المقاومات (Resistors)

Resistors

A resistor is an electronic device which has a specified amount of electrical resistance. The resistor has two terminals and works in both directions. It has no polarization.
The primary characteristic of a resistor is its resistance (Ω) and the power rating (W).

Resistors are usually made out of carbon. Resistors for higher wattages are made out of resistance wire and a body of cement. High precision resistors are metal film resistors.

Wire resistor with 11 W. Wire resistor with 5 W. Carbon resistor with 2 W. Common carbon resistor ¼ W. Chip resistor or SMD (Surface mounted device)

Units, values and symbols

The symbols for resistors in circuits diagram are shown below. Notice that American symbols are different.

Resistor, European and American

In formulas the letter R is used for the resistor and the unit is Ω (Ohm). To keep large numbers small and handy the units are used in conjunction with the SI prefixes.

1 000 Ω is 1 kΩ
and
1 000 kΩ is 1 MΩ

In circuit diagrams very often the dot is replaced by the R or Ω.

47K    = 47 KΩ
1K5    = 1.5 KΩ
1M0    = 1.0 MΩ
2R2    = 2.2 Ω
0Ω22    = 0.22 Ω

The resistors R9 and R14 have the value of 4k7 or 4.7 KΩ. All resistor without any wattage information are common ¼ W resistors. Otherwise it is mentioned. Like the two 5W-types R12 and R13.

Exercises:

To see the answer just  the space behind the values.

Transfer in KΩ:    1 MΩ   1000KΩ
                        2K2   2.2KΩ
                        560 Ω   0.56KΩ
                        3,300 Ω   3.3KΩ

Transfer in Ω:      2.7 KΩ   2700Ω
                        56 KΩ   56,000Ω
                        120 KΩ   120,000Ω
                        2Ω7   2.7Ω

Preferred values

Resistors are not available in all possible values and gradations but only in selected values. The industry provides a specific range of standard values, known as preferred values. The most common group of preferred values is the E12 series with 12 different numbers and their multiples. The gradations are:

10  12  15  18  22  27  33  39  47  56  68  82

Example:    Available resistor are: 33 kΩ, 150 Ω , 2.2 MΩ, 82 Ω
                But the following resistors do not exist: 74 kΩ, 14 MΩ, 460 kΩ, 21 Ω

All resistors of the E12 series are common types with 5%.

Beside the E12 series a E24 with 24 values and even a E48 with 48 values exist. Because the gradation is smaller the series consist of only precise resistors with smaller tolerances. The resistors are metal film resistors with 2% or 1%.

E-12 Series (5%)
1 Ω 1.2 Ω 1.5 Ω 1.8 Ω 2.2 Ω 2.7 Ω 3.3 Ω 3.9 Ω 4.7 Ω 5.6 Ω 6.8 Ω 8.2 Ω	10 Ω 12 Ω 15 Ω 18 Ω 22 Ω 27 Ω 33 Ω 39 Ω 47 Ω 56 Ω 68 Ω 82 Ω	100 Ω 120 Ω 150 Ω 180 Ω 220 Ω 270 Ω 330 Ω 390 Ω 470 Ω 560 Ω 680 Ω 820 Ω	1 kΩ 1.2 kΩ 1.5 kΩ 1.8 kΩ 2.2 kΩ 2.7 kΩ 3.3 kΩ 3.9 kΩ 4.7 kΩ 5.6 kΩ 6.8 kΩ 8.2 kΩ	10 kΩ 12 kΩ 15 kΩ 18 kΩ 22 kΩ 27 kΩ 33 kΩ 39 kΩ 47 kΩ 56 kΩ 68 kΩ 82 kΩ	100 kΩ 120 kΩ 150 kΩ 180 kΩ 220 kΩ 270 kΩ 330 kΩ 390 kΩ 470 kΩ 560 kΩ 680 kΩ 820 kΩ	1 MΩ 1.2 MΩ 1.5 MΩ 1.8 MΩ 2.2 MΩ 2.7 MΩ 3.3 MΩ 3.9 MΩ 4.7 MΩ 5.6 MΩ 6.8 MΩ 8.2 MΩ

Exercises:

The result of resistance calculations are the following. Which resistors can be used?
To see the answer just the space behind the values.

235 Ω   220Ω
1.4 kΩ   1.5kΩ
620 Ω  680_or_560kΩ
13 kΩ   12kΩ
1.35 MΩ  1.2_or_1.5MΩ
995 Ω  1kΩ
13.5 kΩ 12kΩ_or_15kΩ

Resistor Combinations

There are two different ways to connect resistors: Serial and parallel connection. In addition to that a combination of this two principles is possible, the serial-parallel connection.

Resistor in Series

Two or more resistors can put together like a chain. The values of the single resistors simply have to be added to get the value of the whole combination.

In series connection the total resistance is always higher than the highest value of a single resistor.
Example:    The total value of this resistor combination is:   10 Ω + 22 Ω + 33 Ω = 65 Ω

Respect the prefixes Ω, kΩ, MΩ. Do not mix them.

Resistors in Parallel

The calculation of a resistor combination in parallel is slightly more difficult.
But in general one can say:

In parallel connection the total resistance is always lower than the lowest value of a single resistor.
Example:    The total value of this resistor combination is:

 
If only two resistors are put in parallel a more simple formula can be used (Fig.11).
Then, the total resistance is the product of the two resistors, divided by the sum of the two resistors.

Example:

Much easier is the calculation when resistors with the same resistance are taken.

For two resistors the result is half the of resistor value. For three resistors the result is one third of resistor value. For four resistors the result is one fourth of the value.

And so on...

Example:

2 resistors of 10 kΩ 3 resistors of 330 kΩ 4 resistors of 100 Ω

R = 5 kΩ                   R = 110 kΩ R = 25 Ω

Colour code

The resistance and the tolerance of the resistor are printed on the body of the resistor with a colour code. The power rating is determined by the physical size of the resistor.
Common carbon resistors have four colour bands (three for the value, one for the tolerance) and metal film resistors have five colour bands.
In the common four band system the first two bands represents the number of the value and the third band the multiplier or easier number of zeros. The last band shows the tolerance (mostly gold) and also indicates the direction of reading (always right).

For reading the colour code the band of the tolerance lays always right (here gold).

	Colour	1st colour band	2nd colour band	3rd colour band
	black	0	0	-
	brown	1	1	0
	red	2	2	00
	orange	3	3	000
	yellow	4	4	0 000
	green	5	5	00 000
	blue	6	6	000 000
	violet	7	7	0 000 000
	grey	8	8	00 000 000
	white	9	9	000 000 000

The resistor above (brown-black-red) has the following value:

brown   = 1
black    = 0
red       = 2 x 0 = 00

= 1000 Ω or 1 kΩ

The 4th colour band indicates the tolerance of the resistor value or the precision of the resistor value. The smaller the value the more precise the value. The following tolerances exist:

silver    = 10%    (no more common, in old equipment)
gold     = 5%    (most common)
red      = 2%    (for measurement purposes)
brown  = 1%    (for precise measurement purposes)

Example:     A 100 KΩ with a golden band has a tolerance of +/- 5%. The value will be
                 between 95 KΩ (100 KΩ – 5 KΩ) and 105 KΩ (100 kΩ + 5 KΩ)

With this system all resistor values can be outlined, as long as they are not under 10 Ω. Brown–black–black is the smallest value which can be expressed with the system.
If a resistance of less than 10 Ω has to be outlined, then the 3rd band is gold. The golden band in this case stands for a dot between the 1st and 2nd band.
The colour code of red–red–gold stands for 2.2 Ω.

But those resistors are uncommon and in practice resistors with small resistance values are bigger wire-wound resistors where the value is printed in numbers on the body.

Problems reading the colours

Very often the colour is not easy to define. Green could be blue and orange maybe red. A short look at the E-12 preferred value list helps.

Example:    Is the first band green the second must be blue
                Is the first band red the second can only be red or violett


Exercise:   
Which value have the following resistors?
To see the answer just  the space behind the resistors.

560 Ω 330 Ω 2.2 KΩ 470 Ω 100 KΩ 270 Ω 10 KΩ 100 Ω 4.7 KΩ 1 Ω

Wattage

The wattage of a resistor is identify by its size.
Smaller resistance values are needed where higher current flows. The wattage which is produced by the resistor gets higher and the produced heat has to be delivered to the surrounded air. The resistors gets bigger.
The high power resistors are wire-wound resistors with a body of cement or ceramic. Wattages of 5 W, 7 W, 11 W and 17 W are common.

The common resistor has a power rating of ¼ W.

5 W wire resistor 7 W wire resistor, both with cement body. More seldom and expensive 50 W resistor in metal housing

The resistor R 77 is a bigger 2 W-type. The wattage of the other resistors is not mentioned. In this case they are common carbon resistors with ¼ W.

Metal film resistors

In measurement or reference circuits (e.g. digital multimeter, ECG and other measurement equipment) high quality resistors with low tolerance are needed. Metal film resistors with 2% (red) or 1% (brown) from the E24 or E48 series are used.
Because the values get more precise and the numbers get bigger an additional colour band is needed. With a 5th colour band a value of 432 kΩ (E48) can be expressed.

Metal film resistor with 2% or 1% have five colour bands. The last colour band indicates the tolerance: red = 2 %, brown = 1 %

The gradation of the E24 series are the following:

10  11  12  13  15  16  18  20  22  24  27  30  33  36  39  43  47  51  56  62  68  75  82  91

The metal resistor above has the following value:

yellow    = 4
violet     = 7
black     = 0
orange   = 3 x 0 = 000
= 470 000 Ω
= 470 kΩ

The 5th colour band is brown. The resistor has a tolerance of 1 %.

E-24 Series (2%)
1 Ω 1.1 Ω 1.2 Ω 1.3 Ω 1.5 Ω 1.6 Ω 1.8 Ω 2.0 Ω 2.2 Ω 2.4 Ω 2.7 Ω 3.0 Ω 3.3 Ω 3.6 Ω 3.9 Ω 4.3 Ω 4.7 Ω 5.1 Ω 5.6 Ω 6.2 Ω 6.8 Ω 7.5 Ω 8.2 Ω 9.1 Ω	10 Ω 11 Ω 12 Ω 13 Ω 15 Ω 16 Ω 18 Ω 20 Ω 22 Ω 24 Ω 27 Ω 30 Ω 33 Ω 36 Ω 39 Ω 43 Ω 47 Ω 51 Ω 56 Ω 62 Ω 68 Ω 75 Ω 82 Ω 91 Ω	100 Ω 110 Ω 120 Ω 130 Ω 150 Ω 160 Ω 180 Ω 200 Ω 220 Ω 240 Ω 270 Ω 300 Ω 330 Ω 360 Ω 390 Ω 430 Ω 470 Ω 510 Ω 560 Ω 620 Ω 680 Ω 750 Ω 820 Ω 910 Ω	1 kΩ 1.1 kΩ 1.2 kΩ 1.3 kΩ 1.5 kΩ 1.6 kΩ 1.8 kΩ 2.0 kΩ 2.2 kΩ 2.4 kΩ 2.7 kΩ 3.0 kΩ 3.3 kΩ 3.6 kΩ 3.9 kΩ 4.3 kΩ 4.7 kΩ 5.1 kΩ 5.6 kΩ 6.2 kΩ 6.8 kΩ 7.5 kΩ 8.2 kΩ 9.1 k Ω	10 kΩ 11 kΩ 12 kΩ 13 kΩ 15 kΩ 16 kΩ 18 kΩ 20 kΩ 22 kΩ 24 kΩ 27 kΩ 30 kΩ 33 kΩ 36 kΩ 39 kΩ 43 kΩ 47 kΩ 51 kΩ 56 kΩ 62 kΩ 68 kΩ 75 kΩ 82 kΩ 91 k Ω	100 kΩ 110 kΩ 120 kΩ 130 kΩ 150 kΩ 160 kΩ 180 kΩ 200 kΩ 220 kΩ 240 kΩ 270 kΩ 300 kΩ 330 kΩ 360 kΩ 390 kΩ 430 kΩ 470 kΩ 510 kΩ 560 kΩ 620 kΩ 680 kΩ 750 kΩ 820 kΩ 910 k Ω	1 MΩ 1.1 MΩ 1.2 MΩ 1.3 MΩ 1.5 MΩ 1.6 MΩ 1.8 MΩ 2.0 MΩ 2.2 MΩ 2.4 MΩ 2.7 MΩ 3.0 MΩ 3.3 MΩ 3.6 MΩ 3.9 MΩ 4.3 MΩ 4.7 MΩ 5.1 MΩ 5.6 MΩ 6.2 MΩ 6.8 MΩ 7.5 MΩ 8.2 MΩ 9.1 M Ω

Other fixed resistors

Fixed resistors sometimes appear in other versions. Modern electronic boards are often equipped with SMD devices. SMD stands for Surface Mounted Devices. SMD are very small and have not connection wires. They are mounted directly on the board.

SMD resistors and capacitors (below) in comparison with common resistors (above).

SMD resistors are not marked with a colour code. But the numbers which are printed on the body follows the same rules as the colour code. The first two are numbers and the third numbers indicates the number of zeros.

Example:    564 = 5 6 0000 = 560 kΩ
                222 = 2 2 00 = 2.2 kΩ
                105 = 1 0 00000 = 1 MΩ

When a lot of resistors of the same value are needed electronic manufactures sometime use resistor network. Several resistors of the same value are conflated in one package.

Two resistor networks in an electronic board of a UPS device.

Sometimes resistors with only one black band can be found. These resistors do not have a resistance. Their value is 0 Ω. They are used when robots assemble the boards because robots can not handle wire bridges.

The lower resistor really is a 0 Ω resistor!

Variable resistors

Beside the fixed resistor there are also variable resistors.
All variable resistors have three pins. Two ends with the resistor in between and one wiper. The wiper can take a resistor value between zero and the maximum according to the position.

Variable resistors which are set with a little screwdriver are called trimmer. They are mounted on the electronic board and made for the technician to calibrate the circuit. Where fine calibration is needed multi-turn trimmers are used. From one end to the other the adjustment screw then has to be turned 10 turns or more.

Resistors which can be set from outside by the user are called potentiometer or just pots.
For audio purpose (e.g. volume control) a stereo potentiometer is used.

Potentiometer (pot) in stereo version for audio purpose and trimmer. The last trimmer is a 10-turn trimmer for fine calibration.

The symbols for variable resistors in circuits diagram are shown below. American symbols again are different.

Trimmer European new and old, American Potentiometer European new and old, American

Potentiometers are available in two different versions: Linear or logarithmic (lin or log)
The final value is the same but the change of resistance compare to the position of the control shaft is different. In general all pots which set voltages and DC applications are linear and pots for audio use, especially for volume control, are logarithmic ones.

The change of the resistor compare to the rotation angel. The blue line shows a lin pot, the yellow line a log pot.

Applications

Trimmer or pots have 3 connecting pins (1) and can be connected in different ways for different purposes.
The most common method is shown in (2). The resistor is variable and has 2 pins.
For audio applications the variable resistor is always connected as a voltage divider (3). Input and output are related to ground and the input resistor is always stable.
For stereo usage 2 pots have to be used. Both are working against ground (4)

Function check

Resistors can checked directly with an ohmmeter or multimeter. Therefore the equipment has to be switched off and one connector of the resistor has to be disconnected from the board. Otherwise other devices on the board can distort the measurement result.

When R5 would be measured while connected with the board, the resistances of R2, R5, T1, T2 will deliver a wrong result.

Also checking a removed resistor by holding the probes with the fingers will lead to a wrong result. The body resistance distort the measurement.

It is allowed to touch one terminal of the resistor during the measurement, but the second must not be touched.

With some experience it is sometimes easier and faster to check the function of a resistor by switching on the equipment and measuring the voltage over the resistor. A voltage drop indicates that the resistor works.

In general a measurement is really not necessary. Because a defective resistor is usually burned the defect is visible. Bigger power resistors always get warm during operation. Just touch the resistor. If heat is produced the resistor is OK.

Common problems

When resistors get broken they always become high-resistance or interrupted. Compare to capacitors the resistance never get smaller. Interrupted in practice means burned and burned resistors are easy to spot. It is always a good idea to do a thoroughly optical inspection of the board first.

Keep in mind that a burned resistor always has a reason. The reason is an unusual high current which can not produced by the resistor itself. Check the following device (specially transistors) for shorts. After replacing and switching on the equipment be prepared to switch off immediately when the resistor gets hot again. Sometimes it is a good idea to disconnect the following stage or device first to surround the fault.

Bigger power resistors get hot and can produce cold solder joints. Very often the solder joints of power resistors are the source for faults. It is good practice to resolder all poor solder joints.

Defective resistors are easy to spot. This resistor is burned. It of course has to be replaced but the resistor is NOT the cause of the problem. A burned resistors always means: There is a problem somewhere else.

For changing a resistor not only the value is important but also the wattage and the tolerance. That means also the size and the last colour band must be respected.

Sometimes for a repair the needed value is not available. Then two or more resistors can put together according to Ohm's law. And because also the wattage increases it is also possible to put several small resistors together to get a resistor with a higher wattage.

Pots very often are 'jumping' or in audio amplifiers 'cracking' and 'scratching' when turning. Just dirt inside the pot housing is the cause. Contact spray helps or just some fast turns from one end to the other.

Broken SMD resistors or network resistor can replaced by common carbon resistors.

Prices

Resistors are cheap and a selection of standard values of the E-12 series belongs in every workshop. Here are the average prices for resistors in Europe:

Standard carbon resistor ¼ W	0.05 €
SMD resistor	0.05 €
Carbon resistor 2 W	0.30 €
Metal film resistor 1 %	0.10 €
Wire resistor 5W	0.40 €
Wire resistor 17W	0.80 €
Trimmer	0.20 €
Multi turn trimmer	0.50 €
Pot	0.70 €
Pot stereo	1.40 €

 
 
 

Sources and additional information

Resistor: http://en.wikipedia.org/wiki/Resistor
Resistor, practical: http://www.kpsec.freeuk.com/components/resist.htm
Potentiometer: http://en.wikipedia.org/wiki/Potentiometer
Thermistor: http://en.wikipedia.org/wiki/Thermistor
Potentiometers: http://sound.westhost.com/pots.htm
Colour code calculator: http://www.ese.upenn.edu/rca/calcjs.html