Conductors, Capacitors and Dielectrics

AP Physics Rapid Learning Series - 15
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Conductors,
C it dCapacitors, and
Dielectrics
Rapid Learning CoreTutorial Series
www.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
3/40
dielectric materials in a
capacitor.
Concept Map
Physics
Studies
Previous content
New content
Resistivity
Forces
Electrical
Forces
Conductors
y
Length
Area
and
and
4/40
Electric Charge
Caused by
Stored in
Capacitors
store Electrical
Energy
Dielectrics

Conductors
For electrons to move or flow, they must
travel through some substance This is a
5/40
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.
6/40
Don’t try this at home...

Insulators
Insulators: Materials where electrons are bound
and don’t flow easily. Examples include glass,
rubber, and plastic.
7/40
Semiconductors
Semiconductors: Materials in between insulator
and conductor. Examples include silicon, and
germanium.
Used in transistors and other electronic
components.
8/40

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.
9/40
Resistors
Resistors are used to control the amount of
electric charge flowing.
R i tResistor
symbol
Many types exist.
U ll l d i
10/40
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.
11/40
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
12/40
g

Resistance Formula
Resistance,
Ω
Resistivity of
material, Ωm
A
ρL
R =
Ω
Cross
sectional
area of wire Length of
13/40
Notice, units turn out to equal Ω for resistance. This
unit will be discussed further in a later tutorial.
area of wire,
m2
g
wire, 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.
14/40
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
15/40
everyday use. Maybe in the future...
Capacitors
Sometimes there isn’t enough electrical
energy available for a particular need
16/40
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
17/40
Symbol for a capacitor:
Capacitor Construction
A capacitor consists
of two separated
conductive plates
connected to an +connected to an
electric potential
difference.
+ -
Positive charge
builds up on one
plate, negative
18/40
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
19/40
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.
20/40
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.
=
−
μF1
F10
xμF100
6
F1x10 4−
21/40
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
d
Aε
C o
=
Area of each
plate, m2εo = permittivity
of free space
8.85 x10-12 C2/Nm2
22/40
d
Capacitance,
Farads, F
Distance
between
plates, m

Increasing Area
23/40
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
24/40
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.
25/40
charged capacitor
can temporarily
power the light bulb
as it is discharged.
Uses
In the flash of a camera, charge is stored by a
capacitor until needed (flash).
26/40
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).
27/40
Dielectrics
A dielectric is a material that enhances
the capacity of a capacitor
28/40
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
29/40
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
30/40
additional capacitance.

Dielectric Constant, k
Sometimes it is included in the capacitance formula.
εo = permittivity of free space
8 85 10 12 C2/N 2
Akε
C 0
=
Area of each
plate, m2
8.85 x10-12 C2/Nm2
Dielectric
Constant, k,
no units
31/40
d
C
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
32/40
+
+
+
+
+
_
_
_
_
_
+- +-+-
+- +-+-
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?
?
33/40
Capacitance Example Solution
d
Akε
C 0
=
Rearranging for k gives:
Aε
Cd
k
o
=
Substitute given values:
34/40
))(1.7m/NmC(8.85x10
m)F)(1.0x10(5x10
k 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.
qV
2
1
UC =Energy
stored in
capacitor, J
Charge C
Electric
potential, V
35/40
Charge, C
Additional Energy Formula
Since q= CV the previous formula can be
rewritten with that substitution.
Electric
2
C CV
2
1
U =
Energy
stored in
capacitor, J
Electric
potential, V
36/40
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?
2
C CV
2
1
U =
2
(1F)(12V)
1
U 2
V
C
72 72CV
J
72C=
37/40
C (1F)(12V)
2
U =
72JUC =
2
V
V
72= 72CV=
C
72C=
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
qV
2
1
UC =
2
C CV
2
1
U =
Capacitance of aCapacitance of a
A
ρL
R =
ate a s
placed between
the plates of a
capacitor.
ate a s
placed between
the plates of a
capacitor.
Charge stored in aCharge stored in a
38/40
Capacitance of a
capacitor:
Capacitance of a
capacitor:
d
Akε
C 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
Wh t’ N t
Chemistry :: Biology :: Physics :: Math
What’s Next …
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Step 2: Practice – Interactive Problem Drill
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Conductors, Capacitors and Dielectrics

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