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A resistor in electrical circuits and electronics is an element that resists the flow of an electrical current. As a result it limits the current and consequently results in a voltage drop across itself. A resistor is a passive element, meaning it is incapable of producing energy or supplying it to the circuit. Unlike capacitors, diodes and other elements, the resistor is not a polarized device i.e. it can be placed in a circuit without any concerns of it "facing" a particular direction.

Figure 1: shows the representation of the resistor in a circuit diagram or schematic. It may also be shown as a rectangle in some conventions (mainly European). Commonly resistors are used with fixed values (measured in Ohms). However, some tuning and other applications require variable resistances which are denoted as shown in Figure 1.

Ohm's Law

Ohm's law represents the relationship between the voltage drop across and the current through an ideal conductor. It states that the voltage drop is proportional to the current and the constant of proportionality is the resistance R of the conductor. This relationship holds true for most practical applications and the resistance is measured, therefore, in Ohms Ω.

Color Coding

To denote the value of resistors, unfortunately it was initially not feasible to write the exact values on them. Instead, the resistance of a resistor is expressed by colored bands which are easier to print on the components. However, the drawbacks include the limitations of use by color blind people and ambiguity in case of close colors (for example red and brown) especially after overheating of the element. Many modern elements have values printed on them. Nonetheless, color coded resistors are more widespread and dominant.

4-Band Code

The 4-band code is more common. Figure 2 shows a 1.0 kΩ with the 4-band color coding. To denote the left to right sequence there is a larger gap between the third and fourth band. The first band represents the first digit, the next band represents the second digit and the third band represents the multiplier. The fourth band represents the tolerance as provided by the manufacturer.

5-Band Code

The 5-band color code is similar to the 4-band code except that the third band represent the third digit and the fourth band the multiplier. The last i.e. fifth band represents the tolerance as before. Again the bands are read left to right and the gap helps to figure that out.

Coding Table

The coding table (Table 1) lists the values represented by each color at the each band. This table is applicable for both 4 band coding and 5 band coding. Naturally, in the 4-band color coding scheme the third band is the multiplier.

Series And Parallel Connection

Resistances when connected in series add up, provided that there is no active element between the connections.

Consider Figure 4, which shows the series connection of four 10 kΩ resistors. In this circuit, the resistance between the two terminals is simply the addition of the resistances.

i.e. RT = 10 kΩ + 10 kΩ + 10 kΩ + 10 kΩ = 40 kΩ

On the other hand, resistors in parallel offer different paths to the flowing current. The lower the resistance of the path, the higher will be the current value through that path. For example, consider Figure 5, if R2 < R1 then I2 > I1. The effective resistance between the terminals RT is calculated using:

This is derived using again Kirchhoff's laws for current and voltage. Many resistive circuits can be decomposed to be a combination of series and parallel connection of resistors and therefore the above relationships come in handy calculating effective resistance of the circuit.

Selection of Resistors

As current flows through resistors, it produces heat which leads to the rise in temperature of the resistances above the normal operating temperature of the circuit and ambient temperature. An effective resistive element must be able to physically withstand the deterioration due to temperature rise. Hence, it must be able to dissipate certain wattage without reaching the "hot-spot". Therefore wattage of the resistor is particularly important. Commonly available resistors are of ¼ Watt while higher wattage elements include ½ W and 1 W and higher. Also lower wattages of ⅛ and 1/10 are available for small circuitry as higher wattages usually translate to bigger sizes. If the selected resistor experiences constant power dissipation higher than its rated wattage, it may be permanently damaged and would not exhibit resistance it was originally specified. Therefore selection of resistors is a particularly important issue and must be addressed accordingly.

Calculation of Resistance and Watts

The most common practice is to determine the resistance by using the values of the desired voltage and current. From simple circuit analysis, voltage across the resistor can be determined (at least to a tolerable range) and the current through the resistor as well. What remains is the use of Ohm's law to calculate the resistance R. Practically not all resistor values are available and usually the closest standard (or the closest higher standard) value is chosen of the resistor. This means that the current and voltage must be determined again according to the selected value of the resistor. To achieve some particular values, series and/or parallel connections of resistances can be used. The power in watts can be determined using any of the formulas below:

Naturally to calculate power in watts, the current must be in Amperes (A), voltage in Volts (V), and resistance in Ohms (Ω). Calculation of wattage is particularly important as it can be seen from the formulas above, small changes in current I or voltage V can lead to significant changes in power. For example an increase of 20% in current will result in 44% increase in power. Therefore, the worst case scenario must be taken into account to adequately select the proper resistor.

Finding the Correct 'Watt Size'

The 'watt-size' is the physical size which corresponds to the wattage selected for the resistor. If a resistor is operated at a constant wattage, it will reach a constant temperature which is dependent upon the physical size of the resistor and the dissipation. If the resistor has a higher surface area per watt dissipated, there would be faster heat loss and lower temperature rise. While a larger physical size of the resistor may lead to stable values and lower temperature rise, it may be unpractical for specific circuitry. Therefore, a resistor size should be selected keeping in mind its placement on the circuitry and the power determined in the first step.

Types of Resistors

There are many types of resistors each coined to fit a particular application. Some of them are much more popular while others offer service under harsh conditions such as very high temperatures. The technologies vary among the different types and are discussed accordingly in the following.

Carbon Composition Resistors

This is the most widely used type of resistors for up to most semi-professional applications. Carbon composition resistors are fixed type resistors and are typically very cheap and therefore very popular for initial research and non-professional circuitry construction. They are more commonly referred to as carbon resistors. Many carbon resistors are made of a cylindrical carbon clay composition that is covered by plastic and then a color coding (described previously) is printed on the resistor to denote its value. The leads are made from copper that is covered by tin to avoid chemical corrosion etc. The resistance is set from the ratio of the carbon to the ceramic (or other fill material). They are inexpensive, highly durable, and available in a huge range of values from 1Ω to several mega ohms. However, the drawback of carbon resistors is that they are highly temperature dependent (compared to other types). Also with overlong exposure to humid environments, the resistors change their resistance value. These drawbacks make carbon resistors not favorable for sensitive and professional circuits. However, if temperature variations aren’t significant and other negative parameters are non-existent, carbon resistors can provide very reliable and durable resistance considering their small sizes and inexpensive production.

Resistor Networks / Arrays

This type is particularly popular and has many applications. Resistor network (or array) is an IC that contains two or more resistors in a network. Commonly there are multiple leads to connect the external circuit to. Each lead connects the circuit to a different resistance and many multiple values of resistance can be achieved by connecting chosen leads to circuit terminals. Resistor networks (or arrays) are popular because they reduce the space taken by typical carbon resistors on boards. Additionally, most ICs are more reliable than commonly available individual resistors. Similar to the common carbon resistors, resistor networks are also accompanied by a tolerance value. Also inclusive in the important parameters for resistor networks is the Ratio Tolerance, TCR (temperature coefficient of resistance), and TCR Tracking Ratio. The Ratio Tolerance is the allowed deviation from a specified ratio that is formed by two or more values in the resistor network. This also is defined as a percentage. TCR is the expected variation in the value of resistance for change in temperature. It is usually defined in %/oC or PPM/oC.

There are many types of circuits and connections available in resistor networks and therefore many different models of ICs. The "I" or Isolated type standard circuits are shown in Figure 8. Four such circuits are shown which are from different ICs from two manufacturers.

Figure 9 shows four circuits for the second standard type of resistor networks: Bussed Type resistor networks. Again different IC circuits from two different manufacturers have been shown.

Naturally, there are special ICs produced for application based circuits. Among the many applications of resistor networks are AC Terminators, CMOS Terminators, EMI/RFI Filters, R2R Ladder Networks, Single Ended SCSI Terminators, and Differential SCSI Terminators. Like many ICs, they are available in multiple constructions including surface mounted, thick film, single in line, dual in line, and flat chip.

Varistors

A varistor is a special type of resistor that deviates away from the typical Ohm's law relationship between voltage and current. Unlike, the other resistors, varistors have non linear characteristics, much like diodes. However, unlike diodes varistors allow the flow of current in both directions thereby making them effective in compensation circuits. It is important not to confuse varistors with other variable resistors (rheostats and potentionmeters) as the other variable resistors follow the typical Ohm's law relationship. Varistors have high resistance at lower voltages but as the voltage pass a certain level, the varistor becomes highly conductive. The graph in Figure 10 shows this characteristic.

Using these characteristics, varistors can be used as protection devices to protect sensitive circuits from high voltages. These high voltages occur from transients or surges. When a varistor is connected in shunt to sensitive circuitry, it is triggered in case of high voltages and therefore allows maximum current to flow through it; thereby keeping the circuit safe. Modern varistors have very attractive features to make them reliable and economical for use as protection against surges. They are available in a wide range of voltages from about 14 VRMS to 680 VRMS. Many modern varistors have response time as low as 20 ns. Since they have very high stand-by resistance (resistance at low voltages), they offer typically negligible power loss. Also with low capacitance values, modern varistors are favorable to be used in digital circuits. Due to their remarkable features, varistors have found their use in applications such as computers, timers, amplifiers, oscilloscopes, medical analysis equipment, street lighting, tuners, controllers, telecommunications, gas and petrol appliances, electronic home appliances, relays, electromagnetic valves, power supplies, and line ground (earth protection).

Thermistors (Temperature Dependent Resistor)

These resistors are particularly sensitive to changes in temperature. Typically, increasing the temperature results in production of more free electrons hence more current, consequently lower resistance. At low temperatures, the resistance is particularly high. are constructed using semiconductor materials (or sometimes ceramics and polymers) which allows them to exhibit large variations of resistance against small variations in temperature. They therefore make incredibly accurate temperature sensors. The resistance in thermistor varies according to the relationship: ΔR=kΔT

where ΔR is the change in resistance, k is the first-order temperature coefficient, and ΔT is the change in temperature. The classification of thermistor occurs by the sign of the temperature coefficient k. If k is positive, the resistance increases by increasing temperature, and such thermistors are referred to as positive temperature coefficient thermistors (or simply posistors). Vice versa, for negative k, resistance decreases for increasing temperature and thermistors are referred to as negative temperature coefficient thermistors. In other type of resistors, the value of k is kept as close to 0 as possible in order to avoid change in resistance when resistor temperature changes. Generally, negative temperature coefficient thermistors are constructed using semiconductors while positive temperature coefficient resistors are constructed using ceramics. One particular phenomenon is very interesting about thermistors: self-heating. As the thermistor conducts current, it heats up due to its own current and therefore causes a change in temperature that is only due to the conduction of current. When measuring ambient or other temperatures, this effect is taken into account to avoid error. Thermistors find their applications in temperature sensors, self-regulating heating elements, temperature alarm circuits, and surge current limiting (inrush current limiting). Table 2 distributes few applications by temperature coefficient type.

Foil Resistors

Foil resistors are the modern resistors with the most desirable characteristics. They act as high precision resistances with low temperature coefficients, long term stability, low noise, low capacitance, and no inductance. The resistance is offer by a very thin piece of metal. The low temperature coefficients translate to the stability of the element value and characteristics despite significant changes in temperature. As said before, this is a particularly important trait especially in modern boards. The foil is usually composed of alloys of Nichrome which are mounted on a ceramic carrier. This ceramic carrier features high heat conductivity. The resistance value is set by a photoetched resistive pattern in the foil, which is itself only few micrometers thick. Foil resistors are specially designed to avoid introducing any delays in the circuit due to capacitance and inductance of the element. Wire-wound resistors introduce such delays.

Foil resistors find their applications in many modern circuits. Most audio components are constructed using foil resistors. They exploit the accurate value of the resistors and also their capability to function without noise or distortion. The photoetched design can also alter foil resistors into potentiometers. Foil resistors with high signal to noise ratio (SNR) are used in audio components. Foil resistors can also withstand very high ambient temperatures. One particular case is with oil rigs where temperatures may go up to 500 degrees. The foil resistors for such cases are especially design and manufactured to work with reliability and precision in such environments. Modern foil resistors can have tolerances as low as 0.005% and therefore offer very high precision resistance. Therefore, they are widely used in aviation and applications where accuracy is particularly vital. This high precision resistance is also exploited in electronic scales

Wire Wound Resistors

Wire wound resistors are constructed by winding a metal wire around a core (usually ceramic) with the wire ends connected to caps or rings. This structure is then coated with protective material, which may include molded plastic or baked enamel coating. High power wire wound resistors an additional ceramic or aluminum outer case is used. Aluminum cases can be attached to heat sinks since wire wound resistors are particularly designed to withstand very high temperatures typically up to 450 degrees. Especially designed wire wound resistors can function for 1000 Watts or more.

Since wire wound resistors are constructed with coils around a core, they intend to introduce inductances in AC circuits. Therefore, they are not particularly liked especially at higher frequencies and in fact possess the worst properties among resistors as high frequency applications. However, wire wound resistors find their use in various other applications. One such is their use as circuit breakers because of their high power characteristics. At higher currents, the resistor heats up and the soldering melts, breaking the circuit naturally while leaving the resistor intact. The inherent inductance of the wire wound resistors is helpful in using them as current sensors. They are used in circuits with high currents like large cooling pumps or freezer units.

Metal Film Resistors

Metal film resistors look very similar to carbon resistors but have significantly enhanced characteristics in stability, accuracy and reliability. A thin metal layer acts as the resistive element which is kept in an insulating body. To achieve high accuracy, the metal is aged manually at very low temperatures. At the ends are metal covers connected to the leads. To set the resistance value, a spiral shaped slot is cut into the film using lasers or any other suitable technology. Metal film resistors have multiple protection layers that are baked individually to offer maximum protection to the resistor.

Metal film resistors are favored in circuits that demand low noise and high linearity characteristics. Active filters or bridge circuits are two such applications where metal film resistors are used. However, to maintain the reliability of the metal film resistors, they are operated normally between 20 to 80 percent of their rated power. A variant of metal film resistors is the metal oxide film resistors. They offer superior characteristics (like power rating, overload capability, withstanding higher temperatures etc.) than both carbon resistors and metal film resistors. However, they are less stable than metal film resistors.

Pententiometers, Rheostats and Trimmers

Potentiometers are three terminal resistors that work as variable resistors when two terminals are used. They usually have a rotating or sliding piece which varies the resistance between the two terminals. They are particularly popular in simple volume controls and similar applications. Potentiometers are suited largely for low currents and low powers. If used at higher power (usually >1 W), they tend to cause significant losses. Rheostats are also a type of variable resistors but differ from potentiometers in that rheostats typically possess only two terminals. They are formed by a coil of wire around a core. One terminal is attached to the end of the coil while the other taps the coil and moves along as the rheostats value is varied. The term rheostat is now largely replaced with potentiometer. Trimmers is a broad term for electrical component whose value can be varied by turning a screw on them. Trimmers include variable inductors, variable capacitors, and variable resistors (generally referred as potentiometers). Most variable resistors are used to calibrate equipment and are used in initial phases of designing (particularly in hit and trial).

Fuse Resistors

Fuse resistors are used, as the name suggests, mostly as fuses to protect the circuits against high currents. Unlike the typical fuses, fuse resistors can also limit the current by offering resistance. When the current goes higher than a set value, the fuse resistor is damaged and breaks the circuit. In this way it protects the main circuit from damage. Fuse resistors act as normal resistors under normal operating conditions and as a fuse only under severe fault conditions.