Introduction to Resistors

1. Resistors

Resistors are the most commonly used component in electronics and their purpose is to create specified values of  current and voltage in a circuit. A number of different resistors are shown in the photos. (The resistors are on millimeter paper, with 1cm spacing to give some idea of the dimensions).  Photo 1.1a shows some low-power resistors, while photo 1.1b shows some higher-power resistors. Resistors with power dissipation below 5 watt (most commonly used types) are cylindrical in shape, with a wire protruding from each end for connecting to a circuit (photo 1.1-a). Resistors with power dissipation above 5 watt are shown below (photo 1.1-b).

Fig. 1.1a: Some low-power resistors	Fig. 1.1b: High-power resistors and rheostats

The symbol for a resistor is shown in the following diagram (upper: American symbol, lower: European symbol.)

Fig. 1.2a: Resistor symbols

The unit for measuring resistance is the OHM. (the Greek letter Ω - called Omega). Higher resistance values are represented by "k" (kilo-ohms) and M (meg ohms). For example, 120 000 Ω is represented as 120k, while 1 200 000 Ω is represented as 1M2. The dot is generally omitted as it can easily be lost in the printing process. In some circuit diagrams, a value such as 8 or 120 represents a resistance in ohms. Another common practice is to use the letter E for resistance in ohms. The letter R can also be used. For example, 120E (120R) stands for 120 Ω, 1E2 stands for 1R2 etc.

1.1 Resistor Markings

Resistance value is marked on the resistor body. Most resistors have 4 bands. The first two bands provide the numbers for the resistance and the third band provides the number of zeros. The fourth band indicates the tolerance. Tolerance values of  5%, 2%, and 1% are most commonly available.

The following table shows the colors used to identify resistor values:

COLOR	DIGIT	MULTIPLIER	TOLERANCE	TC
Silver		x 0.01 W	±10%
Gold		x 0.1 W	±5%
Black	0	x 1 W
Brown	1	x 10 W	±1%	±100*10-6/K
Red	2	x 100 W	±2%	±50*10-6/K
Orange	3	x 1 kW		±15*10-6/K
Yellow	4	x 10 kW		±25*10-6/K
Green	5	x 100 kW	±0.5%
Blue	6	x 1 MW	±0.25%	±10*10-6/K
Violet	7	x 10 MW	±0.1%	±5*10-6/K
Grey	8	x 100 MW
White	9	x 1 GW		±1*10-6/K

  ** TC - Temp. Coefficient, only for SMD devices

Fig. 1.2: b. Four-band resistor, c. Five-band resistor, d. Cylindrical SMD resistor, e. Flat SMD resistor

    The following shows all resistors from 0R1 (one tenth of an ohm) to 22M:

NOTES:
The resistors above are "common value"  5% types.
The fourth band is called the "tolerance" band. Gold = 5%
(tolerance band Silver =10% but no modern resistors are 10%!!)
"common resistors" have values 10 ohms to 22M.

RESISTORS LESS THAN 10 OHMS
When the third band is gold, it indicates the value of the "colors" must be divided by 10.
Gold = "divide by 10" to get values 1R0 to 8R2
See 1st Column above for examples.

When the third band is silver, it indicates the value of the "colors" must be divided by 100.
(Remember: more letters in the word "silver" thus the divisor is "larger.")
Silver = "divide by 100" to get values 0R1 (one tenth of an ohm) to 0R82
e.g: 0R1 = 0.1 ohm     0R22 =  point 22 ohms  
See 4th Column above for examples.

The letters "R, k and M" take the place of a decimal point. The letter "E" is also used to indicate the word "ohm."
e.g: 1R0 = 1 ohm     2R2 = 2 point 2 ohms   22R = 22 ohms  
2k2 = 2,200 ohms     100k = 100,000 ohms
2M2 = 2,200,000 ohms

Common resistors have 4 bands. These are shown above. First two bands indicate the first two digits of the resistance, third band is the multiplier (number of zeros that are to be added to the number derived from first two bands) and fourth represents the tolerance.

Marking the resistance with five bands is used for resistors with tolerance of 2%, 1% and other high-accuracy resistors. First three bands determine the first three digits, fourth is the multiplier and fifth represents the tolerance.

For SMD (Surface Mounted Device) the available space on the resistor is very small. 5% resistors use a 3 digit code, while 1% resistors use a 4 digit code.

Some SMD resistors are made in the shape of small cylinder while the most common type is flat. Cylindrical SMD resistors are marked with six bands - the first five are "read" as with common five-band resistors, while the sixth band determines the Temperature Coefficient (TC), which gives us a value of resistance change upon 1-degree temperature change.

The resistance of flat SMD resistors is marked with digits printed on their upper side. First two digits are the resistance value, while the third digit represents the number of zeros. For example, the printed number 683 stands for 68000W , that is 68k.

It is self-obvious that there is mass production of all types of resistors. Most commonly used are the resistors of the E12 series, and have a tolerance value of 5%. Common values for the first two digits are: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68 and 82.
The E24 series includes all the values above, as well as: 11, 13, 16, 20, 24, 30, 36, 43, 51, 62, 75 and 91. What do these numbers mean?  It means that resistors with values for digits "39" are: 0.39W, 3.9W, 39W, 390W, 3.9kW, 39kW, etc are manufactured. (0R39, 3R9, 39R, 390R, 3k9, 39k)

For some electrical circuits, the resistor tolerance is not important and it is not specified. In that case, resistors with 5% tolerance can be used. However, devices which require resistors to have a certain amount of accuracy, need a specified tolerance.

1.2 Resistor Dissipation

If the flow of current through a resistor increases,  it heats up, and if the temperature exceeds a certain critical value, it can be damaged. The wattage rating of a resistor is the power it can dissipate over a long period of time.
Wattage rating is not identified on small resistors. The following diagrams show the size and wattage rating:

Fig. 1.3: Resistor dimensions

Most commonly used resistors in electronic circuits have a wattage rating of 1/2W or 1/4W. There are smaller resistors  (1/8W and 1/16W) and higher (1W, 2W, 5W, etc).
In place of a single resistor with specified dissipation, another one with the same resistance and higher rating may be used, but its larger dimensions increase the space taken on a printed circuit board as well as the added cost.

Power (in watts) can be calculated according to one of the following formulae, where U is the symbol for Voltage across the resistor (and is in Volts), I is the symbol for Current in Amps and R is the resistance in ohms:

For example, if the voltage across an 820W resistor is 12V, the wattage dissipated by the resistors is:

A 1/4W resistor can be used.

In many cases, it is not easy to determine the current or voltage across a resistor. In this case the wattage dissipated by the resistor is determined for the "worst" case. We should assume the highest possible voltage across a resistor, i.e. the full voltage of the power supply (battery, etc).
If we mark this voltage as V_B, the highest dissipation is:

For example, if V_B=9V, the dissipation of a 220W resistor is:

A 0.5W or higher wattage resistor should be used

1.3 Nonlinear resistors

Resistance values detailed above are a constant and do not change if the voltage or current-flow alters. But there are circuits that require resistors to change value with a change in temperate or light. This function may not be linear, hence the name NONLINEAR RESISTORS.

There are several types of nonlinear resistors, but the most commonly used include : NTC resistors (figure a) (Negative Temperature Co-efficient) - their resistance lowers with temperature rise. PTC resistors (figure b) (Positive Temperature Co-efficient) - their resistance increases with the temperature rise. LDR resistors (figure c) (Light Dependent Resistors) - their resistance lowers with the increase in light. VDR resistors (Voltage dependent Resistors) - their resistance critically lowers as the voltage exceeds a certain value. Symbols representing these resistors are shown below.

Fig. 1.4: Nonlinear resistors - a. NTC, b. PTC, c. LDR

In amateur conditions where nonlinear resistor may not be available, it can be replaced with other components. For example, NTC resistor may be replaced with a transistor with a trimmer potentiometer, for adjusting the required resistance value. Automobile light may play the role of PTC resistor, while LDR resistor could be replaced with an open transistor. As an example, figure on the right shows the 2N3055, with its upper part removed, so that light may fall upon the crystal inside.

 
1.4 Practical examples with resistors
Figure 1.5 shows two practical examples with nonlinear and regular resistors as trimmer potentiometers, elements which will be covered in the following chapter.

Fig. 1.5a: RC amplifier

Figure 1.5a represents an RC voltage amplifier, that can be used for amplifying low-frequency, low-amplitude audio signals, such as microphone signals. The signal to be amplified is brought between node 1 (amplifier input) and gnd, while the resulting amplified signal appears between node 2 (amplifier output) and gnd. To get the optimal performance (high amplification, low distortion, low noise, etc) , it is necessary to "set" the transistor's operating point. Details on the operating point will be provided in chapter 4; for now, let's just say that DC voltage between node C and gnd should be approximately one half of battery (power supply) voltage. Since battery voltage equals 6V, voltage in node C should be set to 3V. Adjustments are made via resistor R1.
Connect a voltmeter between node C and gnd. If voltage exceeds 3V, replace the resistor R1=1.2MW with a smaller resistor, say R1=1MW. If voltage still exceeds 3V, keep lowering the resistance until it reaches approximately 3V. If the voltage at node C is originally lower than 3V, increase the resistance of R1.
The degree of amplification of the stage depends on R2 resistance: higher resistance - higher amplification, lower resistance - lower amplification. If the value of R2 is changed, the voltage at node C should be checked and adjusted (via R1).
Resistor R3 and 100µF capacitor form a filter to prevent feedback from occurring. This feedback is called "Motor-boating" as it sounds like the noise from a motor-boat. This noise is only produced when more than one stage is employed.
As more stages are added to a circuit, the chance of feedback, in the form of instability or motor-boating, will occur.
This noise appears at the output of the amplifier, even when no signal is being delivered to the amplifier.
The instability is produced in the following manner:
Even though no signal is being delivered to the input, the output stage produces a very small background noise called "hiss. This comes from current flowing through the transistors and other components.
This puts a very small waveform on the power rails. This waveform is passed to the input of the first transistor and thus we have produced a loop for "noise-generation." The speed with which the signal can pass around the circuit determines the frequency of the instability. By adding a resistor and electrolytic to each stage, a low-frequency filter is produced and this "kills" or reduces the amplitude of the offending signal. The value of R3 can be increased if needed. 

Practical examples with resistors will be covered in the following chapters as almost all circuits require resistors.

Fig. 1.5b: Sound indicator of changes in temperature or the amount of light

A practical use for nonlinear resistors is illustrated on a simple alarm device shown in figure 1.5b. Without trimmer TP and nonlinear NTC resistor it is an audio oscillator. Frequency of the sound can be calculated according to the following formula:

In our case, R=47kW and C=47nF, and the frequency equals:

When, according to the figure, trim pot and NTC resistor are added, oscillator frequency increases. If the trim pot is set to minimum resistance, the oscillator stops. At the desired temperature, the resistance of the trim pot should be increased until the oscillator starts working again. For example, if these settings were made at 2°C, the oscillator remains frozen at higher temperatures, as the NTC resistor's resistance is lower than nominal. If the temperature falls the resistance increases and at 2°C the oscillator is activated.
If an NTC resistor is installed in a car, close to the road surface, the oscillator can warn driver if the road is covered with ice. Naturally, the resistor and two copper wires connecting it to the circuit should be protected from dirt and water.
If, instead of an NTC resistor, a PTC resistor is used, the oscillator will be activated when the temperature rises above a certain designated value. For example, a PTC resistor could be used for indicating the state of a refrigerator: set the oscillator to work at temperatures above 6°C via trimmer TP, and the circuit will signal if anything is wrong with the fridge.
Instead of an NTC, we could use an LDR resistor - the oscillator would be blocked as long as a certain amount of light is present. In this way, we could make a simple alarm system for rooms where a light must be always on.
The LDR can be coupled with resistor R. In that case, the oscillator works when the light is present, otherwise it is blocked. This could be an interesting alarm clock for huntsmen and fishermen who would like to get up at the crack of dawn, but only if the weather is clear. For the desired moment in the early morning, the trim pot should be set to the uppermost position. Then, the resistance should be carefully reduced, until the oscillator starts. During the night the oscillator will be blocked, since there is no light and LDR resistance is very high. As the amount of light increases in the morning, the resistance of the LDR drops and the oscillator is activated when the LDR is illuminated with the required amount of light.
The trim pot from the figure 1.5b is used for fine adjustments. Thus, TP from figure 1.5b can be used for setting the oscillator to activate under different conditions (higher or lower temperature or amount of light).

1.5 Potentiometers
Potentiometers (also called pots) are variable resistors, used as voltage or current regulators in electronic circuits. By means of construction, they can be divided into 2 groups: coated and wire-wound.
With coated potentiometers, (figure 1.6a), insulator body is coated with a resistive material. There is a conductive slider moving across the resistive layer, increasing the resistance between slider and one end of pot, while decreasing the resistance between slider and the other end of pot.

Fig. 1.6a: Coated potentiometer

Wire-wound potentiometers are made of conductor wire coiled around insulator body.  There is a slider moving across the wire, increasing the resistance between slider and one end of pot, while decreasing the resistance between slider and the other end of pot.
Coated pots are much more common. With these, resistance can be linear, logarithmic, inverse-logarithmic or other, depending upon the angle or position of the slider. Most common are linear and logarithmic potentiometers, and the most common applications are radio-receivers, audio amplifiers, and similar devices where pots are used for adjusting the volume, tone, balance, etc.
Wire-wound potentiometers are used in devices which require more accuracy in control. They feature higher dissipation than coated pots, and are therefore in high current circuits.
Potentiometer resistance is commonly of E6 series, including the values: 1, 2.2 and 4.7. Standard tolerance values include 30%, 20%, 10% (and 5% for wire-wound pots).
Potentiometers come in many different shapes and sizes, with wattage ranging from 1/4W (coated pots for volume control in amps, etc) to tens of watts (for regulating high currents). Several different pots are shown in the photo 1.6b, along with the symbol for a potentiometer.

Fig. 1.6b: Potentiometers

The upper model represents a stereo potentiometer. These are actually two pots in one casing, with sliders mounted on shared axis, so they move simultaneously. These are used in stereophonic amps for simultaneous regulation of both left and right channels, etc.
Lower left is the so called slider potentiometer.
Lower right is a wire-wound pot with a wattage of 20W, commonly used as rheostat (for regulating current while charging a battery etc).
For circuits that demand very accurate voltage and current values, trimmer potentiometers (or just trim pots) are used. These are small potentiometers with a slider that is adjusted via a screwdriver.
Trim pots also come in many different shapes and sizes, with wattage ranging from 0.1W to 0.5W. Image 1.7 shows several different trim pots, along with the symbol.

Fig. 1.7: Trim pots

Resistance adjustments are made via a screwdriver. Exception is the trim pot on the lower right, which can be adjusted via a plastic shaft. Particularly fine adjusting can be achieved with the trim pot in the plastic rectangular casing (lower middle). Its slider is moved via a screw, so that several full turns is required to move the slider from one end to the other.

1.6 Practical examples with potentiometers
As previously stated, potentiometers are most commonly used in amps, radio and TV receivers, cassette players and similar devices. They are used for adjusting volume, tone, balance, etc.
As an example, we will analyze the common circuit for tone regulation in an audio amp. It contains two pots and is shown in the figure 1.8a.

Fig. 1.8 Tone regulation circuit: a. Electrical scheme, b. Function of amplification

Potentiometer marked BASS regulates low frequency amplification. When the slider is in the lowest position, amplification of very low frequency signals (tens of Hz) is about ten times greater than the amplification of mid frequency signals (~kHz). If slider is in the uppermost position, amplification of very low frequency signals is about ten times lower than the amplification of mid frequency signals. Low frequency boost is useful when listening to music with a beat (disco, jazz, R&B...), while Low Frequency amplification should be reduced when listening to speech or classical music.
Similarly, potentiometer marked TREBLE regulates high frequency amplification. High frequency boost is useful when music consists of high-pitched tones such as chimes, while for example High Frequency amplification should be reduced when listening to an old record to reduce the background noise.
Diagram 1.8b shows the function of amplification depending upon the signal frequency. If both sliders are in their uppermost position, the result is shown with curve 1-2. If both are in mid position function is described with line 3-4, and with both sliders in the lowest position, the result is shown with curve 5-6. Setting the pair of sliders to any other possible results in curves between curves 1-2 and 5-6.
Potentiometers BASS and TREBLE are coated by construction and linear by resistance.
The third pot in the diagram is a volume control. It is coated and logarithmic by resistance (hence the mark log)