Topic 9 Capacitors

Capacitors consist of two metal plates separated by a layer of insulating material called a dielectric.

  Capacitance is measured in units called farads (F). A farad is a very big unit, and we are much more likely to use microfarads (mF) or nanofarads (nF).

•     1 mF = 1 × 10^-6 F
•     1 nF = 1 × 10^-9 F

  The symbol for a capacitor is shown below:

There are two types of capacitor, electrolytic and non-electrolytic.

• Electrolytic capacitors hold much more charge
• Electrolytic capacitors have to be connected with the correct polarity, otherwise they can explode.

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.

Stability

As capacitors age, their values can change.  This too can lead to poor stability in circuits.

Temperature Coefficient

Capacitors, especially electrolytic, can lose their capacitance, i.e. hold less charge, when they get hot.  The decrease in capacitance can change the characteristics of the circuit so much that it will not work properly.  Therefore it is essential that the temperature in which the circuit is going to operate at is taken into consideration when designing a circuit and choosing the components.

The results are like this:

From this graph we can see that:

• Mica capacitors are very stable with temperature
• Ceramic bead capacitors have a linear relationship.

Other types of capacitor have a temperature at which their capacitance is at a maximum.  It falls away either side of the optimum.

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

Click HERE to find out more about capacitors.  You won’t need to know this for the AS exam, but you might be interested.

Capacitors in Series and Parallel

Parallel Capacitors

Here is a circuit consisting of two capacitors in parallel.  They have values C1 and C2 and are connected to a battery of voltage V.

• Like all parallel circuits the voltage across the capacitors is the same.
• The total charge is the sum of the charges on the capacitors.  It’s like the currents in parallel resistors adding up.

  Ctot = C1 + C2

  This is true for any number of parallel capacitors, so

  Ctot = C1 + C2 + C3 + … + Cn

 Click HERE for a worked example

Series Capacitors

Here is a circuit consisting of two capacitors in series.  They have values C1 and C2 and are connected to a battery of voltage V.

  In any series circuit:

• The voltages add up to the battery voltage
• The current (charge) is the same all the way round.

• Since Q = It, it is reasonable to say that the charge that has moved is the same all the way round.  If a number of electrons of total charge of Q crowds onto the negative plates of C₂ then the same number of electrons are repelled away from the positive plates.  These crowd onto the negative plates of C₁ and repel the same number away from the positive plates.

Now we know that V = Q/C and that Vtot = V1 + V2.  So we can write:

                                     1   =  1   +    1

                                    Ctot    C1       C2

This gives us a general relationship for any number of series capacitors:

                                     1   =  1   +  1  +  1  +  …  +  1

                                    Ctot    C1     C2    C3               Cn

We can tackle problems that involve both series and parallel capacitors in a similar way to the way we tackle problems with combined series and parallel arrays of resistors.

  Click HERE for a worked example.

When you tackle problems involving both series and parallel capacitors in the same circuit, you may find it helpful to adopt the following problem solving strategy:

• Work out the single capacitor equivalent of the parallel capacitors
• Then use this answer to work out the single capacitor equivalent of the series capacitors.