Capacitance & DielectricsAP E&M

IntroductionWhat 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:

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Always positive

Measured in [C/V] also known as [F] Farads1 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.

Capacitance

Parallel Plate:

Cylindrical:

Spherical:

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CAd

0

CL

2k ln ba

Cab

k b a

Energy stored in a capacitorSuppose 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)?

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dW Vdq

dW qCdq

W qC0

Q 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

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UCV 2

2C12CV2

UQ2

2 QV

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Energy stored in a parallel-plate capacitorWe can consider the energy to be stored in

the electric field of the capacitor.

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U12CV2

CAd

0

V Ed

UA02d

Ed 2

U12Ad0E

2

Energy DensityFor 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:

U12Ad0E

2

uE UAd

120E

2

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The energy density in any field is proportional to the square of the electric field in the unit volume.

Capacitors with dielectricsDielectric: a nonconducting

material such as rubber, glass, or waxed paper.

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VV0

CQ0

VQ0

V0 /C0

1

Capacitors with dielectrics

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If 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

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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.

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