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ultiplicator 1 an r is used instead of the decimal separator for example 1r2 indicates 1 2 ω and 18r indicates 18 ω theory of operation the hydraulic analogy compares electric current flowing through circuits to water flowing through pipes when a pipe left is clogged with hair right it takes a larger pressure to achieve the same flow of water pushing electric current through a large resistance is like pushing water through a pipe clogged with hair it requires a larger push voltage to drive the same flow electric current 1 ohm s law main article ohm s law an ideal resistor i e a resistance without reactance obeys ohm s law v i r displaystyle v i cdot r ohm s law states that the voltage v displaystyle v across a resistor is proportional to the current i displaystyle i passing through it where the constant of proportionality is the resistance r displaystyle r for example if a 300 ohm resistor is attached across the terminals of a 12 volt battery then a current of 12 300 0 04 amperes flows through that resistor the ohm symbol ω is the si unit of electrical resistance named after georg simon ohm an ohm is equivalent to a volt per ampere since resistors are specified and manufactured over a very large range of values the derived units of milliohm 1 mω 10 3 ω kilohm 1 kω 10 3 ω and megohm 1 mω 10 6 ω are also in common usage 2 3 p 20 series and parallel resistors main article series and parallel circuits the total resistance of resistors connected in series is the sum of their individual resistance values r e q i 1 n r i r 1 r 2 r n displaystyle r_ mathrm eq sum _ i 1 n r_ i r_ 1 r_ 2 cdots r_ n the total resistance of resistors connected in parallel is the reciprocal of the sum of the reciprocals of the individual resistors 3 p 20ff r e q i 1 n 1 r i 1 1 r 1 1 r 2 1 r 3 1 r n 1 displaystyle r_ mathrm eq left sum _ i 1 n frac 1 r_ i right 1 left 1 over r_ 1 1 over r_ 2 1 over r_ 3 dots 1 over r_ n right 1 for example a 10 ohm resistor connected in parallel with a 5 ohm resistor and a 15 ohm resistor produces 1 1 10 1 5 1 15 ohms of resistance or 30 11 2 727 ohms a resistor network that is a combination of parallel and series connections can be broken up into smaller parts that are either one or the other some complex networks of resistors cannot be resolved in this manner requiring more sophisticated circuit analysis generally the y δ transform or matrix methods can be used to solve such problems 4 5 6 power dissipation resistor warming caused by electrical current captured by thermal camera at any instant the power p watts consumed by a resistor of resistance r ohms is calculated as p i v i 2 r v 2 r displaystyle p iv i 2 r frac v 2 r where v volts is the voltage across the resistor and i amps is the current flowing through it using ohm s law the two other forms can be derived this power is converted into heat which must be dissipated by the resistor s package before its temperature rises excessively 3 p 22 resistors are rated according to their maximum power dissipation discrete resistors in solid state electronic systems are typically rated as 1 10 1 8 or 1 4 watt they usually absorb much less than a watt of electrical power and require little attention to their power rating an aluminium encased power resistor rated for dissipation of 50 w when mounted on a heat sink power resistors are required to dissipate substantial amounts of power and are typically used in power supplies power conversion circuits and power amplifiers this designation is loosely applied to resistors with power ratings of 1 watt or greater power resistors are physically larger and may not use the preferred values color codes and external packages described below if the average power dissipated by a resistor is more than its power rating damage to the resistor may occur permanently altering its resistance this is distinct from the reversible change in resistance due to its temperature coefficient when it warms excessive power dissipation may raise the temperature of the resistor to a point where it can burn the circuit board or adjacent components or even cause a fire there are flameproof resistors that will not produce flames with any overload of any duration resistors may be specified with higher rated dissipation than is experienced in service to account for poor air circulation high altitude or high operating temperature all resistors have a maximum voltage rating this may limit the power dissipation for higher resistance values 7 for instance among 1 4 watt resistors a very common sort of leaded resistor one is listed with a resistance of 100 mω 8 and a maximum rated voltage of 750 v however even placing 750 v across a 100 mω resistor continuously would only result in a power dissipation of less than 6 mw making the nominal 1 4 watt rating meaningless vzr power resistor 1 5 kω 12 w manufactured in 1963 in the soviet union nonideal properties practical resistors have a series inductance and a small parallel capacitance these specifications can be important in high frequency applications and while even an ideal resistor inherently has johnson noise some resistors have worse noise characteristics and so may be an issue for low noise amplifiers or other sensitive electronics in some precision applications the temperature coefficient of the resistance may also be of concern the unwanted inductance excess noise and temperature coefficient are mainly dependent on the technology used in manufacturing the resistor they are not normally specified individually for a particular family of resistors manufactured using a particular technology 9 a family of discrete resistors may also be characterized according to its form factor that is the size of the device and the position of its leads or terminals this is relevant in the practical manufacturing of circuits that may use them practical resistors are also specified as having a maximum power rating which must exceed the anticipated power dissipation of that resistor in a particular circuit this is mainly of concern in power electronics applications resistors with higher power ratings are physically larger and may require heat sinks in a high voltage circuit attention must sometimes be paid to the rated maximum working voltage of the resistor while there is no minimum working voltage for a given resistor failure to account for a resistor s maximum rating may cause the resistor to incinerate when current is run through it fixed resistors main article list of resistors a single in line sil resistor package with 8 individual 47 ohm resistors this package is also known as a sip 9 one end of each resistor is connected to a separate pin and the other ends are all connected together to the remaining common pin pin 1 at the end identified by the white dot lead arrangements axial resistors with wire leads for through hole mounting through hole components typically have leads pronounced l iː d z leaving the body axially that is on a line parallel with the part s longest axis others have leads coming off their body radially instead other components may be smt surface mount technology while high power resistors may have one of their leads designed into the heat sink carbon composition old style dog bone resistors with body tip dot color code marking three carbon composition resistors in a 1960s valve vacuum tube radio carbon composition resistors ccr consist of a solid cylindrical resistive element with embedded wire leads or metal end caps to which the lead wires are attached the body of the resistor is protected with paint or plastic early 20th century carbon composition resistors had uninsulated bodies the lead wires were wrapped around the ends of the resistance element rod and soldered the completed resistor was painted for color coding of its value the resistive element in carbon composition resistors is made from a mixture of finely powdered carbon and an insulating material usually ceramic a resin holds the mixture together the resistance is determined by the ratio of the fill material the powdered ceramic to the carbon higher concentrations of carbon which is a good conductor result in lower resistances carbon composition resistors were commonly used in the 1960s and earlier but are not popular for general use now as other types have better specifications such as tolerance voltage dependence and stress carbon composition resistors change value when stressed with over voltages moreover if internal moisture content such as from exposure for some length of time to a humid environment is significant soldering heat creates a non reversible change in resistance value carbon composition resistors have poor stability with time and were consequently factory sorted to at best only 5 tolerance 10 these resistors are non inductive which provides benefits when used in voltage pulse reduction and surge protection applications 11 carbon composition resistors have higher capability to withstand overload relative to the component s size 12 carbon composition resistors are still available but relatively expensive values ranged from fractions of an ohm to 22 megohms due to their high price these resistors are no longer used in most applications however they are used in power supplies and welding controls 12 they are also in demand for repair of vintage electronic equipment where authenticity is a factor carbon pile a carbon pile resistor is made of a stack of carbon disks compressed between two metal contact plates adjusting the clamping pressure changes the resistance between the plates these resistors are used when an adjustable load is required such as in testing automotive batteries or radio transmitters a carbon pile resistor can also be used as a speed control for small motors in household appliances sewing machines hand held mixers with ratings up to a few hundred watts 13 a carbon pile resistor can be incorporated in automatic voltage regulators for generators where the carbon pile controls the field current to maintain relatively constant voltage 14 this principle is also applied in the carbon microphone carbon film carbon film resistor with exposed carbon spiral tesla tr 212 1 kω in manufacturing carbon film resistors a carbon film is deposited on an insulating substrate and a helix is cut in it to create a long narrow resistive path varying shapes coupled with the resistivity of amorphous carbon ranging from 500 to 800 μω m can provide a wide range of resistance values carbon film resistors feature lower noise compared to carbon composition resistors because of the precise distribution of the pure graphite without binding 15 carbon film resistors feature a power rating range of 0 125 w to 5 w at 70 c resistances available range from 1 ohm to 10 megaohm the carbon film resistor has an operating temperature range of 55 c to 155 c it has 200 to 600 volts maximum working voltage range special carbon film resistors are used in applications requiring high pulse stability 12 printed carbon resistors carbon resistors black rectangles printed directly onto the smd pads on the pcb of a psion organiser ii from 1989 carbon composition resistors can be printed directly onto printed circuit board pcb substrates as part of the pcb manufacturing process although this technique is more common on hybrid pcb modules it can also be used on standard fibreglass pcbs tolerances are typically quite large and can be in the order of 30 a typical application would be non critical pull up resistors thick and thin film laser trimmed precision thin film resistor network from fluke used in the keithley dmm7510 multimeter ceramic backed with glass hermetic seal cover thick film resistors became popular during the 1970s and most smd surface mount device resistors today are of this type the resistive element of thick films is 1000 times thicker than thin films 16 but the principal difference is how the film is applied to the cylinder axial resistors or the surface smd resistors thin film resistors are made by sputtering a method of vacuum deposition the resistive material onto an insulating substrate the film is then etched in a similar manner to the old subtractive process for making printed circuit boards that is the surface is coated with a photo sensitive material covered by a pattern film irradiated with ultraviolet light and then the exposed photo sensitive coating is developed and underlying thin film is etched away thick film resistors are manufactured using screen and stencil printing processes 12 because the time during which the sputtering is performed can be controlled the thickness of the thin film can be accurately controlled the type of material also varies consisting of one or more ceramic cermet conductors such as tantalum nitride tan ruthenium oxide ruo 2 lead oxide pbo bismuth ruthenate bi 2 ru 2 o 7 nickel chromium nicr or bismuth iridate bi 2 ir 2 o 7 the resistance of both thin and thick film resistors after manufacture is not highly accurate they are usually trimmed to an accurate value by abrasive or laser trimming thin film resistors are usually specified with tolerances of 1 and 5 and with temperature coefficients of 5 to 50 ppm k they also have much lower noise levels on the level of 10 100 times less than thick film resistors 17 thick film resistors may use the same conductive ceramics but they are mixed with sintered powdered glass and a carrier liquid so that the composite can be screen printed this composite of glass and conductive ceramic cermet material is then fused baked in an oven at about 850 c when first manufactured thick film resistors had tolerances of 5 but standard tolerances have improved to 2 or 1 in the last few decades timeframe temperature coefficients of thick film resistors are typically 200 or 250 ppm k a 40 kelvin 70 f temperature change can change the resistance by 1 thin film resistors are usually far more expensive than thick film resistors for example smd thin film resistors with 0 5 tolerances and with 25 ppm k temperature coefficients when bought in full size reel quantities are about twice the cost of 1 250 ppm k thick film resistors metal film a common type of axial leaded resistor today is the metal film resistor metal electrode leadless face melf resistors often use the same technology metal film resistors are usually coated with nickel chromium nicr but might be coated with any of the cermet materials listed above for thin film resistors unlike thin film resistors the material may be applied using different techniques than sputtering though this is one technique used the resistance value is determined by cutting a helix through the coating rather than by etching similar to the way carbon resistors are made the result is a reasonable tolerance 0 5 1 or 2 and a temperature coefficient that is generally between 50 and 100 ppm k 18 metal film resistors possess good noise characteristics and low non linearity due to a low voltage coefficient they are also beneficial due to long term stability ...