

u = energy per unit volume

ε0 = permittivity of free space (8.85× 10-12)

E = energy

Capacitors in Parallel:

Ceff = C1 + C2 +……

For parallel capacitors the total q is equal to the sum of the charge on each capacitor

Capacitors in Series:

1/ Ceff = 1/C1 + 1/C2 +….

Capacitors connected in series all have the same charge q.

Self-capacitance

It is the amount of electrical charge that must be added to an isolated conductor to raise its electrical potential by one unit. The reference point for this potential is a theoretical hollow conducting sphere, of infinite radius, centered on the conductor.

C= 4πε0 R

where R is the radius of the sphere

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