PHYS 122 - Capacitors and Dielectrics

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 * E_free

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) = Q_{free, inside}/E₀

Electric Energy in a Two Conductor Capacitor

U = ½ * Q²/C

Energy Density for a Capacitor with Dielectric

½kEpsilon(Nought)E²