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# Resistor

An ideal resistor is a component with an electrical resistance that remains constant regardless of the applied voltage or current flowing through the device.

While "real world" resistors cannot attain this perfect goal, they are designed to present little variation in electrical resistance when subjected to changing temperature and other environmental factors.

Resistors may be fixed or variable. Variable resistors are also called potentiometers or rheostats (see below) and allow the resistance of the device to be altered by turning a shaft or sliding a control.

A few resistor types

Some resistors are long and thin, with the actual resisting material in the centre, and a conducting metal leg on each end. This is called an axial package. The photo below right shows a row of commonly used resistors in a bandolier. Resistors used in computers and other devices are typically much smaller, often in surface-mount (Surface-mount technology) packages without leads. Larger power resistors come in more sturdy packages designed to dissipate heat efficiently, but they are all basically the same structure.

Resistors are used as part of electrical networks and incorporated into microelectronic semiconductor devices. The critical measurement of a resistor is its resistance, which serves as a ratio of voltage to current and is measured in ohms, an SI unit. A component has a resistance of 1 ohm if a voltage of 1 volt across the component results in a current of 1 ampere, or amp, which is equivalent to a flow of one coulomb of electrical charge (approximately 6.241506 × 1018 electrons) per second in the opposite direction. (see: Current)

Any physical object is a kind of resistor. Most metals are conductors, and have low resistance to the flow of electricity. The human body, a piece of plastic, or even a vacuum has a resistance that can be measured. Materials that have very high resistance are called insulators.

Resistors packaged in a bandolier

The relationship between voltage, current, and resistance through an object is given by a simple equation, derived from and often confused with Ohm's Law:

$V = I \times R$

where V is the voltage across the object in volts, I is the current through the object in amperes, and R is the resistance in ohms. If V and I have a linear relationship -- that is, R is constant -- along a range of values, the material of the object is said to be ohmic over that range. An ideal resistor has a fixed resistance across all frequencies and amplitudes of voltage or current.

Superconducting materials at very low temperatures have zero resistance. Insulators (such as air, diamond, or other non-conducting materials) may have extremely high (but not infinite) resistance, but break down and admit a larger flow of current under sufficiently high voltage.

The resistance of a component can be calculated from its physical characteristics. Resistance is proportional to the length of the resistor and to the material's resistivity (a physical property of the material) and inversely proportional to cross-sectional area. The equation to determine resistance of a section of material is:

$R = {\rho \cdot L \over A}$

$\mathbf\rho$ is the resistivity of the material, $\mathbf{L}$ is the length, and $\mathbf{A}$ is the cross-sectional area. This can be extended to an integral for more complex shapes, but this simple formula is applicable to cylindrical wires and most common conductors. This value is subject to change at high frequencies due to the skin effect, which decreases the available surface area.

Standard resistors are sold in values from a few milliohms to about a gigohm; only a limited range of values called preferred values are available. In practice, the discrete component sold as a "resistor" is not a perfect resistance, as defined above. Resistors are often marked with their tolerance (maximum expected variation from the marked resistance). On color coded resistors a rightmost silver band denotes 10% tolerance, a gold band 5% tolerance, a red band 2% tolerance, and a brown band 1% tolerance. Closer tolerance resistors, called precision resistors, are also available.

A resistor has a maximum working voltage and current above which the resistance may change (drastically, in some cases) or the resistor may be physically damaged (burn up, for instance). Although some resistors have specified voltage and current ratings, most are rated with a maximum power which is determined by the physical size. Common power ratings for carbon composition and metal-film resistors are 1/8 watt, 1/4 watt, and 1/2 watt. Metal-film resistors are more stable than carbon resistors against temperature changes and age. Larger resistors are able to dissipate more heat because of their larger surface area. Wire-wound and sand-filled resistors are used when a high power rating is required, such as 20 watts.

Furthermore, all real resistors also introduce some inductance and capacitance, which change the dynamic behavior of the resistor from the ideal equation.

Resistors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent resistance (Req):

$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}$

The parallel property can be represented in equations by two vertical lines "||" (as in geometry) to simplify equations. For two resistors,

$R_{eq} = R_1 \| R_2 = {R_1 R_2 \over R_1 + R_2}$

The current through resistors in series stays the same, but the voltage across each resistor can be different. The sum of the potential differences (voltage) is equal to the total voltage. To find their total resistance:

$R_{eq} = R_1 + R_2 + \cdots + R_n$

A resistor network that is a combination of parallel and series can sometimes be broken up into smaller parts that are either one or the other. For instance,

$R_{eq} = \left( R_1 \| R_2 \right) + R_3 = {R_1 R_2 \over R_1 + R_2} + R_3$

However, many resistor networks cannot be split up in this way. Consider a cube, each edge of which has been replaced by a resistor. Determining the resistance between (say) two opposite vertices requires matrix methods for the general case. However, if all twelve resistors are equal, the corner-to-corner resistance is 5/6 of any one of them.

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## Variable resistor

The variable resistor is a resistor whose value can be adjusted by a mechanical movement, for example by being turned by hand.

Variable resistors can be cheap single-turn types or multi-turn types with a helical element. Some even have a mechanical display to count the turns.

Traditionally, variable resistors have been unreliable, because the wire or metal would corrode or wear. Some modern variable resistors use plastic materials that do not corrode.

(Another method of control, which is not actually a resistor, but behaves like one, involves a photoelectric sensor system which measures the optical density of a piece of film. Since the sensor does not touch the film, no wear is possible.)

A rheostat is a variable resistor with two terminals, one fixed and one sliding. It is often used with high currents.

A potentiometer is a common type of variable resistor. One common use is as volume controls on audio amplifiers.

A Metal Oxide Varistor, or M.O.V. is a special type of resistor which has 2 very different resistance values, a very high resistance at low voltage (below the trigger voltage) and very low resistance at high voltage (above the trigger voltage). It is usually used for short circuit protection in power strips or lightning bolt "arrestors" on street power poles, or as a "snubber" in back electromotive force circuits.

A thermistor is a temperature dependent resistor. There are two kinds, classified according to their temperature coefficients:

• PTC resistor is a resistor with a positive temperature coefficient. When the temperature rises the resistance of the PTC increases. PTC's are often found in televisions in series with the demagnetizing coil where they are used to provide a short current burst through the coil when the TV is turned on. One specialized version of a PTC is the polyswitch which acts as a self repairing fuse.
• NTC resistor is also a temperature dependent resistor, but with a negative temperature coefficient. When the temperature rises the resistance of the NTC drops. NTC's are often used in simple temperature detectors and measuring instruments.

## Identifying Resistors

Most axial resistors use a pattern of coloured stripes to indicate resistance. SMT ones follow a numerical pattern. Cases are usually brown, blue, or green, though other colours are occasionally found like dark red or dark gray.

### 4-band Axial Resistors

(See: Electronic colour code)

4 band identification is the most commonly used colour coding scheme on all resistors. It consists of four coloured bands that are painted around the body of the resistor. The scheme is simple: The first two numbers are the first two significant digits of the resistance value, the third is a multiplier, and the fourth is the tolerance of the value. Each colour corresponds to a certain number, shown in the chart below. The tolerance for a 4-band resistor will be 2%, 5%, or 10%

Colour 1st band 2nd band 3rd band (multiplier) 4th band (tolerance) Temp. Coefficient
Black 0 0 ×100
Brown 1 1 ×101 ±1% (F) 100 ppm
Red 2 2 ×102 ±2% (G) 50 ppm
Orange 3 3 ×103   15 ppm
Yellow 4 4 ×104   25 ppm
Green 5 5 ×105 ±0.5% (D)
Blue 6 6 ×106 ±0.25% (C)
Violet 7 7 ×107 ±0.1% (B)
Gray 8 8 ×108 ±0.05% (A)
White 9 9 ×109
Gold     ×0.1 ±5% (J)
Silver     ×0.01 ±10% (K)
None       ±20% (M)

Note that red to violet are the colours of the rainbow where red is low energy and violet is higher energy. Resistors use specific values, which are determined by their tolerance. These values repeat for every exponent; 6.8, 68, 680, etc. This is useful because the digits, and hence the first two or three stripes, will always be similar patterns of colours, which make them easier to recognize.

### 5-band Axial Resistors

5-band identification is used for higher tolerance resistors (1%, 0.5%, 0.25%, 0.1%), to notate the extra digit. The first three bands represent the significant digits, the fourth is the multiplier, and the fifth is the tolerance.