Resource Lesson
Dielectrics: Beyond the Fundamentals
Printer Friendly Version
Gauss' Law has shown us that the
electric field between two parallel plates
can be calculated with the formula
If the strength of the electric field between the plates becomes too strong, then the air between them can no longer insulate the charges from sparking, or discharging, between the plates. For air, this breakdown occurs when the electric field is greater than 3 x 10
^{6}
V/m. In order to keep this from happening, an insulator, or
dielectric,
is often inserted between the plates to reduce the strength of the electric field, without having to reduce the voltage being placed across the plates.
A
dielectric is a polar material
whose electric field aligns to oppose the original electric field already established between the plates. The dielectric is measured in terms of a dimensionless constant, κ ≥ 1, whose value is usually referenced from a table.
Material
κ
air
1.00054
ethanol
24.3
glass
5-10
mica
3-6
paper
2-4
paraffin
2.1-2.5
polystyrene
2.3-2.6
porcelain
5.7
rubber
2-3
teflon
2.1
water
80
If this insulating material is insufficient then the capacitor can still leak allowing current to flow between the plates. When this occurs the electric device "smells as if something is burning."
κ = E
_{original}
/ E
_{dielectric}
κ = E
_{o}
/ E
_{d}
κ = C
_{dielectric}
/ C
_{original}
κ = C
_{d}
/ C
_{o}
When the battery is removed, the dielectric will decrease the electric field strength and the voltage between the plates while it increases their capacitance.
E = V/d
Using the fact that V = Ed and that capacitance is the ratio of the charge stored per unit volt we derived the following formula for the capacitance based on the geometry of a parallel-plate capacitor.
Refer to the following information for the next five questions.
A 90 µF capacitor is initially charged to 12 volts without a dielectric in place.
If the battery remains connected while a paper dielectric having a constant of κ = 2.0 is inserted between the capacitor's plates, then what will be its new capacitance?
How much charge will be on its plates?
If instead, the capacitor is disconnected from the battery before the paper dielectric is inserted, what would be the capacitor's new capacitance?
How much charge would be on its plates?
What would be the new voltage across its plates?
For more practice with capacitors and both connected and disconnected batteries, reference this
worksheet
.
Dielectric Configurations
Often capacitors can have complicated dielectric configurations based on available materials and circuit requirements. The good news is that they can be solved based on the principles of capacitors in series and in parallel, in combination with the formulas for the electric field and the geometry of a parallel plate capacitor.
If the capacitors are
arranged in series
(one after another along a single path), then
C
_{series}
= (1/C
_{1}
+ 1/C
_{2}
+ 1/C
_{3}
)
^{-1}
If the capacitors
arranged in parallel
(strung along multiple paths that cross the same section), then
C
_{parallel}
= C
_{1}
+ C
_{2}
+ C
_{3}
Let's work a few examples.
Refer to the following information for the next seven questions.
In each of the following cases, the charged plates are 10 cm by 20 cm and the gap between the plates is 6 mm.
cream signifies a gap only filled with air, κ = 1.0
orange represents a dielectric with κ = 2.0
yellow represents a dielectric with κ = 3.0
purple represents a dielectric with κ = 4.0
What is the capacitance of this air-filled capacitor?
If a metal conducting slab 2 mm thick is placed in the air gap between the plates, what would be the capacitor's new capacitance?
What is the new capacitance if the gap is completely filled with a dielectric having κ = 3.0?
What is the capacitance when its gap is only half-filled with a dielectric having κ = 3.0?
What is the capacitance when its gap is half-filled with a dielectric having κ = 3.0 and the other half is filled with a dielectric having κ = 2.0?
How is the capacitance changed when the gap is half-filled with a dielectric having κ = 3.0 and the other half is filled with a dielectric having κ = 2.0 but in this new orientation?
And what is the capacitance of this final configuration?
Related Documents
Lab:
CP -
Series and Parallel Circuits
Labs -
Aluminum Foil Parallel Plate Capacitors
Labs -
Electric Field Mapping
Labs -
Electric Field Mapping 2
Labs -
Magnetic Field in a Solenoid
Labs -
Mass of an Electron
Labs -
Parallel and Series Circuits
Labs -
RC Time Constants
Labs -
Resistance and Resistivity
Labs -
Resistance, Gauge, and Resistivity of Copper Wires
Labs -
Telegraph Project
Labs -
Terminal Voltage of a Lantern Battery
Labs -
Wheatstone Bridge
Resource Lesson:
RL -
A Comparison of RC and RL Circuits
RL -
A Guide to Biot-Savart Law
RL -
A Special Case of Induction
RL -
Ampere's Law
RL -
An Introduction to DC Circuits
RL -
Capacitors and Dielectrics
RL -
Continuous Charge Distributions: Charged Rods and Rings
RL -
Continuous Charge Distributions: Electric Potential
RL -
Coulomb's Law: Beyond the Fundamentals
RL -
Coulomb's Law: Suspended Spheres
RL -
Derivation of Bohr's Model for the Hydrogen Spectrum
RL -
Electric Field Strength vs Electric Potential
RL -
Electric Fields: Parallel Plates
RL -
Electric Fields: Point Charges
RL -
Electric Potential Energy: Point Charges
RL -
Electric Potential: Point Charges
RL -
Electricity and Magnetism Background
RL -
Electrostatics Fundamentals
RL -
Famous Experiments: Millikan's Oil Drop
RL -
Filaments
RL -
Gauss' Law
RL -
Inductors
RL -
Kirchhoff's Laws: Analyzing Circuits with Two or More Batteries
RL -
Kirchhoff's Laws: Analyzing DC Circuits with Capacitors
RL -
LC Circuit
RL -
Magnetic Field Along the Axis of a Current Loop
RL -
Magnetism: Current-Carrying Wires
RL -
Maxwell's Equations
RL -
Meters: Current-Carrying Coils
RL -
Parallel Plate Capacitors
RL -
RC Time Constants
RL -
RL Circuits
RL -
Shells and Conductors
RL -
Spherical, Parallel Plate, and Cylindrical Capacitors
RL -
Torque on a Current-Carrying Loop
Review:
REV -
Drill: Electrostatics
REV -
Electrostatics Point Charges Review
Worksheet:
APP -
The Birthday Cake
APP -
The Circuit Rider
APP -
The Cycle Shop
APP -
The Electrostatic Induction
CP -
Coulomb's Law
CP -
DC Currents
CP -
Electric Potential
CP -
Electric Power
CP -
Electrostatics: Induction and Conduction
CP -
Ohm's Law
CP -
Parallel Circuits
CP -
Power Production
CP -
Power Transmission
CP -
RIVP Charts #1
CP -
RIVP Charts #2
CP -
Series Circuits
NT -
Brightness
NT -
Electric Potential vs Electric Potential Energy
NT -
Electrostatic Attraction
NT -
Light and Heat
NT -
Lightning
NT -
Parallel Circuit
NT -
Photoelectric Effect
NT -
Potential
NT -
Series Circuits
NT -
Shock!
NT -
Van de Graaff
NT -
Water Stream
WS -
Capacitors - Connected/Disconnected Batteries
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Combinations of Capacitors
WS -
Coulomb Force Extra Practice
WS -
Coulomb's Law: Some Practice with Proportions
WS -
Electric Field Drill: Point Charges
WS -
Electric Fields: Parallel Plates
WS -
Electric Potential Drill: Point Charges
WS -
Electrostatic Forces and Fields: Point Charges
WS -
Electrostatic Vocabulary
WS -
Induced emf
WS -
Introduction to R | I | V | P Charts
WS -
Kirchhoff's Laws: DC Circuits with Capacitors
WS -
Kirchhoff's Laws: Sample Circuit
WS -
Parallel Reading - The Atom
WS -
Resistance, Wattage, and Brightness
WS -
Standard Model: Particles and Forces
TB -
34A: Electric Current
TB -
35A: Series and Parallel
TB -
Advanced Capacitors
TB -
Basic Capacitors
TB -
Basic DC Circuits
TB -
Electric Field Strength vs Electric Potential
TB -
Multiple-Battery Circuits
TB -
Textbook Set #6: Circuits with Multiple Batteries
PhysicsLAB
Copyright © 1997-2022
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton