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Conductors, C it dCapacitors, and Dielectrics

Rapid Learning CoreTutorial Series

Rapid Learning Centerwww.RapidLearningCenter.com/© Rapid Learning Inc. All rights reserved.

Wayne Huang, Ph.D.Keith Duda, M.Ed.

Peddi Prasad, Ph.D.Gary Zhou, Ph.D.

Michelle Wedemeyer, Ph.D.Sarah Hedges, Ph.D.



Learning Objectives

Understand the factors that affect conduction

By completing this tutorial, you will:

that affect conduction.

Learn about the construction and use of capacitors.

Describe the effects of dielectric materials in a

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dielectric materials in a capacitor.

Concept MapPhysics

Studies

Previous content

New content

Resistivity

Forces

Electrical Forces

Conductors

y

Length

Area

and

and

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Electric Charge

Caused by

Stored inCapacitors

store Electrical Energy

Dielectrics



Conductors

For electrons to move or flow, they must travel through some substance This is a

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travel through some substance. This is a conductor.

Conductors

Conductors: Material where electrons are loosely bound and are able to flow throughout due to the free electrons. Examples include metals, impure water, and human bodies.

6/40Don’t try this at home...



Insulators

Insulators: Materials where electrons are bound and don’t flow easily. Examples include glass, rubber, and plastic.

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Semiconductors

Semiconductors: Materials in between insulator and conductor. Examples include silicon, and germanium.

Used in transistors and other electronic components.

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Superconductors

Superconductor: a material where electrons flow without any resistance. Generally, superconductivity only occurs at very low temperatures. Magnetically

f flevitated fast trains are one application of superconductivity.

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Resistors

Resistors are used to control the amount of electric charge flowing.

R i tResistor symbol

Many types exist. U ll l d i

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Usually a color code is used to determine the value.



Resistivity

An intrinsic property of a material is its resistivity, ρ . Along with other factors, this is used to determine the resistance to electron flow of a particular piece of wire.

ρ has units of Ω m. Thus, resistivity is a measure of resistance per length of a material.

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However, length is not the only factor to determine resistance.

Factors of Wire Resistance

The resistance of a wire can depend on several things including:

thi k ( ) f i

length of wire

thickness (area) of wire

temperature of wire

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g



Resistance Formula

Resistance, Ω

Resistivity of material, Ωm

AρLR =

Ω

Cross sectional

area of wire Length of

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Notice, units turn out to equal Ω for resistance. This unit will be discussed further in a later tutorial.

area of wire, m2

gwire, m

Temperature and Resistance

Resistance of a wire does depend on temperature. In general, a higher temperature means a higher resistance.

Imagine the atoms of a hotter wire moving very rapidly. This could interfere with the conduction of electrons, thus increasing resistance.

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Cold atoms Warmer atoms



Superconducting

In 1911, it was first observed that mercury at 4.2K has a resistance of zero!

This state is called superconducting.

Generally, only very cold materials are superconducting, so it isn’t very practical for everyday use Maybe in the future

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everyday use. Maybe in the future...

Capacitors

Sometimes there isn’t enough electrical energy available for a particular need

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energy available for a particular need. Capacitors are used to store energy for future use.



Capacitors

A capacitor ( condenser ) is a device used to store electrical energy.

They accumulate and store energy for later use. It’s like saving your pennies in a piggy bank for a large future purchase.

S b l f it

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Symbol for a capacitor:

Capacitor ConstructionA capacitor consists of two separated conductive plates connected to an +connected to an electric potential difference.

+ -

Positive charge builds up on one plate, negative

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Battery or voltage source

+ -charge builds up on the other.

Overall, the net charge on a capacitor is zero.



Charge Stored in a Capacitor

The amount of charge a particular capacitor can store depends on the voltage, and the “rating” or capacitance of the particular capacitor.

CVq =

Electric potential, VCharge, C

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Capacitance, Farads, F.

1 Farad = 1Coulomb/Volt

One Farad

One Farad would be a particularly large capacitor. This would be large in physical size and charge storage.and charge storage.

1 μF=10-6 F

Most are much smaller, usually in units of micro Farads, μF.

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1 μF 10 F

The capacitance unit is named after Michael Faraday. He also invented the notion of field or force lines.



Charge Storage Example

How much charge is stored in a 100 μF capacitor that is connected to a 12V battery (electric potential source).

First change μF to F.

=−

μF 1F10 x μF 100

6

F1x10 4−

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CVq =

== − F)(12V)(1x10q 4 C12x10 4−

1 Farad = 1Coulomb/Volt

Capacitance Formula

This rating or capacitance of a capacitor depends on a few factors.

Area of each

dAεC o=

Area of each plate, m2εo = permittivity

of free space8.85 x10-12 C2/Nm2

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dCapacitance,

Farads, F Distance between plates, m



Increasing Area

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To have a more “powerful” capacitor, you would want a larger area. However, that may be impractical, so some capacitors are rolled to maximize space. This give the typical round or cylindrical shape of capacitors.

Discharging

A capacitor “fills up” while electrons are being deposited onto one of the plates.

The capacitor can be discharged if the two plates are connected. (A switch is usually used)

This causes all the accumulated electrons to

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suddenly flow back. This movement of charge can be used.



Discharging Diagram

+

+ -

-The switch is closed to complete the

+ -

Notice how the h d it

circuit and discharge the capacitor.

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charged capacitor can temporarily power the light bulb as it is discharged.

UsesIn the flash of a camera, charge is stored by a capacitor until needed (flash).

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A short time is needed for that charge to re-accumulate, then the flash can be used again.



Analogy

Imagine a stream gradually running into, and filling a dam (capacitor). The water (charge) accumulates until it is released (discharged).

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Dielectrics

A dielectric is a material that enhances the capacity of a capacitor

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the capacity of a capacitor.



Dielectrics - Illustrated

Often an insulating material is inserted between the plates of a capacitor. This substance is called a dielectric.

+++++++

______

Dielectric

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Dielectrics resist charge flow more than air. Thus higher voltages can be applied before the charge jumps or discharges, thus more capacitance.

+ _

Increased Capacitance

With a dielectric instead of air, the plates can be placed closer. Thus, more capacitance.

Because of the presence of the dielectric, capacitance is increased. It’s increased by a dielectric constant, k, which describes the factor of dditi l it

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additional capacitance.



Dielectric Constant, k

Sometimes it is included in the capacitance formula.

εo = permittivity of free space8 85 10 12 C2/N 2

AkεC 0=Area of each

plate, m2

8.85 x10-12 C2/Nm2Dielectric Constant, k,

no units

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dC

Distance between plates, m

Capacitance, Farads, F

Polarized Particles

Inside the dielectric, the molecules are polarized to the opposing charged plate. This increases the capacitance.

+++++

____

+- +-+-

+- +-+-Diagram and molecules not shown

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+++++

_____

+- +-+-

+- +-+-

dielectric

to scale.



Capacitance Calculation

A parallel plate capacitor has a capacitance of 5x10-6F when filled with a dielectric. The area of each plate is 1.7 m2, and the separation between them is 1.0x10-5m. What is the dielectric constant of that material?

?

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Capacitance Example Solution

dAkεC 0=

Rearranging for k gives:

AεCdk

o

=

Substitute given values:

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))(1.7m/NmC(8.85x10m)F)(1.0x10(5x10k 22212-

-5-6

= 3.3=

The dielectric constant has no units.



Energy Stored in a Capacitor

El t i

An expression can be derived for the energy stored in a capacitor.

qV21UC =Energy

stored in capacitor, J

Charge C

Electric potential, V

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Charge, C

Additional Energy Formula

Since q= CV the previous formula can be rewritten with that substitution.

Electric

2C CV

21U =

Energy stored in

capacitor, J

Electric potential, V

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Capacitance, Farads, F.



Energy Storage Example

A booming car stereo system uses a 1 F capacitor connected to the 12V battery. How much energy is stored in this setup?stored in this setup?

2C CV

21U =

2(1F)(12V)1U 2VC72 72CVJ72C=

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C (1F)(12V)2

U =

72JUC =

2VV

72= 72CV= C72C=

Electrical units can be a bit confusing.

Energy stored in a capacitor:Energy stored in a capacitor:

1

Resistance of a wire:

Resistance of a wire:

Dielectrics are insulating materials

Dielectrics are insulating materials

Learning Summary

qV21UC =

2C CV

21U =

Capacitance of aCapacitance of a

AρLR =

ate a splaced between the plates of a

capacitor.

ate a splaced between the plates of a

capacitor.

Charge stored in aCharge stored in a

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Capacitance of a capacitor:

Capacitance of a capacitor:

dAkεC 0=

Charge stored in a capacitor:

q = CV

Charge stored in a capacitor:

q = CV



Congratulations

You have successfully completed the tutorial

Conductors, Capacitors, and Dielectricsand Dielectrics

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