Resistors

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. Resistors act to reduce current flow, and, at the same time, act to lower voltage levels within circuits.

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 below shows some low-power 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.

 

This photo shows some higher-power resistors, with power dissipation above 5 watt are shown below.

 

 

 

 

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

 

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

 

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:

 

 

a. Four-band resistor, b. Five-band resistor, c. Cylindrical SMD resistor, d. Flat SMD resistor

 

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.

 

Resistor Power 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:

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 820 Ω 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 U_B, the highest dissipation is:

For example, if U_B=9V, the dissipation of a 220 Ω resistor is:

 

A 0.5W or higher wattage resistor should be used.

 

 

 

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Ohm's Law

 

The relationship between Voltage, Current and Resistance in any DC electrical circuit was firstly discovered by the German physicist Georg Ohm. Ohm found that, at a constant temperature, the electrical current flowing through a fixed linear resistance is directly proportional to the voltage applied across it, and also inversely proportional to the resistance.

This relationship between the Voltage, Current and Resistance forms the bases of Ohms Law and is shown below.

 

 Ohm's Law Relationship

 

By knowing any two values of the Voltage, Current or Resistance quantities we can use Ohm's Law to find the third missing value. Ohm's Law is used extensively in electronics formulas and calculations so it is “very important to understand and accurately remember these formulas”.

 

To find the Voltage ( V )

[ V = I x R ]      V (volts) = I (amps) x R (Ω)

 

To find the Current ( I )

[ I = V ÷ R ]      I (amps) = V (volts) ÷ R (Ω)

 

To find the Resistance ( R )

[ R = V ÷ I ]      R (Ω) = V (volts) ÷ I (amps)

 

It is sometimes easier to remember Ohms law relationship by using pictures. Here the three quantities of V, I and R have been superimposed into a triangle (affectionately called the Ohm's Law Triangle) giving voltage at the top with current and resistance at the bottom. This arrangement represents the actual position of each quantity in the Ohms law formulas.

 

Ohms Law Triangle

 

Transposing the above Ohms Law equation gives us the following combinations of the same equation:

 

Then by using Ohms Law we can see that a voltage of 1V applied to a resistor of 1Ω will cause a current of 1A to flow and the greater the resistance, the less current will flow for any applied voltage. Any Electrical device or component that obeys “Ohms Law” that is, the current flowing through it is proportional to the voltage across it ( I α V ), such as resistors or cables, are said to be “Ohmic” in nature, and devices that do not, such as transistors or diodes, are said to be “Non-ohmic” devices.

 

Ohm's Law Example

For the circuit shown below find the Voltage (V), the Current (I), the Resistance (R)

 

Voltage   [ V = I x R ] = 2 x 12Ω = 24V

Current   [ I = V ÷ R ] = 24 ÷ 12Ω = 2A

Resistance   [ R = V ÷ I ] = 24 ÷ 2 = 12 Ω

Georg Simon Ohm, Alessandro Volta, André-Marie Ampère

 

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