# Resistors

### What do resistors do?

Resistors limit current. In a typical application, a resistor is connected in series with an LED:

Enough current flows to make the LED light up, but not so much that the LED is damaged. Later in this Chapter, you will find out how to calculate a suitable value for this resistor. (LEDs are described in detail in Chapter 5.)

The ‘box’ symbol for a fixed resistor is popular in the UK and Europe. A ‘zig-zag’ symbol is used in America and Japan:

Resistors are used with **transducers** to make **sensor subsystems**. Transducers are electronic components which convert energy from one form into another, where one of the forms of energy is electrical. A **light dependent resistor**, or **LDR**, is an example of an **input transducer**. Changes in the brightness of the light shining onto the surface of the LDR result in changes in its resistance. As will be explained later, an input transducer is most often connected along with a resistor to to make a circuit called a **potential divider**. In this case, the output of the potential divider will be a voltage signal which reflects changes in illumination.

Microphones and switches are input transducers. **Output transducers** include loudspeakers, filament lamps and LEDs. Can you think of other examples of transducers of each type?

In other circuits, resistors are used to direct current flow to particular parts of the circuit, or may be used to determine the voltage gain of an amplifier. Resistors are used with capacitors (Chapter 4) to introduce time delays.

Most electronic circuits require resistors to make them work properly and it is obviously important to find out something about the different types of resistor available, and to be able to choose the correct resistor value, in , , or M, for a particular application.

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### .

Fixed value resistors

The diagram shows the construction of a **carbon film** resistor:

During manufacture, a thin film of carbon is deposited onto a small ceramic rod. The resistive coating is spiralled away in an automatic machine until the resistance between the two ends of the rod is as close as possible to the correct value. Metal leads and end caps are added, the resistor is covered with an insulating coating and finally painted with coloured bands to indicate the resistor value.

Carbon film resistors are cheap and easily available, with values within ±10% or ±5% of their marked, or ‘nominal’ value. **Metal film** and **metal oxide** resistors are made in a similar way, but can be made more accurately to within ±2% or ±1% of their nominal value. There are some differences in performance between these resistor types, but none which affect their use in simple circuits.

**Wirewound** resistors are made by winding thin wire onto a ceramic rod. They can be made extremely accurately for use in multimeters, oscilloscopes and other measuring equipment. Some types of wirewound resistors can pass large currents without overheating and are used in power supplies and other high current circuits.

### .

Colour code

How can the value of a resistor be worked out from the colours of the bands? Each colour represents a number according to the following scheme:

Number |
Colour |

0 | black |

1 | brown |

2 | red |

3 | orange |

4 | yellow |

5 | green |

6 | blue |

7 | violet |

8 | grey |

9 | white |

The first band on a resistor is interpreted as the FIRST DIGIT of the resistor value. For the resistor shown below, the first band is yellow, so the first digit is 4:

The second band gives the SECOND DIGIT. This is a violet band, making the second digit 7. The third band is called the MULTIPLIER and is not interpreted in quite the same way. The multiplier tells you how many noughts you should write after the digits you already have. A red band tells you to add 2 noughts. The value of this resistor is therefore 4 7 0 0 ohms, that is, 4 700 , or 4.7 . Work through this example again to confirm that you understand how to apply the colour code given by the first three bands.

The remaining band is called the TOLERANCE band. This indicates the percentage accuracy of the resistor value. Most carbon film resistors have a gold-coloured tolerance band, indicating that the actual resistance value is with + or – 5% of the nominal value. Other tolerance colours are:

Tolerance |
Colour |

±1% | brown |

±2% | red |

±5% | gold |

±10% | silver |

When you want to read off a resistor value, look for the tolerance band, usually gold, and hold the resistor with the tolerance band at its right hand end. Reading resistor values quickly and accurately isn’t difficult, but it does take practice!

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### .

Colour code convertor

The colour code convertor is a special purpose computer program which will help you identify the value of a resistor from its colour code. Alternatively, the program lets you find out what colours to look for by typing in or selecting the resistor value.

The program works with *Windows 95* and looks like this:

To download the program (~210K), click on its image.

### .

More about colour codes

The colour code as explained above allows you to interpret the values of any resistor from 100 upwards. How does the code work for values less than 100 ? Here is the code for 12 :

brown, red, black

The multiplier colour black represents the number 0 and tells you that *no* noughts should be added to the first two digits, representing 1 and 2.

What would be the colour code for 47 ? The answer is:

yellow, violet, black

Using this method for indicating values between 10 and 100 means that all resistor values require the same number of bands.

For values bewteen 1 and 10 , the multiplier colour is changed to gold. For example, the colours:

brown, black, gold

indicate a 1 resistor, while the colours:

red, red, gold

refer to a 2.2 resistor.

Metal film resistors, manufactured to 1 or 2% tolerance, often use a code consisting of *four* coloured bands instead of three. The code works in the same way, with the first three bands interpreted as digits and the fourth band as the multiplier. For example, a 1 metal film resistor has the bands:

brown, black, black, brown (+brown or red for tolerance)

while a 56 metal film resistor has the bands:

green, blue, black, red

It is worth pointing out that the multiplier for metal film resistors with values from 1 upwards is brown (rather than red, as in the three colour system), while the multiplier for 10 upwards is red (instead of orange).

You are likely to use low value resistors and metal film resistors on some occasions and it is useful to know how to read their codes. However, most of the resistors you use in building electronic circuits will be carbon film types with values indicated using the three band colour code. It is this system which you should master first.

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### .

E12 and E24 values

If you have any experience of building circuits, you will have noticed that resistors commonly have values such as 2.2 , 3.3 , or 4.7 and are not available in equally spaced values 2 , 3 , 4 , 5 and so on. Manufacturers don’t produce values like these – why not? The answer is partly to do with the fact that resistors are manufactured to a *percentage *accuracy. Look at the table below which shows the values of the **E12** and **E24 series**:

E12 series10% tolerance |
E24 series5% tolerance |

10 | 10 |

11 | |

12 | 12 |

13 | |

15 | 15 |

16 | |

18 | 18 |

20 | |

22 | 22 |

24 | |

27 | 27 |

30 | |

33 | 33 |

36 | |

39 | 39 |

43 | |

47 | 47 |

51 | |

56 | 56 |

62 | |

68 | 68 |

75 | |

82 | 82 |

91 |

Resistors are made in multiples of these values, for example, 1.2 , 12 , 120 , 1.2 , 12 , 120 and so on.

Consider 100 and 120 , adjacent values in the E12 range. 10% of 100 is 10 , while 10% of 120 is 12 . A resistor marked as 100 could have any value from 90 to 110 , while a resistor marked as 120 might have an actual resistance from 108 to 132 . The ranges of possible values overlap, but only slightly.

Further up the E12 range, a resistor marked as 680 might have and actual resistance of up to 680+68=748 , while a resistor marked as 820 might have a resistance as low as 820-82=738 . Again, the ranges of possible values just overlap.

The E12 and E24 ranges are designed to cover the entire resistance range with the minimum overlap between values. This means that, when you replace one resistor with another marked as a higher value, its *actual* resistance is almost certain to be larger.

From a practical point of view, all that matters is for you to know that carbon film resistors are available in multiples of the E12 and E24 values. Very often, having calculated the resistance value you want for a particular application, you will need to choose the nearest value from the E12 or E24 range.

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Current limiting

You are now ready to calculate a value for the resistor used in series with an LED. Look at the circuit diagram:

A typical LED requires a current of 10 mA and has a voltage of 2 V across it when it is working. The power supply for the circuit is 9 V. What is the voltage across resistor R1? The answer is 9-2=7 V. (The voltages across components in series must add up to the power supply voltage.)

You now have two bits of information about R1: the current flowing is 10 mA, and the voltage across R1 is 7 V. To calculate the resistance value, use the formula:

Substitute values for *V* and *I*:

Look out! The formula works with the fundamental units of resistance, voltage and current, that is, ohms, volts and amps. In this case, 10 mA had to be converted into amps, 0.01 A, before substitution.

If a value for current in mA is substituted, the resistance value is given in :

The calculated value for R1 is 700 . What are the nearest E12/E24 values? Resistors of 680 , 750 and 820 are available. 680 is the obvious choice. This would allow a current slightly greater than 10 mA to flow. Most LEDs are undamaged by currents of up to 20 mA, so this is fine. What is the colour code for a 680 resistor?

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### .

Resistors in series and parallel

In a **series** circuit, the current flowing is the same at all points. The circuit diagram shows two resistors connected in series with a 6 V battery:

*Resistors in series*

It doesn’t matter where in the circuit the current is measured, the result will be the same. The total resistance is given by:

In this circuit, *R*_{total}=1+1=2 . What will be the current flowing? The formula is:

Substituting:

Notice that the current value is in mA when the resistor value is substituted in .

The same current, 3 mA, flows through each of the two resistors. What is the voltage across R1? The formula is:

Substituting:

What will be the voltage across R2? This will also be 3 V. It is important to point out that the sum of the voltages across the two resistors is equal to the power supply voltage.

The next circuit shows two resistors connected in **parallel** to a 6 V battery:

*Resistors in parallel*

Parallel circuits always provide alternative pathways for current flow. The total resistance is calculated from:

This is called the **product over sum formula** and works for any *two* resistors in parallel. An alternative formula is:

This formula can be extended to work for more than two resistors in parallel, but lends itself less easily to mental arithmetic. Both formulae are correct.

What is the total resistance in this circuit?

The current can be calculated from:

How does this current compare with the current for the series circuit? It’s more. This is sensible. Connecting resistors in parallel provides alternative pathways and makes it easier for current to flow. How much current flows through each resistor? Because they have equal values, the current divides, with 6 mA flowing through R1, and 6 mA through R2.

To complete the picture, the voltage across R1 can be calculated as:

This is the same as the power supply voltage. The top end of R1 is connected to the positive terminal of the battery, while the bottom end of R1 is connected to the negative terminal of the battery. With no other components in the way, it follows that the voltage across R1 *must* be 6 V. What is the voltage across R2? By the same reasoning, this is also 6 V.

^{ }KEY POINT: |
When components are connected in parallel, the voltage across them is the same. |

Here is a slightly more complex circuit, with both series and parallel parts:

*Circuit with series and parallel resistors*

To find the overall resistance, the first step is to calculate the resistance of the parallel elements. You already know that the combined resistance of two 1 resistors in parallel is 0.5 , so the total resistance in the circuit is 1+0.5=1.5 . The power supply current is:

This is the current which flows through R1. How much current will flow through R2? Since there are two equally easy pathways, 2 mA will flow through R2, and 2 mA through R3.

The voltage across R1 is given by:

This leaves 2 V across R2 and R3, as confirmed by the calculation for R2:

Again, the sum of the voltages around the circuit is equal to the power supply voltage.

Check through this section carefully. A clear understanding of the concepts involved will help tremendously.

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### .

Power rating

When current flows through a resistance, electrical energy is converted into heat. This is obvious in an electric torch where the lamp filament heats up and glows white hot, see Chapter 1. Although the result may be less evident or imperceptible, exactly the same process of energy conversion goes on when current flows through *any* electronic component.

The **power** output of a lamp, resistor, or other component, is defined as the rate of change of electrical energy to heat, light, or some other form of energy. Power is measured in **watts**, **W**, or **milliwatts**, **mW**, and can be calculated from:

where *P* is power.

What is the power output of a resistor when the voltage across it is 6 V, and the current flowing through it is 100 mA?

0.6 W of heat are generated in this resistor. To prevent overheating, it must be possible for heat to be lost, or **dissipated**, to the surroundings at the same rate.

A resistor’s ability to lose heat depends to a large extent upon its surface area. A small resistor with a limited surface area cannot dissipate (=lose) heat quickly and is likely to overheat if large currents are passed. Larger resistors dissipate heat more effectively.

Look at the diagram below which shows resistors of different sizes:

The standard size of carbon film resistor used in most circuits has a power rating of 0.5 W. This means that a resistor of this size can lose heat at a *maximum* rate of 0.5 W. In the example above, the calculated rate of heat loss was 0.6 W, so that a resistor with a higher power rating, 1 W or 2 W, would be needed. Some resistors are designed to pass very large currents and are cased in aluminium with fins to increase surface area and promote heat loss.

Input and signal processing subsystems in electronic circuits rarely involve large currents, but power rating should be considered when circuits drive output transducers, such as lamps, LEDs, and loudspeakers.