Topic 2 - Capacitor Circuits

In the exam you are expected to know:

• Maximum working voltage;

• Temperature coefficient;

• Polarisation and leakage current;

• Use of data sheets;

• Relative advantages and disadvantages of different kinds of capacitor;

• Use of

• Use of

• 5RC as the time taken for a capacitor to discharge completely;

• Reactance to sinusoidal wave-forms only;

• Use of

• Sketch graph of the variation of reactance with frequency;

• Simple RC filter circuits as a voltage divider;

• Square waveforms.

• Use of the CRO.

How do Capacitors Work?

A capacitor is a device for storing of small amounts of charge.  At its simplest it consists of two metal plates separated by a few mm of air or other insulating material.  It stores a charge because electrons crowd onto the negative plate, and repel electrons on the positive plate, thereby inducing an equal and opposite charge.

You will be familiar with the units of the capacitor, Farads (F), and the relationships associated with them.  If you are not sure, this is a useful time to revise Q = CV, as well as E = ½ QV, and E = ½ CV².  These relationships will not be discussed further, and familiarity with them will be assumed.  Refer to A2 Module 4

Capacitance is defined as:

The ratio of charge stored on an isolated conductor to the change in potential.

Since we have a positive and negative plate, we have an electric field.

A 1 farad capacitor with its plates separated by 1 mm of air would need plates 10 km ´ 10 km, which is rather impractical.  A farad is a very big unit, and we are much more likely to use microfarads (mF) or nanofarads (nF).

The insulating gap between the plates of a capacitor is called the dielectric.  The reference dielectric is a vacuum, but air gives a value that is very similar.  We can use a dielectric other than air.  Some insulating materials do not affect the capacitance of the capacitor at all, but there are others, for example polythene or waxed paper that make the capacitance rise quite a lot.

Click HERE if you want to find out about the Physics of Capacitors.

Practical Capacitors

Very few capacitors consist of flat plates that we have looked at so far.  Instead, they consist of two layers of aluminium foil alternating between two layers of dielectric.  The whole lot is rolled up like a Swiss roll to make a compact shape.

Non electrolytic capacitors have a mica or polyester dielectric.  The value of the capacitors made in this way is quite low, up to about 10 mF.

Electrolytic capacitors are capable of holding a much bigger charge.  The aluminium metal plates are either side of a sheet of paper soaked in aluminium borate.  When the capacitor is charged up, there is a chemical reaction that deposits an aluminium oxide layer on the positive plate.  This acts as the dielectric.  The electrolyte soaked paper acts as the negative plate.

·        The electrolyte itself acts as the negative plate

·        The aluminium oxide layer is the dielectric.

·        The dielectric layer is very thin (10 ^–4 m), which results in a very large capacitance.  This can be as much as 100 000 mF.

Question 1 Describe the difference between an electrolytic and a non-electrolytic capacitor.   ANSWER

Leakage Current

In an electrolytic capacitor there has to be a current to maintain the aluminium oxide layer.  This is about 1 mA.  Over a period of time the charge leaks away.  This is called the leakage current.  Also it is important that the polarity of the capacitor is correct, otherwise the aluminium oxide layer is not made and the component will conduct.  The resulting heating effect can result in the capacitor exploding.

Working Voltage

All capacitors have a maximum working voltage.  All insulators have a maximum voltage at which they will retain their insulating properties.  The breakdown voltage is quoted in units of volts per metre, so it is actually an electric field.  The breakdown voltage of air is 3000 V/mm, so a 5 mm gap will insulate up to 15 000 V. The actual voltage at which the breakdown occurs depends on the thickness of the material.  The thinner the material, the lower the voltage that is needed before sparking will occur.  If sparking occurs over a dielectric, then a hole will be burned in the dielectric and that is the end of the useful life for the capacitor.

Capacitors with a high working voltage tend to be rather larger than capacitors of the same value at a low working voltage.  This is because the dielectrics tend to be thicker.

Question 2   What is meant by working voltage?  What would happen if you used a capacitor with a working voltage of 16 V at a voltage of 40 V?  ANSWER

Stability

As capacitors age, their values can change.  This too can lead to poor stability in circuits.  The graph below shows the capacitance change with age for an electrolytic capacitor at 105 ^oC.

From this graph, we can see that the capacitance falls as the capacitor gets older.  The effect is more marked with higher temperature.

Question 3 An electronics engineer is looking for a capacitor with a very specific value.  He cannot find the right type in the catalogue but comes across exactly the right type in a box of old recycled components.  Would he be wise to use it?

ANSWER

Temperature Coefficient

Capacitors, especially electrolytic, can lose their capacitance, i.e. hold less charge, when they get hot.  Physical and chemical changes can occur which would adversely affect the performance of the capacitor (in an electrolytic capacitor, this could be as simple as the electrolyte drying out).  The extent to which they do this is referred to as the temperature coefficient, which can be used to measure how much capacitance is lost.

Temperature coefficient is measured in parts per million per Kelvin (ppm/K). You will find nothing about temperature coefficient in the standard A-level texts, but it can be measured easily in a school physics laboratory.

We can see the effect qualitatively by setting up the simple experiment as above:

·        If the capacitor is cooled down with the freezer spray, we observe that the capacitance falls.

·        If we heat the capacitor with a hair dryer, we see the capacitance rise to a maximum, then it starts to fall away.

·        We can work out the temperature coefficient by working out the fraction by which the capacitance has changed and dividing that by the temperature change.

·        We can then convert that into parts per million.  1 % = 10 000 ppm.

We can show this as a graph:

Note:

·        If we increase the temperature, a maximum value is reached, and then the capacitance then falls away.

·        A mica capacitor shows hardly any change at all with temperature.  Its capacitance is stable compared with that of a ceramic bead capacitor.

This is important when capacitors are used in hot environments.  This graph shows how the capacitance of a capacitor falls as the temperature rises:

We should note the following about this graph:

·        The data was gained from a 22 mF capacitor operating at 10 V.

·        The capacitor was operating at 120 Hz

·        The capacitance change was measured after 1000 hours.

The decrease in capacitance can change the characteristics of the circuit so much that it will not work properly.

Question 4 Explain why it is essential that the temperature in which the circuit is going to operate at, is taken into consideration when choosing capacitors.  ANSWER

Data Sheets

Electronic engineers need to know the specifications of the components they are going to use.  They refer to data sheets in catalogues, which give them all the information that they need to make a choice.  For capacitors, data sheets might include:

·        Tolerance

·        Working voltage

·        Temperature coefficient

·        Physical size

·        Price

The table below shows data on several different values of ceramic capacitor.  These are actual values from a catalogue.

Notice that some tolerances are very slack.  In many applications, this doesn’t matter, but in others, such as tuned circuits, this can be significant.

If we needed a 4700 pF (4.7 nF) capacitor to work in a hot environment, we would see that its value is quite likely to be different to what we would expect, as it has a temperature coefficient that is 10%.  A high stability silvered mica capacitor has a much lower temperature coefficient (35 ppm/K), so would be more useful.  However it would cost £1-20, almost 10 times as much.

Now go on to Different Types of  Capacitor

Home            Physics A2                Module 9