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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.:

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.