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Based of Volume 2 of Physics for Engineers and Scientist 3rd Edition by Ohanian and Markert
Basic Definition of a Capacitor
Any arrangement of conductors used to store electricity
Dielectric
An electrically insulating material
How are charge and potential related?
Q = CV or C = Q/V
Formula for Capacitance
C = 4piEpsilon(nought)R
What is the SI unit for Capacitance?
The Farad. 1 F = 1 C/V
How do we find capacitance for capacitors consisting of 2 conductors?
C = QDeltaV
Another way to calculate the Electric Field between two plates?
E = DeltaV/d
How are conductors represented Schematically?
Two parallel lines with terminals attached.
Parallel Conductors
Have the same voltage, and their net charge is equal to all the capacitances added up times the voltage. So Net capacitance is simply all the capacitances added up.
Series Conductors
Charge can’t flow across the gaps, so it remains on the outside plates. Each Capacitor will have a different voltage but the same charge. Net Capacitance is 1/C = 1/C1 +1C2 + … and so on.
How do Dielectrics affect Electric fields?
They reduce their strength which is useful in a capacitor.
What do we call dielectrics that gain dipoles that are proportional to the strength of the field?
Linear Dielectrics.
Formula for a field within a linear dielectric
E = 1/k * Efree
Formula for potential within a linear dielectric
DeltaV = 1/k*DeltaV0
Formula for Capacitance in a linear dielectric
C = KC0
Dielectric Strength
The maximum field a dielectric can handle.
Gauss’ Law in Large Volume Dielectrics
Path Integral(K EPerpendicular dA) = Qfree, inside/E0
Electric Energy in a Two Conductor Capacitor
U = ½ * Q²/C
Energy Density for a Capacitor with Dielectric
½kEpsilon(Nought)E²
