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CAPACITORS
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ELECTRIC FIELD STRENGTH
What is it? ANS:Is the force that an electric charge
experiences within a specific space(field).
E = F/q
Symbol: E Units:Newtons perCoulomb (NC-1)
Remember that electric fields act either inwardoroutwards
dependent on thecharge:
+ -
Field lines represented
with an arrow henceare vectors.
Field lines are stronger
when closer together.
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FIELD LINES BETWEEN PLATES
If parallel plates are charged then a uniform electric field is then
established:
- - - - - - - - - - - - - - - - - - - -
+ + + + + + + + + + + + + + + + + +
Note:
The field strength is the same wherever the charge happens to be
e.g. A; B or C.
BA
C
At the edges D the field strength is weakeras the field lines are
longer, the plates being further apart.
D
If a charge is moved from the negative plate
to the positive then potential energy (EP) is
produced or a potential difference set up V.
This is also dependent on the distance d
between the plates thus two equations can
be produced:
EP = qV
E = V/d
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CAPACITORS
What is it? ANS:It is an electrical component that can
store electrical charge and release itsome time later.
Symbol:C Units: Farad (F)
USES
1. Storing energy as in flashphotography
2. Time delays in electroniccircuits
3. As filters in electronic circuits
4. In tuning circuits
Often made like a swiss
roll by rolling metal plates
with a insulator (dielectric)
in between and wires
attached to each plate.
CEveryday capacitors are measured in either
QF (10-6); nF (10-9); pF (10-12).
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BASIC CONSTRUCTION
INSULATOR
(DIELECTRIC)
CONDUCTOR CONDUCTOR
+-
TWO
OPPOSITELY
CHARGED
CONDUCTORSSEPARATED
BY AN
INSULATOR -
WHICH MAYBE AIR
The Parallel Plate Capacitor
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WHAT DOES A CAPCITOR DO?
+
+
+
+
+
+
+
+
-
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+-
The battery causes the
flow of electrons to
accumulate on one plateand attracts an equal
number of electrons fro
the other plate, leaving the
plates oppositely charged.
When fully charged:
Flow of e- stops.
Both plates equal &
oppositely charged.
Pd across plates, V =
Vsupply.
Electric field, E exists
between plates E = V/d.
dE = electric field strength
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CAPACITANCE
This is the amount of charge a capacitor can store when connected
across a potential difference of 1 volt. Obviously the larger the
capacitor the more charge it can contain.
The capacitance (C) of a capacitor which stores a charge, Q
coulombs on each plate when connected across a supply of volts, V,
is given by:
C = Q/V
Capacitors have a finite voltage at which they work at. If the voltage is
exceeded then the dielectric will melt and the plates suddenly come
into contact. Short circuit, capacitor explodes!!
BOOM
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Charge stored [Q] depends on p.d. [Volts] applied [V]
Q
V
Gradient = C
Remember that the capacitance, C, is defined as
the charge required to raise the potential by one voltthe charge required to raise the potential by one volt
Hence C = Q/V
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WHAT FACTORS DETERMINE CAPACITANCE?
Depend upon three factors:
1. The area, A, of the parallel plates.
2. The distance, d, separating the plates.
3. The properties of the dielectric material
between the plates.
1. Plates that
have a greater
area can store
more charge,
thus:
2. Plates that are
closer
together can
store more
charge, thus:
C w A C w 1/d
C = constant x A/d
Constant = absolute
permittivity of free
space (Io)
I0 = 8.84x10-12 Fm-1
C = (IoA)
d
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Area ofPlate overlap
= A
dd = plate separation
Medium relativepermittivity = Ir
d
AC
rII0
!
I0 = the permittivity of freespace = 8.86. X 10-12 F m-1
For air or a vacuum, Ir = 1
THE DIELECTRIC CONSTANT:
Different materials insulate at
differing amounts thus changing
the capacitance, called dielectric
effect. The dielectric constant (Ir)gives the proportion by which C
increases when dielectric placed
between the plates.
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The dielectric constant does not a have a unit as it is the ratio
between two capacitance values:
Ir= Cdielectric
Cair
Examples of dielectric
constants include:
Dielectric material IrAir 1.0
Oiled paper 2.0
Polystyrene 2.5
Glass 6.0
Water 80
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THE ENERGY STORED IN CAPACITOR:
As charge, Q, is packed onto the plates work needs to be done.
Repulsive forces want to push the electrons away from the negativeplate towards the positive. The battery supplies the push, energy, to
pack these electrons. The push, pd, the battery has the greater the
capacitance, C. Thus energy provided by the cell must equal:
E = Q x V
Area undergraph= energychange
= Q x V
Q
V
For a
capacitor
V vs Q isa straight
line
graph
V
Q
Area
under
graph =
x Q x V
Energy provided by cell Energy stored in capacitor
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As capacitance is the amount of
stored charged then the energy
inside a capacitor then two
formulae can be produced.
EP = CV2 [Substituting Q = CV into EP = QV]
EP = Q2/C [Substituting V = Q/C into EP = QV]
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CAPACITORS IN SERIES & PARALLEL:
+-
Q- Q-Q+ Q+
C1 C2
V2V1
V
Charge on each capacitor is
the same.
V = V1 + V2
For two or more capacitors:
1 = 1 + 1 .
Cs C1 C2
SERIES PARALLEL
+-
V
C1
C2
Q1
Q2
Voltage across each capacitor
same as, V, of cell.
Q = Q1 + Q2
For two or more capacitors:
Cp = C1 + C2 .
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RC CIRCUITS
CHARGING A CAPACITOR:
An RC circuit is one that contains a resistor, R and a capacitor, C.
R
CV
CURRENT:
When a capacitor begins to charge there is a massive flow of charge
to the negative plate. This then decreases with time as repulsion
from that plate pushes electron away.
VOLTAGE:When the capacitor is empty there is zero charge stored. As
electrons rush in there is a huge build up of energy. This begins to
level out as repulsion denies entry of any further charge.
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Imax
time0
From this two graphs can be drawn for the charging of a capacitor
with relation to what happens to current I and voltage V.
Volts
VC
Amps
Current starts at maximum Imax
and then decreases to zero asthe negative plate fills up with
negative charge. Repulsion
pushes against the force of
the battery
Voltage starts at zero and
rapidly increases until itbegins to reach maximum.
Now repulsion prevents any
further charge entering so the
energy remains constant.
CURRENT GRAPH VOLTAGE GRAPH
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DISCHARGING A CAPACITOR:
When a capacitor discharges the voltage and current graphs are the
same. They start at a maximum and follow the inverse curves downtowards zero, although it is worth noting that they dont reach zero.
Volts, V
Time, t0
V0
Current I
Time, t
I0
Explain what is happening in each of thesegraphs andwhy
they are the same.
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TIME CONSTANT:
Time constant is the measure of time it takes for a capacitor to reach
63% of the total amount of voltage or current that it can store/releasedepending on whether it is charging/discharging. The largerX, the
slower the process.
It is given the term tau, X and is measured in seconds, s. The
formula for time constant is:
X = RC
Where:
X = time constant (s)
R = resistance ()
C = capacitance (F)As the voltage never reaches max orAs the voltage never reaches max or
zero, then the total time taken cant bezero, then the total time taken cant be
measured hence that is why 63% of themeasured hence that is why 63% of thetime is used. (time is used. (Same for currentSame for current))
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Volts
63%
VOLTAGE GRAPH
Time, t
Vmax
X
100%
86%
2X
This works exactly thesame for discharging and
for current they are just
reversed.
The second time constant
is 63% of what is left.