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Capacitors and capacitance

Capacitance (symbol C) is a measure of a capacitor’s ability to store
charge. A large capacitance means that more charge can be stored.
Capacitance is measured in farads, (symbol F). However 1F is very
large, so prefixes (multipliers) are used to show the smaller values:
 μ (micro) means 10-6 (millionth), so 1000000μF = 1F.
 n (nano) means 10-9 (thousand-millionth), so 1000nF = 1μF.
 p (pico) means 10-12 (million-millionth), so 1000pF = 1nF.
In a way, a capacitor is a little like a battery. Although they work in
completely different ways, capacitors and batteries both store
electrical energy, inside the battery; chemical reactions produce
electrons on one terminal and absorb electrons at the other terminal.
A capacitor is a much simpler device, and it cannot produce new
electrons – it only stores them.
Like a battery, a capacitor has 2 terminals. Inside the capacitor, the
terminals connect to 2 metal plates separated by a dielectric. The
dielectric can be air, paper, plastic or anything else that does not
conduct electricity and keeps the plates from touching each other.

 The plate on the capacitor that attaches to the negative
terminal of the battery accepts electrons that the battery is
producing.
 The plate on the capacitor that attaches to the positive
terminal of the battery loses electrons to the battery.
Once it’s charged, the capacitor has the same voltage as the battery
(1.5 volts on the battery means 1.5 volts on the capacitor). For a
small capacitor, the capacity is small. But large capacitors can hold
quite a bit of charge.

Here you have a battery, a light bulb and a capacitor. If the capacitor
is pretty big, what you would notice is that, when you connected the
battery, the light bulb would light up as current flows from the battery
to the capacitor to charge it up. The bulb would get progressively
dimmer and finally go out once the capacitor reached its capacity.
Then you could remove the battery and replace it with a wire.
Current would flow from one plate of the capacitor to the other. The
light bulb would light and then get dimmer and dimmer; finally going
out once the capacitor had completely discharged (the same number
of electrons on both plates).
The unit of capacitance is a farad (symbol F).
A 1-farad capacitor can store one coulomb (Q) of charge at 1 volt (V).
A 1-farad capacitor would typically be pretty big. So you typically see
capacitors measured in microfarads (millionths of a farad).
These sub units are:
farads 1microfarad( F)10 F also 10 F 1nano Farad
1000000
1 6 9     
microfarads picofarad pF F 12 1 ( )10
1000000
1  
There is a direct relationship between the Voltage (V) placed across
the plates of a capacitor and the charge (Q) held by them. If the
voltage is doubled the charge is doubled, if the charge is halved then
the voltage is halved etc. This tells us that the ratio of charge to
voltage is constant and this is known as the capacitance (C) of the
capacitor i.e.:

The Maximum power transfer theorem

Earlier it was demonstrated the existence of internal resistance in the
power supply such as in a battery, and the effect that this resistance
has on the voltage supplied to the load was discussed.
The load voltage is the actual voltage given out by the power supply
after it has dropped a percentage of its EMF voltage across its
internal resistance.
How much voltage is dropped across the internal resistance depends
on the value of the internal resistance in relation to the value of the
load.
The relationship between the values of load resistance and internal
resistance is also important for another reason. Maximum power can
be developed in a load resistance only when the values of the load
resistance and the internal resistance of the source are equal.
This statement is known as the maximum power transfer theorem.
Figure shows a 12V EMF source of internal resistance 3 ohms
connected to a load resistance of 1 ohm. The total resistance in the
circuit is 4 ohms and the circuit current is therefore 3 amperes. The
power developed in the load (I2R) is therefore 9 watts.

Figure B shows the same source connected to a load resistance of 3
ohms. The total resistance is now 6 ohms and the current 2
amperes. The power developed in the load is now 12 watts.

Figure C shows the effect of inserting a load of 9 ohms. The total
resistance is now 12 ohms and the current 1 ampere. The power
developed in the load is now 9 watts.

The above examples have used the power formula I2R, but any of the
other
2 formulae, V2/R and I x V could be used.
Example ‘B’ using V2/R would give the same answer by measuring
the volts drop across the load resistance and then dividing the square
of that by the actual load resistance. Try it, it works!
The graph shown below shows these and other results by plotting the
power developed in different values of load resistance. It shows that
maximum power is developed in the load only when the load
resistance is equal in value to the internal resistance of the source
and, thus, illustrates the maximum power transfer theorem.
In many circuits we are interested in transferring the maximum
possible amount of power to a load circuit. To do this we must
‘match’ the load resistance to the internal resistance of the source.
Matching is very important in electronic circuits that usually have a
fairly high source resistance. A typical example is the ‘matching’ of
an audio amplifier to a loudspeaker and we shall consider this and
many others later in the book.
Note however that batteries, generators and other power supply
systems cannot be operated under maximum power transfer
conditions. It can be seen from the previous Fig that to do so would
result in the same amount of power being dissipated in the source as
was supplied to the load. This is obviously extremely wasteful of
energy and power supply systems are always designed to have the
minimum possible internal resistance to minimize losses.

Connection of Cells

All cells contain an internal resistance caused by factors such as the
plate material and size etc. In primary cells this resistance is quite
high, with secondary cells due to the plates having a much larger
cross sectional area compared to primary cells the internal
resistance is considerably lower.
When cells and batteries are connected together the internal
resistance has to be taken into account so as to determine the
output characteristics, this is achieved in the following ways:
3.12.5.1 Series
In order to obtain a high voltage from any cell type it is necessary to
connect the cells in series. In this arrangement the voltage from
each cell is added for example 6, x 2volt cells connected in series
will give an open circuit terminal voltage (EMF) of 12volts. The
disadvantage of a series arrangement will be that the internal
resistance of each cell is also added, this results in a high EMF
voltage but low current output, therefore an increase in current
drawn from the cell will result in a drop in the output voltage due to
the high internal resistance.
In this arrangement all the cells will be required to be of the same
ampere/
hour rating, as this type of connection will take the lowest
ampere/hour rated cell as its output.
3.12.5.2 Parallel
If cells are connected in parallel this will have the effect of the individual
cell voltage being the EMF voltage, due to the large surface area of the
all the cathode plates being connected together, and also all the anode
plates being connected together, the internal resistance is greatly
reduced, in this arrangement the current from each cell is added
together, therefore the current capacity from a parallel connected group
of cells is greatly improved, and as the EMF voltage is the same as the
cell voltage it is considerable more stable when a load is connected to
it also.
In this arrangement the cells ampere/hour rating does not need to be
considered, however the voltage rating of each cell needs to be equal
as this type of connection will reflect the lowest voltage of cell as its
EMF voltage.

Series/Parallel
From the 2 methods of connection above, it would make sense to
connect all cells in a battery in a series/parallel configuration, this
would provide the battery with a high voltage and also a high current
capacity with an overall lower internal resistance, in this
arrangement the power obtained from the battery would be at its
maximum.

EMF (Terminal Voltage) and internal
Resistance
Internal resistance in batteries is mainly due to the resistance of the
electrolyte and the cross sectional area of the plates. The voltage
that is measured across the terminals of the battery when it is off
load is known as the EMF voltage. When a load is connected to a
battery the current flows through the internal resistance and causes
a voltage drop proportional to this resistance, if the internal
resistance remains constant then the fall in the terminal voltage will
be proportional to the load current.
With switch “s” open, the Voltmeter V reads EMF (off load voltage).
With switch “s” closed, the Voltmeter reads Pd (the volt drop across
the load or on-load voltage).

Alkaline Batteries

There are several types of alkaline batteries, so to differentiate the
types, the metal used in the manufacture of the plates usually gives
them their name, for example the most common in use on aircraft is
the Nickel/Cadmium battery as it is these 2 metals that are used for
the plates. However in all alkaline batteries the electrolyte solution
used is Potassium Hydroxide which has a specific gravity of 1.24 to
1.30, dependant on the size and material used for the metal plates
this will determine the value of EMF of the cell, with some cells being
as low as 1.2volts.
Semi Sealed
The cells in these batteries are arranged in steel containers and fitted
with safety valves, this is due to the fact that the cells can be charged
at a high rate – and so can be easily overcharged, this overcharge will
make the electrolyte “bubble” gas and create a large amount of heat,
which can if not dealt with cause the battery to go into a state of
thermal meltdown, Under normal conditions these batteries require
very little maintenance and only a periodic capacity check.
Semi Open
These type of batteries are constructed similar to the semi sealed type,
but when on charge they are deliberately allowed to “gas”, this gassing
is allowed to vent to atmosphere, this aids the temperature control of
the cells and indeed is used to monitor the battery charge by switching
the battery charger on or off dependant on the temperature reached by
the cell.
Due to the cells being allowed to gas during charge the recharge time
is considerably shorter than the semi sealed type however this has the
disadvantage that the electrolyte requires “topping up” more often, the
frequency of this topping up will be determined by the aircraft manual.
The cells are fitted with the same type of vent as the lead acid battery
in that they allow the electrolyte gasses to escape but not the liquid.

Nickel Cadmium Alkaline
This is a common type of alkaline battery; the plates are formed on
a woven wire mesh by heating, the cathode plate is formed by using
Nickel salts and the anode by using Cadmium salts, a separator of
nylon cloth and a gas barrier of cellophane is used between them,
the electrolyte has a specific gravity of 1.3 and consists of
Potassium Hydroxide and distilled water.

Chemical Reaction
The chemical reaction of alkaline batteries works on the same principle
as the lead acid battery:However as can be seen, the difference is that the electrolyte does not
change its specific gravity or chemical structure during
charge/discharge, it is used purely as a medium in which the electrons
can flow through between the plates. As the charge of the battery
cannot be determined from the electrolyte specific gravity as in the lead
acid type, the temperature of the cell has to be monitored to determine
the charge state, for this reason, switching on or off the charge supply
to maintain the correct ampere/hour rating

Lead Acid Batteries

Construction
These batteries use an impact and acid resistant case for each
individual cell, which is made from polystyrene compounds. Each
cell case is moulded so that they provide outlets for the terminal
posts so that each cell can be connected with ease to the adjoining
cell, the case also houses a vent valve, which whilst the battery is
being charged allows gases to escape but does not allow the
electrolyte to leak out, the method of connecting the cells varies
dependant on the required use of the battery, and will be discussed
later.
3.12.3.2 Electrolyte
Lead acid batteries consist of cells with an electrolyte made of
sulphuric acid and water mixed to a specific gravity of 1.270 for a
fully charged battery, only distilled water is used in this mix, as the
impurities found in normal tap water will reduce the life and charge
of the cells.
As the cells are discharged and charged, the level of electrolyte will
decrease and so periodically the battery cells will require a “top up”
of distilled water, if this action is required it is to be noted that the
acid is always added to the water, as the reverse procedure is
extremely dangerous, because the water will react violently with the
acid and literally explode when added.
A fully charged cell will have a voltage in excess of 2.5volts after its
charge this will drop to 2.2volts after an hour standing, during
discharge the cell voltage will drop to 2volts and will remain at this
level for the majority of the cell charge life after this time, which is
dependant on the load connected to the cell, the voltage of the cell

will drop to 1.8volts and is considered to be discharged. Because the
voltage remains at a constant 2volts for the vast majority of the time,
this is considered to be the cells nominal voltage value.

The definition of capacity in terms of batteries is the quantity of
electricity that can be taken from a fully charged cell at a specified
discharged rate measured in amps, before the cells nominal voltage
of 2volts drops to a defined level of 1.8volts. Battery capacity is
therefore measured in terms of current and time i.e. ampere-hours,
and is expressed as a percentage against the maximum available
amps/hours for that specific type of cell. The factors, which affect
the battery capacity, are the area and number of plates, strength of
electrolyte and temperature.

/ discharge voltage versus time
It can be seen that during the discharge the voltage of each individual
cell remains constant for a considerable time at approximately 2volts,
however this is only true if the load connected has a small current
draw, If a larger current is drawn from the cell the discharge will
become more linear as the voltage drops more rapidly. What can also
be determined from the graph is that the voltage value cannot be used
to determine the amount of charge in the battery, consider this graph.

Coulomb and Electron Theory

We have seen that a current of electricity ( ) is a flow of electrons but
the electron itself is too small to be of use as the unit of electrical
quantity and therefore a more practical unit consisting of many
millions of electrons has been chosen. It is called the Coulomb (C)
and is 6.28 x 1018 electrons.
Note: This is a Quantity of electricity (Q) not a measure of current,
but it is used to define the unit of electrical current the
AMPERE (A). When a current of one ampere is flowing in a
conductor, 1 coulomb of electrons pass any point in the
conductor every second. In other words the size of an
electrical current is dependent upon the rate of flow of
electrons not a number of electrons.
We can write this in equation form.
Thus1 ampere of current flowing in a conductor for 1 hour is
equivalent to 3600 Coulombs and this is called an amperehour.
Now we have to look at what makes the electrons flow in a conductor
to form an electric current. Consider the diagram in which 2 bodies
with opposite charges on them are fixed in their position and not
joined.

Electron Theory
If the bodies were free to move they would be attracted to one
another so clearly there is potential mechanical energy between
them. There is also electrical potential energy between them since
we know that if a conductor joins them, electrons will flow from the
negative body to the positive body until the bodies are equally
charged.
Therefore the oppositely charged bodies are producing the energy
required to move the electrons, i.e. to produce a current of electricity.
The oppositely charged bodies are said to have a potential difference
(PD) between them and the size of this PD is measured in the unit of
the Volt (V).

Conventional Theory
Conventional theory, also known as hole theory, states that current
flows from positive to negative. Protons or the lack of electrons (the
holes) move towards the negative. (Current flow direction in hole
theory is the opposite of that in Electron Theory.)

Electrical terminology
Having studied electricity at the atomic level we have met a number
of words, which need to be defined and explained before we move
on.
The laws governing the behaviour of the different units are dealt with
in the relevant section rather than including them in these definitions.
Potential Difference
Is the difference between charge values, which exists at the atomic
level in materials with free electrons.
The unit of potential difference (PD) is the Volt, which is defined as:
‘The difference of potential across a 1 ohm resistor carrying a
current of 1 ampere.’
Electro-Motive Force
This is the ability to cause current to flow in a complete circuit.
The unit of EMF is the Volt (V).
Note: It should be noted that both EMF and PD are measured in the
same units, they are, in fact, both differences in charge potential.
However, it is important to realize that an EMF is the force to do work,
i.e. cause current to flow, whereas PD is the volts drop as a result of
the current flow. Another way to look at it is that the EMF is off- load,
the PD is on-load.