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Introduction
What is a capacitor?
What is a capacitance?
Conductors of equal and opposite charge separated by an insulating material
The ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between them.
Capacitance:
CQ
VAlways positive
Measured in [C/V] also known as [F] Farads
1 farad is very large. A 1 farad capacitor could store 1 coulomb of
charge per unit of voltage.
A measure of how much electric potential energy or charge that a capacitor can store.
Energy stored in a capacitor
Suppose that the charge on a capacitor is q during an instant while charging. At this instant the potential difference is V=q/C.
What is the work necessary to move charge dq from the –q plate to the q plate (which is at higher potential)?
CQ
V
dW Vdq
dW q
Cdq
W q
C0Q dq
W Q2
2C
Energy stored in a capacitor
The work done in charging the capacitor can be considered as the potential energy
U stored in the capacitor.
W Q2
2C
CQ
V
UCV 2
2C1
2CV2
UQ2
2Q
V
1
2QV
Energy stored in a parallel-plate capacitorWe can consider the energy to be stored in
the electric field of the capacitor.
CQ
V
U1
2CV2
CA
d0
VEd
UA02d
Ed 2
U1
2Ad0E
2
Energy Density
For a parallel-plate capacitor, the electric field occupies a space of volume Ad, so we will define
the energy per unit volume, or Energy Density as:
U1
2Ad0E
2
uE U
Ad1
20E
2
CQ
V
The energy density in any field is proportional to the square of the electric field in the unit volume.
Capacitors with dielectrics
Dielectric: a nonconducting material such as rubber, glass,
or waxed paper.
CQ
V
VV0
CQ0
VQ0
V0 /C0
1
Capacitors with dielectrics
CQ
VIf a dielectric fills the space between
conductors in a capacitor, the capacitance increases by a factor of a dimensionless factor, called κ, the dielectric constant.
Capacitors with dielectrics
CQ
VThe dielectric material is polarized. This reduces the effective electric field between plates, which
also reduces the potential difference between plates. Lower potential difference results in
higher capacitance.
Benefits of dielectrics in capacitors:
The dielectric strength (maximum electric field that a material can be exposed to without
breaking down and behaving as a conductor) of most materials is higher than air.
Increases the capacitance of a capacitor.
Increases the maximum operating voltage of a capacitor.
My provide mechanical support between the conducting plates.
CQ
V