Capacitors
Introduction


Capacitors store electric charge. Think of a capacitor as a 'bucket' that can be filled up with charge.

Capacitors are used to introduce time delays into circuits. They are used together with integrated circuits to make pulse-producing astables and monostables. Tone controls and similar filter circuits use capacitors to control which frequencies of signal will be transferred from one part of a circuit to another.



The circuit inside this see-through telephone uses lots of capacitors. Zoom in to see the circuit in more detail.

Capacitors have a wide variety of applications and you will find them in almost every electronic circuit.

What is a capacitor?
All capacitors consist of two regions of a conducting material, called plates. The plates are separated by a space filled with an
insulator
An insulator is a material which prevents the flow of current. Most non-metals are insulators.
insulator
:

Figure 1.   Structure of a capacitor.
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The insulator can be an air-filled gap, as shown in Fig.1, but often other insulators like ceramic or plastic are used.

How can this arrangement store charge? You can understand what is going on from Fig.2, which shows an enormously magnified cross-section of a capacitor.

Figure 2.   Storing charge.
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The small blue dots represent electrons. To fill the capacitor you need to connect a
voltage
Potential difference, or voltage V is a measure of the difference in energy between two points in a circuit. Charges gain energy in the battery and lose energy as they flow round the rest of the circuit.
voltage
across it. Click 'charge' to see how this affects the electrons. In this case, electrons are pushed onto the top plate. Since like charges repel, this means that electrons are also pushed away from the bottom plate.

This effect depends on electrostatic forces between charged particles. No electrons cross the gap between the plates.

The capacitor now has extra electrons on one plate and fewer electrons on the other plate. The capacitor has stored electrical energy, which can be released later.
Select the words which best complete each sentence.

  • A capacitor consists of two plates of , separated by a layer of . When a is applied across the capacitor, is stored.
  • Click here to mark the question


It is possible to increase the charge stored by:

  • increasing the area of overlap of the plates

  • moving the plates closer together

  • using a different insulator (some insulators work much better than others)

  • increasing the voltage across the capacitor

Types of capacitor
Two symbols are used to represent capacitors in
circuit
A circuit is a closed conducting path.
circuit
diagrams:


Figure 3.   Capacitor symbols.
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The first symbol shows a non-polarized capacitor. The symbol reflects the construction of a capacitor: two regions of
conductor
A conductor is a material which allows current to flow easily. Most metals are conductors.
conductor
separated by a space. There is no difference between the plates. This means that a non-polarized capacitor can be connected either way round in a circuit.

The measurement unit for capacitance is the farad, F.
This unit is defined as the capacitance that will store one coulomb of charge when the voltage across the capacitor is one volt.
     It makes sense to define capacitors in fundamental units of charge and voltage. However, a 1 F capacitor turns out to be an absolutely enormous capacitor, more like a swimming pool than a bucket.



The units used to measure real capacitors are much smaller:


Unit Symbol Farad equivalent
microfarad µF 1 × 10−6 F
nanofarad nF 1 × 10−9 F
picofarad pF 1 × 10−12 F



The largest of these, 1 µF, is a million times smaller than a farad. Nevertheless, 1 µF is a large value for a non-polarized capacitor.
Convert 2.2 µF to the equivalent value in nanofarads.
  • Click here to mark the question
Convert 100 pF to the equivalent value in nanofarads.
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Fig.4 shows a selection of non-polarized capacitors:

Figure 4.   Non-polarized capacitors.
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Usually, the capacitor value is printed directly on the component, though you may need good eyesight to see it. Larger values are often marked in µF: '0.01' represents 0.01 µF or 10 nF, while '0.1' indicates 0.1 µF or 100 nF. Sometimes, the μ sign is used in place of the decimal point: μ47 means 0.47 μF = 470 nF.

Smaller values are marked with codes like '102' or '221'. These codes give values in picofarads. The third digit is interpreted in the same way as the
multiplier
The multiplier band of a resistor colour code tells you how many zeros to add to the first and second digit numbers.
multiplier
in the
resistor
A resistor is an electronic component with a particular resistance values. Resistors limit current.
resistor
colour code: '102' means '10' followed by two '0's', that is, 1000 pF = 1 nF. '221' translates to '22' with one '0', 220 pF.

When you start using capacitors, you will quickly become familiar with these codes.

Often, capacitors are named according to the insulator used. Ceramic and polyester types are common.

Figure 5.   Two non-polarized capacitors.
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Which capacitor in Fig.5 do you think will be able to store more charge?
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Other things being equal, bigger capacitors are bigger buckets.

It is interesting to break open a 220 nF or 470 nF polyester capacitor. Rolled up inside you can find a thin sheet of plastic, the polyester, with thin sheets of aluminium foil on either side:

Figure 6.   Foil from a single 470 nF polyester capacitor.
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With care, it is possible to separate the sheets of foil from the polyester layer. You will be surprised by how much foil there is! Capacitors really do consist of two regions of conductor separated by an insulator. One wasted capacitor is enough.

Polarized capacitors, also called electrolytic capacitors, are manufactured to provide capacitors with larger values.

Like the two plates in the symbol, the two plates of a polarized capacitor are not the same. A polarized capacitor must be connected with its positive and negative terminals the right way round.

Fig.7 shows examples of polarized capacitors. They are clearly marked to show you which way round to connect them.

Figure 7.   Radial polarized capacitors.
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The capacitors in Fig.7 are 'radial' capacitors with both leads at the same end. The leads are of different lengths: the longer lead is the positive terminal. Usually, there is a prominent stripe with arrows pointing towards the negative terminal.

'Axial' capacitors have the leads coming out of opposite ends.

Figure 8.   Axial polarized capacitors.
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It is still clear which end is which. The negative terminal is indicated by arrows and is connected to the outside metal case. The positive terminal is insulated from the metal case and is always the end nearer to the bump in the capacitor body.

Examine some polarized capacitors. You will find that physically larger capacitors tend to have larger values. As with non-polarized capacitors, bigger capacitors are bigger buckets.

It is possible to buy polarized capacitors with values up to 10,000 µF, sometimes even more. However, the maximum value you are likely to use for most circuits is about 1000 µF. The minimum value for polarized capacitors you are likely to use is 1 µF.
Match each measurement unit with its equivalent in farads:
  • 10−6 F
    10−9 F
    10−12 F
  • Click here to mark the question
Select the words which best complete each sentence:

  • Capacitors which can be connected either way round in a circuit are called capacitors. They have values measured in .

    Capacitors with separate positive and negative connections are called capacitors. They have values, usually measured in .
  • Click here to mark the question
Working voltage
Capacitors are usually marked with a working voltage. This is the maximum voltage which is allowed across the capacitor and must not be exceeded.

Figure 9.   Capacitors showing working voltage ratings.
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For most non-polarized capacitors, the working voltage is high: 63 V, 100 V, 250 V, or more. In contrast, polarized capacitors tend to have lower working voltages: 6 V, 10 V, 16 V, 25 V, and so on.

Find out about the working voltage in the simulation, Fig.10, by changing the power supply voltage.


Click on the figure below to interact with the model.

 Figure 10.  Investigating working voltage.

What is the maximum working voltage of the capacitor in Fig.10?
  • Click here to mark the question


It is important to check that the working voltage for polarized capacitors is more than the power supply voltage of your circuit. If the working voltage is exceeded, or if a polarized capacitor is connected the wrong way round, it is likely to explode! Check carefully to make sure this does not happen.

Charging and discharging
Operate the switch in the simulation, Fig.11, to charge the capacitor. The stored charge is indicated by small + signs on the positively charged side of the capacitor, with − signs on the negatively charged side.


Click on the figure below to interact with the model.

 Figure 11.  Charging and discharging a capacitor.

Select the alternatives which best describe what happens when the switch in Fig.11 is returned from position B to position A.

  • The stored in the capacitor is released. Current flows through the causing it to light up briefly. For a short time, the acts like a battery making flow round the circuit.
  • Click here to mark the question


The mechanism for storing charge is different and the capacitor doesn't make a very good
battery
A battery consists of two or more cells. The cells may be connected in series or in parallel.
battery
because the stored charge runs out quickly.

The amount of charge stored depends on the size of the capacitor and the voltage across it.
That is:



where Q is charge in coulombs, C is capacitance in farads and V is the voltage across the capacitor.
With C in μF, the charge stored is given in microcoulombs, μC.
     Rearranging gives:
     or     


Calculate the charge stored by a 10 μF capacitor, when the voltage across the capacitor is 5 V.
  •  μC
  • Click here to mark the question
Calculate the voltage across a 100 μF capacitor, if the charge stored is 1000 μC.
  •  V
  • Click here to mark the question


Unlike a battery, a capacitor can release its charge all at once. This is what happens in a camera electronic flash system like that shown in Fig.12. When the camera is switched on, a large capacitor starts to fill up. The battery voltage is often just 1.5 V but a special electronic circuit charges the capacitor to a much higher voltage – 300 V or more.

When enough charge has been stored, a viewfinder
LED
An LED, or light-emitting diode, is illuminated when current passes through it in the forward bias direction.
LED
illuminates to tell you that the flash is ready. Pressing the button to take the picture releases the stored energy in an instant causing a large
current
Current I is a flow of charged particles, usually electrons.
current
to flow through the flash element and producing the flash:

Figure 12.   Sudden energy release from a capacitor.
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Electronic ignition systems in automobiles use capacitors in a similar way.

Depending on how the power supply in your hi-fi is arranged, you may have noticed that music continues to play for a few moments after you have switched off. This happens because large capacitors in the power supply store charge, helping to keep the power supply voltage constant and providing a surge of current when a particularly loud note occurs. The music plays on while these capacitors discharge.

In other appliances, capacitors sometimes remain charged even when the power is switched off. High voltage capacitors inside a TV set can store enough charge to deliver a fatal electric shock. This is why manufacturers put warning notices on the back!
Select the words which best complete each sentence:

  • When capacitors store energy, they are said to become . When energy is released, the capacitor becomes . Capacitors store energy than a battery, but can release it much quickly.
  • Click here to mark the question
Time delays
How quickly can you fill a bucket? The answer depends on the size of the bucket, and also on the rate of flow of water into the bucket.

In electronic circuits, the rate of flow of charge is called current and is controlled using resistors. Therefore, you can control how quickly a capacitor will become filled by placing a resistor in
series
Components are connected in series when they are joined end to end in a circuit, so that the same current flows through each.
series
in the charging circuit.


Click on the figure below to interact with the model.

 Figure 13.  Controlling charging time using a resistor.



Operate the
SPDT
An SPDT, or single-pole double-throw, switch is a changeover switch with a single input terminal and two alternative output terminals.
SPDT
switch and note how the reading on the
voltmeter
A voltmeter measures the voltage, or difference in energy, between two points in a circuit. Voltmeters are connected in parallel and must have a high resistance.
voltmeter
changes. As you can see, the capacitor fills and empties more slowly than before.

Click on the resistor value and change this to 100 kΩ.

What happens when the resistor value in Fig.13 is changed from 10 kΩ to 100 kΩ?
  • Click here to mark the question
When does the voltage reading on the voltmeter in Fig.13 change most quickly?
  • Click here to mark the question


Change the capacitor value to 1000 µF and note the result.

Increasing either the resistor value or the capacitor value increases the charging and discharging time.


The behaviour of resistor–capacitor, or RC, circuits is described according to the time constant, where:



Like all formulae, the time constant formula applies for fundamental units. That is, the time constant comes out in seconds when R values are in ohms and C values in farads. It is often convenient to use other combinations of units as follows:

R units C units units
Ω F s
µF s
µF ms



To take an example, if R = 1 MΩ; and C = 1 µF, then the time constant  = 1 s. You might imagine that this means that the capacitor in the circuit takes 1 second to become charged or discharged. This is not quite true, as you are about to discover.

In the simulation below, R = 1 MΩ and C = 1 µF and the power supply is 10 V:


Click on the figure below to interact with the model.

 Figure 14.  Investigating time constant.



Click the SPDT switch to start the capacitor charging. The voltage across the capacitor changes as it is charged up, quickly at first, then more slowly.

Remember, the time constant for this circuit is 1 second. The capacitor is empty to start with.

Is charging complete 1 second after operating the switch in the simulation of Fig.14?
  • Click here to mark the question


As you can see, the voltage across the capacitor does not reach its target value after 1 second.

During each time constant, the voltage across the capacitor increases by 63 per cent towards its target value.
After 1 second, the voltage across the capacitor has increased to 6.3 V.
This leaves 10 − 6.3 = 3.7 V to go.
During the next time constant, the voltage increases by 63 per cent of 3.7 V = 2.3 V, to around 8.6 V.
     This leaves 1.4 V to go and so on.



This pattern of voltage change is summarized in the diagram below:

Figure 15.   Capacitor charging graph.
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Why is it 63 per cent? The answer is connected with the mathematics of capacitor action. The charging graph belongs to a special family of curves, called exponential curves. The rate of change of voltage depends on where you are on the graph and how far there is to go.

It is not important to understand the mathematics, provided you remember that the time constant is not the total time taken for charging or discharging.

How long does it take for charging to be complete, or nearly complete, in Fig.15?
  • Click here to mark the question
The charging time is approximately five times the time constant.


Return to the simulation and click the switch again. This gives you the discharging graph for the capacitor. After 1 second, the voltage has changed by 63 per cent towards its target voltage, that is, from 10 V to 10 − 6.3 = 3.7 V, as you can see:

Figure 16.   Capacitor discharging graph.
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Discharging appears complete after 5 seconds. That is:

The discharging time is approximately five times the time constant.


Experiment with other values of R and C to confirm that you understand how the time constant affects the charging and discharging times.

What happens to the charging time if R in the simulation, Fig.14, is changed from 1 MΩ to 500 kΩ?
  • Click here to mark the question


Sometimes it is useful to know how long it takes for a capacitor to charge or discharge halfway towards its target voltage. The half charge time is given by:



The behaviour of many
astable
An astable is a subsystem which generates pulses.
astable
and monostable circuits depends upon the half charge time of resistor–capacitor networks. These subsystems are used frequently elsewhere in Absorb Electronics.

Time constant calculator
Figure 17.   Time constant calculator.
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The time constant calculator shown in Fig.17 allows you to calculate the time constant, half charge time, and nearly complete charge time for resistor values between 1 kΩ and 10 MΩ and capacitor values from 1 pF to 1000 μF.

All you need to do is to enter the R and C values and click the 'equals' button.

Use the time constant calculator to answer the following questions. Convert your answer to the appropriate units.

What is the time constant if R = 560 kΩ and C = 4.7 μF?
  •  s   (to one decimal place)
  • Click here to mark the question
What is the half charge time if R = 22 kΩ and C = 100 nF?
  •  ms   (to two decimal places)
  • Click here to mark the question
What is the 'full' charge time if R = 3.3 MΩ and C = 2.2 μF?
  •  s   (to one decimal place)
  • Click here to mark the question


Like other Absorb Electronics calculators, the time constant calculator is always available from the 'Tools' menu. Check that you can find it.

Capacitors in series and parallel
What happens to Ctotal when two capacitors C1 and C2 are connected in series? To find out, experiment with Fig.18:


Click on the figure below to interact with the model.

 Figure 18.  Capacitors in series.



The
SPST
An SPST, or single-pole single-throw, switch is a simple on/off switch.
SPST
switch is closed to bypass C1. Switch the SPDT switch to the charging position. This gives a charging curve with  = 1 s, as before.

Operate the SPDT switch again to discharge the capacitor. Wait for the voltage across C1 to reach 0 V. Now switch off the SPST switch so that the two capacitors are connected in series.

Repeat the charge and discharge cycles.

What is the effect on the time constant when the capacitors in Fig.18 are connected in series?
  • Click here to mark the question
You might be surprised to find that the time constant is reduced to half its original value, that is,  = 0.5 s.
The values of capacitors connected in series do not add together in the same way as resistors connected in series.
In fact, Ctotal for capacitors is calculated from the product-over-sum formula:

Here:

     When two equal value capacitors are in series in this circuit, the voltage across each capacitor is 5 V when fully charged.



Click on C1 and C2 in the simulation and change their values to see the effect on Ctotal and also upon the voltage across each capacitor.

In Fig.19, two capacitors are connected in
parallel
Components are connected in parallel when they are joined side by side in a circuit, so that they provide alternative pathways for current flow.
parallel
:


Click on the figure below to interact with the model.

 Figure 19.  Capacitors in parallel.



This time, when the SPST switch is closed, the time constant becomes 2 s. When capacitors are connected in parallel, Ctotal is calculated from:



This makes sense because the surface area of the plates is increased.
What is the combined capacitance of two 10 μF capacitors connected in series?
  •  μF
  • Click here to mark the question
What is the combined capacitance of two 10 μF capacitors connected in parallel?
  •  μF
  • Click here to mark the question
Decoupling and smoothing
The diagram below shows two capacitors connected in parallel with a battery power supply:
Figure 20.   Connecting decoupling capacitors.
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This is a common circuit arrangement. The main circuit is connected across the power supply. The capacitors provide what is called decoupling.

If there is a sudden change in the power supply current to one part of the circuit (for example, if part of the circuit produces a pulse), there is a tendency for signals to appear on the power supply connections. These signals can interfere with the correct operation of other parts of the circuit.

Connecting capacitors directly across the power supply rails helps to suppress this kind of interference. For maximum effect, decoupling capacitors are connected as close as possible to the parts of the circuit which are likely to produce interference.

What is the total capacitance when 100 μF and 100 nF capacitors are connected in parallel, as in Fig.20?
  •  μF   (to 1 decimal place)
  • Click here to mark the question

Why is the 100 nF capacitor used?
The answer is that real polarized capacitors work well in suppressing low frequency signals, but do not work well with high frequencies.
Real non-polarized capacitors work well with high frequencies.
     In other words, both types of capacitor are needed for effective interference suppression.



A large value capacitor, say 1000 μF, connected across the power supply is often described as a smoothing capacitor. It helps to remove low frequency interference, tending to keep the power supply voltage constant even if the power supply current changes.

Blocking d.c. signals
In the simulation below, Fig.21, the signal generator produces a 100 Hz signal centred around 2.5 V. The peak amplitude of the signal is 1.5 V. This means that voltage increases by 1.5 V from the centre point, that is, up to 2.5 + 1.5 = 4 V, and also decreases by 1.5 V, down to 2.5 − 1.5 = 1 V.


Click on the figure below to interact with the model.

 Figure 21.  Blocking d.c. signals.



Click anywhere in the simulation area to draw the graphs. The red graph shows the voltage signal before the capacitor. The blue graph shows the signal after the capacitor. As you can see, the only difference after the capacitor is that the sine wave is centred around 0 V.

Capacitors allow changing, or
a.c.
In an a.c., or alternating current, circuit, current flows first in one direction, then in the other.
a.c.
, signals to pass, but block steady, or
d.c.
In a d.c., or direct current, circuit, current always flows in the same direction.
d.c.
, signals. This is called d.c. blocking. Capacitors are often used to allow a.c. signals to be transferred from one part of a circuit to another, while at the same time preventing the transfer of d.c. signals between subsystems. This is essential in many amplifier circuits.

Summary


Capacitors store electric charge.

All capacitors consist of two regions of conductor separated by a space filled with an insulator.

The fundamental measurement unit for capacitance is the farad, where 1 farad stores 1 coulomb of electric charge when the voltage across the capacitor is 1 volt. Practical measurement units include:


Unit Symbol Farad equivalent
microfarad µF 1 × 10−6 F
nanofarad nF 1 × 10−9 F
picofarad pF 1 × 10−12 F



Non-polarized capacitors can be connected either way round in a circuit and are manufactured in nF and pF values. Polarized capacitors have separate positive and negative connections which must be connected correctly. Polarized capacitors are manufactured in μF values.

Capacitors are marked with a working voltage which is the maximum voltage allowed across the capacitor. Polarized capacitors often have low values of working voltage.

The charge stored by a capacitor depends on the size of the capacitor and the voltage across it, that is:



where Q is charge in coulombs, C is capacitance in farads, and V is the voltage across the capacitor in volts.

Capacitors can release their stored charge very quickly.

In circuits where current flow into and out of a capacitor is controlled by a resistor, charging and discharging times depend on the time constant τ, where:



During one time constant, the voltage across the capacitor changes by 63 per cent towards the target voltage. Charging or discharging appears complete after five time constants. The half charge time is given by:



When two capacitors are connected in series, the total capacitance is given by:



When two capacitors are connected in parallel, the total capacitance is given by:



Capacitors are connected between the power supply rails to provide interference suppression (decoupling), or to help in keeping power supply voltage constant (smoothing).

Capacitors are used to provide d.c. blocking between subsystems.

Exercises
Figure 22.   Circuit to investigate charging and discharging of a capacitor.
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Figure 23.   V–t graph for capacitor when switch is moved from B to A.
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1. From the graph in Fig.23, what is the time constant of this circuit?
  •  s   (to the nearest whole number)
  • Click here to mark the question
2. If C = 10 μF, what is the value of R?
  • Click here to mark the question
3. Calculate the charge stored by this capacitor when charging is complete.
  •  μC (microcoulombs)   (to the nearest whole number)
  • Click here to mark the question
4. If the capacitor is changed to 4.7 μF, which resistor value will give approximately the same time constant?
  • Click here to mark the question
5. How would you connect two 4.7 μF capacitors to give a combined capacitance as close as possible to 10 μF?
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Well done!
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