Intro To 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

Electric Field Inside a Parallel-Plate Capacitor From Gauss’s Law: +Q -Q For positively charged plate: For negatively charged plate: Between the plates, by the principle of superposition:

Capacitance of Parallel-Plate Capacitor Choose a path from a to b that is anti-parallel to E

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 ?

Energy Storage in Capacitors ,[object Object],[object Object],[object Object],The work required to charge the capacitor from q=0 to q=Q : Energy Stored by a Capacitor = ½CV 2 = ½QV

Example: Electronic Flash for a Camera ,[object Object],[object Object],[object Object]

Stored Energy Density of a Charged Capacitor Stored Energy: Parallel-Plate Capacitor: Stored Energy: Stored Energy Density in the Electric Field:

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]

The Electric Battery ,[object Object],[object Object],Volta’s original battery consisted of alternate layers of zinc and silver and a salt solution. A simple electric cell is the basis of the common 1.5 Volt “ dry cell” flashlight battery.

Common Dry cell ,[object Object],[object Object],[object Object],[object Object],Common dry cell. (AA,AAA, C or D cell) The net result is that the carbon electrode is left with a net positive charge and the zinc electrode a net negative charge, creating a potential difference between them of 1.5 V.

Electric Cell or Battery ,[object Object],[object Object],[object Object],[object Object],+ + – –

Electric Current ,[object Object],[object Object],Simple electric circuit.

Sign Convention for Electric Current ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Resistance and Ohm’s Law ,[object Object],[object Object],V=IR Ohm’s Law Resistance = 1/(Conductance)

Questions: Electric Current ,[object Object],[object Object],[object Object],[object Object],3. What happens to the current supplied by the battery if two identical devices are connected in parallel across it?

Intro To Capacitors

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Intro To Capacitors