Download Chapter 16

Chapter 16
Electrical Energy
And
Capacitance
Review - Electric Potential for a
system of point charges
qi
V   ke
ri
i
General
Physics
In the illustrated dipole with
V=0 at r=, where else is V=0 45?
5
6
7
8
9
10
21
22
23
24
25
26
27
28
29
30
11
12
14
15
16
17
General
se
20%
he
r
e
el
ge
ha
r
ge
pl
a
te
r
13
No
w
4
20%
–)
c
3
At
(
2
Ce
n
1
Ce
n
te
rp
oi
nt
5.
20%
ha
r
4.
20%
+)
c
3.
20%
At
(
2.
Center point
Center plane
At (+) charge
At (–) charge
Nowhere else
ne
1.
18
19
20
Physics
Review – Electric potential and
Conductors in E.S. equilibrium






All of the charge resides at the surface
E = /0 just outside the conductor
The electric field just outside the
conductor is perpendicular to the surface
The electric potential V is constant
everywhere on the surface of the
conductor
E = 0 inside the conductor
The electric potential V is constant
everywhere inside the conductor
(and equal to V at the surface)
General
Physics
Review – Electric Field in a
Parallel-Plate Capacitor

The electric field between
the plates is uniform
E=/0 near the center
 Non-uniform fringes
 The field is nearly zero
outside (above and below)


For calculations, assume:
E=const inside the plates
E=0
outside the plates

Can calculate the potential
difference V = E d
General
Physics
The Electron Volt

The electron volt (eV) is defined as the energy that
an electron gains when accelerated through a
potential difference of 1 V




Electrons in normal atoms have energies of 10’s of eV
Excited electrons have energies of 1000’s of eV or keV’s
High energy gamma rays have energies of millions of eV
or MeV’s
1 eV = 1.6 x 10-19 J
General
Physics
An electron and proton are
accelerated through a potential
45
difference of 1V, -1V respectively,
have kinetic energies KEe, KEp.
Which statement is true?
7
8
9
10
21
22
23
24
25
26
27
28
29
30
11
12
13
KE
=
14
15
16
17
General
...
18
bl
e
6
po
ss
i
5
Im
4
KE
e
3
to
p
p
Ke
>
2
KE
e
1
25%
Ke
Impossible to tell?
<
4.
2.
25%
KE
e
3.
KEe > Kep
KEe = KEp
KEe < Kep
1.
25%
p
25%
19
20
Physics
Capacitance
Sections 6 – 10
General
Physics
Capacitance



A capacitor is a device used in a variety of electric circuits
used to store electric charge (and therefore energy)
The capacitance, C, of a capacitor is defined as the ratio
of the magnitude of the charge on either conductor (plate)
to the magnitude of the potential difference between the
conductors (plates)
Units: Farad (F)



Q
C
V
1F=1C/V
A Farad is very large (often will see µF or pF)
The capacitance of a device depends on the geometric
arrangement of the conductors
General
Physics
Parallel-Plate Capacitor, Example

The capacitor has two parallel plates





Each have area A
They are separated by a distance d
The plates carry equal and opposite
charges Q, -Q
When connected to the battery, charge
is pulled off one plate and transferred
to the other plate
Transfer stops when Vcap = Vbattery
Active Figure: Parallel Plate Capacitors
EX16.6
General
Physics
Parallel-Plate Capacitor

For a parallel-plate capacitor whose plates are
separated by air:
Q
Q
Q
Q
C



V Ed  d Q / A d
0
A
C  o
d
0
for a parallel plate capacitor
General
Physics
Applications of Capacitors –
Camera Flash

The flash attachment on a camera uses a
capacitor



A battery is used to charge the capacitor
The energy stored in the capacitor is released when
the button is pushed to take a picture
The charge is delivered very quickly, illuminating the
subject when more light is needed
General
Physics
Applications of Capacitors –
Computers

Computers use capacitors in
many ways



Some keyboards use capacitors
at the bases of the keys
When the key is pressed, the
capacitor spacing decreases
and the capacitance increases
The key is recognized by the
change in capacitance
General
Physics
Capacitors in Circuits
A circuit is a collection of objects usually
containing a source of electrical energy
(such as a battery) connected to elements
that convert electrical energy to other
forms
 A circuit diagram can be used to show the
path of the real circuit

General
Physics
Capacitors in Parallel

When capacitors are first connected in the
circuit, electrons are transferred from the
left plates through the battery to the right
plate, leaving the left plate positively
charged and the right plate negatively
charged

The flow of charges ceases when the
voltage across the capacitors equals that of
the battery

The capacitors reach their maximum
charge when the flow of charge ceases
General
Physics
More About Capacitors in Parallel

The total charge is equal to the sum of the
charges on the capacitors
 Q1 + Q2 = Q

The potential difference across the
capacitors is the same
 ΔV1 = ΔV2 =ΔV

The capacitors can be replaced with one
capacitor with a capacitance of
 Ceq = C1 + C2 + …

The equivalent capacitor must have
exactly the same external effect on the
circuit as the original parallel capacitors
The equivalent capacitance of a parallel
combination of capacitors is greater than
any of the individual capacitors

General
Physics
Equivalent Capacitance – Parallel: An
Example

Four parallel capacitors are replaced with their
equivalent capacitance
Active Figure: Capacitors Combined in Parallel
EX16.7
General
Physics
Capacitors in Series

When a battery is connected to the
circuit, electrons are transferred from the
left plate of C1 to the right plate of C2
through the battery

As this negative charge accumulates on
the right plate of C2, an equivalent
amount of negative charge is removed
from the left plate of C2, leaving it with
an excess positive charge

All of the right plates gain charges of –Q
and all the left plates have charges of
+Q
General
Physics
More About Capacitors in Series

The charge on the capacitors is the same
 Q1 = Q2 = Q

The total potential difference is equal to
the sum of the potential differences across
the capacitors
 ΔV1 + ΔV2 =ΔV

The capacitors can be replaced with one
capacitor with a capacitance of
 1/Ceq = 1/C1 + 1/C2 + …

The equivalent capacitor must have
exactly the same external effect on the
circuit as the original series capacitors
The equivalent capacitance of a series
combination of capacitors is less than the
smallest of the individual capacitors

General
Physics
Equivalent Capacitance – Series: An
Example

Four series capacitors are replaced with their
equivalent capacitance
Active Figure: Capacitors Combined in Series
EX16.8
General
Physics
In demo, two equal capacitors were charged
in parallel and then reconnected in series.
What the total voltage be?
60
3
4
5
6
7
8
9
10
21
22
23
24
25
26
27
28
29
30
11
12
13
14
o.
ge
.
Ze
r
ar
rg
e
la
fa
as
ice
2
Tw
1
St
a
yt
he
sa
m
e
4.
sl
3.
15
Ha
l
2.
Stay the same
Twice as large.
Half as large.
Zero.
25% 25%
...
1.
25% 25%
16
General
17
18
19
20
Physics
Problem-Solving Strategy

Combine capacitors following the formulas

When two or more unequal capacitors are connected in
series, they carry the same charge, but the potential
differences across them are not the same


The capacitances add as reciprocals and the equivalent
capacitance is always less than the smallest individual
capacitor
When two or more capacitors are connected in parallel, the
potential differences across them are the same, but the
charges on them are not the same


The charge on each capacitor is proportional to its capacitance
The capacitors add directly to give the equivalent capacitance
General
Physics
More on Problem-Solving Strategy

Repeat the process until there is only one single
equivalent capacitor

A complicated circuit can often be reduced to one
equivalent capacitor



Replace capacitors in series or parallel with their equivalent
Redraw the circuit and continue
To find the charge on, or the potential difference
across, one of the capacitors, start with your
final equivalent capacitor and work back through
the circuit reductions
General
Physics
Problem-Solving Strategy,
Equation Summary

Use the following equations when working through the
circuit diagrams:
 Capacitance equation: C = Q / V

Capacitors in parallel:
Ceq = C1 + C2 + …
Q1 + Q2 = Q
ΔV1 = ΔV2 =ΔV

Capacitors in series:
1/Ceq = 1/C1 + 1/C2 + …
Q1 = Q2 = Q
ΔV1 + ΔV2 =ΔV
EX16.9
General
Physics
Energy Stored in a Capacitor
Energy stored = ½ Q ΔV
 From the definition of capacitance, this
can be rewritten in different forms

2
1
1
Q
Energy  QV  CV 2 
2
2
2C
EX16.10
General
Physics
Applications

Defibrillators



When fibrillation occurs, the heart produces a rapid,
irregular pattern of beats
A fast discharge of electrical energy through the heart
can return the organ to its normal beat pattern
In general, capacitors act as energy reservoirs
that can slowly charged and then discharged
quickly to provide large amounts of energy in a
short pulse
General
Physics
Capacitors with Dielectrics

A dielectric is an insulating
material that, when placed
between the plates of a
capacitor, increases the
capacitance


Dielectrics include rubber,
plastic, or waxed paper
C = κCo = κ(εoA/d)

The capacitance is multiplied by the factor κ when the
dielectric completely fills the region between the plates
General
Physics
Dielectric Strength
For any given plate separation, there is a
maximum electric field that can be
produced in the dielectric before it breaks
down and begins to conduct
 This maximum electric field is called the
dielectric strength

EX16.11
General
Physics
An Atomic Description of
Dielectrics
Polarization occurs when there is a
separation between the “centers of
gravity” of its negative charge and its
positive charge
 In a capacitor, the dielectric becomes
polarized because it is in an electric field
that exists between the plates

General
Physics
More Atomic Description
The presence of the
positive charge on the
dielectric effectively
reduces some of the
negative charge on the
metal
 This allows more
negative charge on the
plates for a given
applied voltage
 The capacitance
increases

General
Physics