Capacitors

Capacitors ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Types of Capacitors Parallel-Plate Capacitor Cylindrical Capacitor A cylindrical capacitor is a parallel-plate capacitor that has been rolled up with an insulating layer between the plates.

Capacitors and Capacitance Charge Q stored: The stored charge Q is proportional to the potential difference V between the plates. The capacitance C is the constant of proportionality, measured in Farads. Farad = Coulomb / Volt A capacitor in a simple electric circuit.

Parallel-Plate Capacitor ,[object Object],[object Object],[object Object],+Q -Q +Q -Q

What is a capacitor? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Capacitor construction ,[object Object],[object Object],[object Object],[object Object],[object Object]

Defining capacitance ,[object Object],[object Object],[object Object],[object Object],[object Object]

Graphical representation ,[object Object],Gradient term is the capacitance of the capacitor Charge stored is directly proportional to the applied voltage Q V

Energy stored by a capacitor ,[object Object],[object Object],[object Object],Area term is the energy stored in the capacitor Q V

Other expressions for energy ,[object Object]

Charging a capacitor ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],I t

Discharging a capacitor ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],I t

Discharging a Capacitor ,[object Object],[object Object],[object Object],As water level falls, rate of flow decreases

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object]

Voltage and charge characteristics ,[object Object],V or Q t V or Q t

Dielectrics ,[object Object],[object Object],[object Object],[object Object],ε = κε o = permittivity of the material.

Properties of Dielectric Materials ,[object Object],[object Object],[object Object],[object Object],[object Object],Dielectric Strength (V/m) Dielectric Constant κ Material 3 x 10 6 1.0006 air 8 x 10 6 300 strontium titanate 150 x 10 6 7 mica 15 x 10 6 3.7 paper

Practice Quiz ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Capacitors in Parallel Capacitors in Parallel:

Capacitors in Series For n capacitors in series:

Circuit with Capacitors in Series and Parallel a b 15 μF 3 μF 6 μF What is the effective capacitance C ab between points a and b? 20 μF C 1 C 2 C 3 C 4 C ab ?

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Time constant

When t equals tau during discharge ,[object Object],[object Object]

Graphical determination of tau ,[object Object],[object Object],[object Object],V or Q t

Logarithmic discharge analysis ,[object Object],[object Object],[object Object],[object Object]

Logarithmic discharge graph Gradient term is the -1/Tau lnV t

www.search for... ,[object Object]

Capacitors

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Capacitors

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