Capacitance and Dielectrics 1.Capacitance Definition How to calculate the capacitance 2.Capacitor...
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Transcript of Capacitance and Dielectrics 1.Capacitance Definition How to calculate the capacitance 2.Capacitor...
Capacitance and Dielectrics
1.CapacitanceDefinitionHow to calculate the capacitance
2.Capacitor3.Energy stored in a capacitor4.Capacitor with dielectrics5.Dielectrics explained in an atomic
view
Lect. (4)
1
Capacitance: the definition. The capacitance, C, is defined as the ratio
of the amount of the charge Q on the conductor to the potential increase ΔV of the conductor because of the charge:
This ratio is an indicator of the capability that the object can hold charges. It is a constant once the object is given, regardless there is charge on the object or not. This is like the capacitance of a mug which does not depend on there being water in it or not.
The SI unit of capacitance is the farad (F)
V
QC
QV
C=
1V
1C F1
2
More About Capacitance
Capacitance will always be a positive quantity The capacitance of a given capacitor is constant The capacitance is a measure of the capacitor’s
ability to store charge The farad is an extremely large unit, typically you
will see
microfarads (mF=10-6F),
nanofarads (nF=10-9F), and
picofarads (pF=10-12F)
3
Capacitors are devices that store electric charge Any conductors can store electric charge, but Capacitors are specially designed devices to store a lot of
charge
Examples of where capacitors are used include: radio receivers filters in power supplies to eliminate sparking in
automobile ignition systems energy-storing devices in
electronic flashes
4
How to Make a Capacitor?
Requirements: Hold charges The potential increase
does not appear outside of the device, hence no influence on other devices.
For example, a `parallel plate’ capacitor, has capacitance
area surface theis
,0
0
A
d
A
d
A
Ed
A
V
QC
02
E
00 22
E
0E0
E 0E
d
EdV 5
A Real Parallel Plate Capacitor charged up with a battary Each plate is connected to a terminal of the battery
The battery is a source of potential difference If the capacitor is initially uncharged, the battery
establishes an electric field in the connecting wires This field applies a force on electrons in the wire just
outside of the plates The force causes the electrons to move onto the
negative plate This continues until equilibrium is achieved
The plate, the wire and the terminal are all at the same potential
At this point, there is no field present in the wire and the movement of the electrons ceases
The plate is now negatively charged A similar process occurs at the other plate, electrons
moving away from the plate and leaving it positively charged
In its final configuration, the potential difference across the capacitor plates is the same as that between the terminals of the battery
V
6
Energy stored in a charged capacitor
Consider the circuit to be a
system Before the switch is closed, the
energy is stored as chemical energy in the battery
When the switch is closed, the energy is transformed from chemical to electric potential energy
The electric potential energy is related to the separation of the positive and negative charges on the plates
A capacitor can be described as a device that stores energy as well as charge
7
How Much Energy Stored in a Capacitor?
q -q
dq
To study this problem, recall that the work the field force does equals the electric potential energy loss:
VQUWE
E
V
dqC
qVdqdWB
When the charge buildup is q, move a dq, the work is
This also means that when the battery moves a charge dq to charge the capacitor, the work the battery does equals to the buildup of the electric potential energy:
UWB
We now have the answer to the final charge Q:
UC
Qdq
C
qdWW
BB 2
2
008
Energy in a Capacitor, the formula
When a capacitor has charge stored in it, it also stores electric potential energy that is
This applies to a capacitor of any geometry The energy stored increases as the charge
increases and as the potential difference (voltage) increases
In practice, there is a maximum voltage before discharge occurs between the plates
22
)(2
1
2VC
C
QU E
9
Energy in a Capacitor, final discussion
The energy can be considered to be stored in the electric field
For a parallel-plate capacitor, the energy can be expressed in terms of the field as
U = ½ (εoAd)E2
It can also be expressed in terms of the energy density (energy per unit volume)
uE = ½ eoE2
10
11
Circuit Symbols
A circuit diagram is a simplified representation of an actual circuit
Circuit symbols are used to represent the various elements
Lines are used to represent wires
The battery’s positive terminal is indicated by the longer line
12
Capacitors are in Series:
When capacitors are in series,
the charge is the same on each capacitor.
321 VVVVt C
QVCVQ
3
3
2
2
1
1
C
Q
C
Q
C
Q
C
Q
t
t
321 QQQQt
321
1111
CCCCt
Capacitors are in Parallel
When capacitors are in parallel ,
the total charge is the sum of that on each capacitor.
321 QQQQt CVQ
332211 VCVCVCVC tt
321 VVVVt
321 CCCCt
Equivalent Capacitance, Example
The 1.0-mF and 3.0-mF capacitors are in parallel as are the 6.0-mF and 2.0-mF capacitors
These parallel combinations are in series with the capacitors next to them
The series combinations are in parallel and the final equivalent capacitance can be found 15
A dielectric is a nonconducting material, an electrical insulator, such as rubber, glass, or waxed paper.
When a dielectric is inserted between the plates of a capacitor, the capacitance increases by a dimensionless factor , which is called the dielectric constant of the material.
The dielectric constant is the ratio of the field without the dielectric (Eo) to the net field (E) with the dielectric:
= Eo /E
Dielectrics
16
• Dielectrics
• The dielectric constant varies from one material to another.
The voltages with and without the dielectric are related by the factor as follows:
17
if E0 is the electric field without the dielectric, the field in the presence of a dielectric is
18