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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.