# Discover General Technical Information

## 1. Definitions

Resistivity (ρ)

Resistivity is a physical characteristic proper to the materials. It can be defined as the electrical resistance given by a prisme of material having a length “l” of 1 cm and section of 1 cm², expressed by the following equation: (Ω ⋅ cm)

Resistance (R)

The resistance is declined by applying a voltage to the leads of a resistor, measuring the current value “l” and performing the following ratio: (Ω)

The resistance is declined by applying a voltage to the leads of a resistor, measuring the current value “l” and performing the following ratio.

Resistive element

It is the portion of material (having specific resistivity characteristics) comprised between two leads. Generally it consists of a resistive wire wound on an insulating body.

Non-Inductive Resistive Element

A resistive element constructed in such way to reduce the inductance of the resistor to the minimum.

Resistor

Straight line passive dipole with resistance R. It consists of a resistive element connected between two leads. Resistor with intermediate taps-Voltage Divider

A resistor with fixed electrical connections (taps) derived from the body of the resistive element. Connecting one of the leads with the different taps different resistance values are obtained.

A resistor with a tapping band which can be adjusted on the body of the resistive element so that the resistance between the tap and anyone of the leads can be changed. Nominal Resistance (Rn)

The resistance value printed on the resistor body.

Nominal Voltage (Vn)

The voltage value derived from the rated power and the nominal resistance. Nominal Current (In) Rated Power (Pn)

It is the power printed on the resistor body or in the tables. It corresponds to the maximum power that a resistor can continuously keep dissipating at 25°C ambient temperature.

Specific Power

It is the power per surface unit dissipated by the resistor body. It is expressed in W/cm2

Limiting Voltage (Vlim)

It is the maximum voltage applicable to the resistor.

Critical Resistance (Rc

The resistance value resulting from the maximum voltage and the rated power. Ambient Temperature

It is the temperature of the air surrounding the resistor under load not too near to the resistor body.

Power-Ambient Temperature Characteristic

It expresses the maximum power that can be dissipated according to the ambient temperature.

Surface Temperature

The temperature of the hot spot of the resistor body when it is under load.

Power-Surface Temperature Characteristics

It is the relation connecting the resistor surface temperature to the dissipated power.

It is the test performed to ensure that the resistor is fit to dissipate the rated power, for the length of time and the conditions prescribed by the relevant specifications, without any failure or resistance change beyond the acceptable limit.

It is the test performed to ensure that the resistor is fit to withstand an overload up to ten times the rated power for 5 seconds, according to the testing rules stated in MIL-R-26 specifications, without exceeding the acceptable limits of failure and resistance changes

Temperature Coefficient

It is the resistance change of the resistive element for 1°C ambient temperature change as compared to a stated temperature and for each ohm of initial resistance. It is generally expressed in ppm/°C (part per million per degree centigrade) by the following equation: (ppm/°C)

where:

• R1 = resistance in ohm at a stated temperature
• R2 = resistance in ohm at the testing temperature
• T1 = reference temperature in °C
• T2 = test temperature in °C
For special applications which require very constant resistance, it may be necessary to specify the maximum permissible TCR for the range of temperature involved. This would limit the choice of wire to only certain types of resistance alloys. The commonly known low TCR alloys consist largely of nickel and chromium alloyed with small amounts of aluminum and either copper or iron. Other low resistivity alloys, consist primarily of nickel and copper with only traces of other metals.
The TCR does not change in a linear way as shown in the two grafs below: the one on the left refers to Ni/Cr 80/20 the one on the right to Ni/Cr 40.  The circuit designer should carefully consider the actual needs of the circuit before specifying limits on the TCR of a desired resistor. Wherever possible it is best to select a resistor for a critical  application so that it operates at a low temperature rise. This will also provide the maximum  stability over a long period.
In the catalogue we indicate TCR range from minimum 20 (CuNi44) to maximum 1.000 for resistor made with AISI304.
In the following table there are the values of TCR for the most common alloys used.

 Alloy TCR CuNi 44 20 Ni/Cr 80/20 60 Ni/Cr 60/15 170 Ni/Cr 40/20 240 90/95 450 AISI310 500 AISI304 940

Insulation resistance

It is the resistance measured according to MIL -R-26 specifications, between the leads connected together and the outside coat or the mounting devices.

Dielectric withstanding voltage

It is the maximum sinusoidal AC rms voltage applicable according to MIL-R-26 specifications, between the terminals connected together and the outside insulating coat or the mounting devices or housing that can be tolerated by the resistor without any failure or surface flash or disruptive discharge.

Thermal Time Constant

It is indicated with τ and represents one forth of the time necessary to reach the steady temperature. (ppm/°C)

## 2. Fundamental formulae of resistors

OHM’s Law

It expresses the relations between voltage “V” applied to the terminals of a resistor the current “l” passing through it and the resistance “R” bucking the flow of the current. The above expression allows to find the third term when two terms are known and Resistors in series

The total resistance of several resistors in series is equal to the sum of the resistances of each unit: Resistors in parallel

The total resistance of several resistors in parallel is equal to the reciprocal of the sum of the reciprocals of the single resistors: Dissipated Power

The power W dissipated by a resistor is the result of the voltage “V” applied to its terminals multiplied by the current “I” passing through it: Replacing V and I with the respective expressions deduced from OHM’s law, we have the following expression: and Joule’s Law where “Q” is the heat generated by a constant current “I” flowing through a conductor of electrical resistance “R”, for a time “t”. When current, resistance and time are expressed in amperes, ohms, and seconds respectively, are used the unit of Q is the joule.

Fourier’s Law where:

• Q is the amount of heat transferred
• t is the time taken
• k is the materials conductivity. (this generally varies with temperature, but the variation can be small, over a significant range of temperatures, for some common materials.)
• S is the area through which the heat is flowing
• T is the temperature.
The above differential equation, when integrated for a simple linear situation, where uniform temperature across equally sized end surfaces and perfectly insulated sides exist, gives the heat flow rate between the end surfaces as: where

• A is the cross-sectional surface area,
• ΔT is the temperature difference between the ends,
Δx is the distance between the ends.

Conductance Fourier’s law can also be stated as: where

• U is the conductance.

The reciprocal of conductance is resistance, R, given by: and it is resistance which is additive when several conducting layers lie between the hot and cool regions, because A and Q are the same for all layers. In a multilayer partition, the total conductance is related to the conductance of its layers by: So, when dealing with a multilayer partition, the following formula is usually used: When heat is being conducted from one fluid to another through a barrier, it is sometimes important to consider the conductance of the thin film of fluid which remains stationary next to the barrier. This thin film of fluid is difficult to quantify, its characteristics depending upon complex conditions of turbulence and viscosity, but when dealing with thin high-conductance barriers it can sometimes be quite significant.

## 3. Types of resistors

Fixed Resistor

The resistive element is wound on a ceramic body (generally with a cylindric shape) and is fixed to the two terminals.

Tapped Resistor

It is a resistor with fixed tappings derived from the body of the resistive element. By making connections between one terminal and one of the various tappings different resistance values are achieved. A tapped resistor is fully defined by the rated power and the nominal current of each single section.

A resistor with a tapping band, fitted around the body, which can be adjusted and locked to the resistive element so that the resistance between the tapping band and anyone of the terminals can be changed.

The nominal resistance Rn of adjustable resistors is referred to resistors having only one tapping band. The tolerance of these types of resistors is specified in the positive field; normally from 0 to + 15%. Additional tapping bands are supplied on request. However, it should be noted that each tapping band short-circuits some turns of the resistive element with relevant reductions on the total resistance. The rated power P, refers to the load distributed uniformly along the whole length of the resistor. Therefore when the load is not uniformly distributed it is necessary to check that the intensity of the current specified in the labels is not exceeded in any of the sections made by the tapping bands.

Wire Diameter and Maximum Resistance

To guarantee good reliability MlL-R-26 specifications establish the minimum diameter of resistive wires to be used in normal windings. The maximum resistance according to MIL specs is the maximum resistance which can be achieved by using wires with a diameter not smaller than the dimensions specified in the specs.

## 4. Operational characteristics

Rated Power - Derating Versus Ambient Temperature

A resistor operated at a constant wattage will attain a steady temperature which is determined largely by the ratio between the size (surface area) and the wattage dissipated, The temperature stabilizes when the sum of the heat loss rates (by radiation, convection and conduction) equals the heat input rate (proportional to wattage). The greater the resistor area per watt to be dissipated, the greater the heat loss rate and therefore the lower the temperature rise. The relation between the losses varies for different resistors.

The heating of a resistor is due to Joule Effect.

The relation of the Watt Rating of a resistor, is to be set at such a figure that when operated at their rated watts, the temperature rise of the hottest spot shall not exceed a certain temperature as measured by a thermocouple when the temperature of the surrounding air does not exceed 25°C.

The maximum power that can be dissipated decreases with the increase of ambient temperature. Derating drops to zero at 350°C ambient temperature from nominal rating at 25%. The graph below  allows to determine the derating percentage with respect to ambient temperature. Power Dissipation - Surface Temperature Characteristic

The surface temperature of a resistor rises in a non-linear way according to the power dissipation. The graph below shows the typical curve of the surface temperature rise of a vitreous enamelled resistor with respect to power dissipation.

Therefore to obtain the effective surface temperature one must add up the ambient temperature to the value stated in the graph. Surface Temperature

It is the temperature of the hot spot of the resistor under load. In case of a rod or tube type resistor, loaded in horizontal position, in calm air, this hot point will be in the upper central area.

The temperature rise varies (following a curve) along the length of the resistor with the hot spot at the center-top. When the resistor is vertical, the hot spot shifts upwards a little and the top end is hotter than the bottom.

If the customer needs to mount in vertical a resistor with the cable (like aluminium case), it is strictly recommended to do it with the cables in the bottom.

Limited Maximum Temperature

Sometimes it might happen that some components or materials which can be damaged by heat are too near to the resistor therefore it cannot operate at its rated power because its surface temperature would be too high. Obviously the surface temperature of a resistor can be lowered to acceptable values by proper derating. The following histogram shows the maximum surface temperature achieved by the various types of resistors with power rating at 25°C ambient temperature. 1. Aluminum case resistors – 250°C
2. RSE,RFX – 300°C
3. Tubolar resistors – 350°C
4. In air resistor – 400°C
5. Grid/plate resistors – 450°C

The maximum permissible operating temperature for a given resistor is basically determined by the temperature limitations imposed by the materials used in its construction. Generally speaking, these limits cannot be sharply defined in terms of temperature alone. Other factors such as resistance stability versus time, deterioration rates of insulation and moisture-resistance characteristics, type and size of resistance wire, all enter into consideration of “acceptable service life.”  Maximum limits are stipulated for parameter changes as a result of various tests. It is also assumed that the temperature rise at a given wattage is independent of the ambient temperature in which this wattage is being dissipated. The wattage ratings used in this catalogue are on the basis of the nominal operating temperature indicated in the previous histogram. For the class of aluminium case resistor we suggest to consider 250°C as maximum operating surface temperature. For this kind of product is anyhow possible to reach over temperature but only for limited period of time. For the in air resistor (RDP, RMS and RNP-RNT) is possible to reach a steady temperature of 400°C of the active material and for Grid/Plate resistors is possible to have a steady temperature of the material of 450°C.

The absolute temperature rise for a specific resistor is roughly related to the area of its radiating surface. It is also dependent upon a number of other factors, however, such as thermal conductivity of the core and coating materials, emissivity factor of the outer surfaces, ratio of length to diameter, heat-sink effect of mountings, and other minor factors.

Generally speaking, the factors which affect the temperature rise act independently of each other and are summarized as follows:

Ambient Temperature

As the maximum permissible operating temperature is a set amount, any increase in the ambient temperature subtracts from the permissible temperature rise and therefore reduces the permissible watt load.

Enclosure

Enclosure limits the removal of heat by convection currents in the air and by radiation. The walls of the enclosure also introduce a thermal barrier between the air contacting the resistor and the outside cooling air. Hence, size, shape, orientation, amount of ventilating openings, wall thickness, material and finish all affect the temperature rise of the enclosed resistor.

The amount of derating required, if any, because of enclosure is affected by a number of factors, most of which are hard to determine accurately.

Grouping

If resistors mounted in groups are not properly derated, the surface temperature of each single unit would exceed the permissible maximum values due to the reciprocal heating by radiation, conduction and conveyance. Within certain limits, the resistors reciprocal influence is as greater as their number is larger and the distance between their surfaces is smaller. Therefore problems must be investigated one by one to establish the best operating conditions.

Altitude

The amount of heat which air will absorb varies with the density, and therefore with the altitude above sea level. At altitudes above 3.000 mt, the air is so rare that the resistor loses heat practically only by radiation.

Pulse Operation

This is not an environmental condition but a circuit condition. Unlike the environmental factors, which result in reduction of the watt rating, pulse operation may permit higher power in the pulses than the continuous duty rating.

The exact temperature rise, of course, varies with each resistor, depending on size, ohms winding, etc. Ratings for single adiabatic pulses in the milli-second range (and up to 1 to 2 seconds) require individual calculation. This is because the ratings vary greatly with the resistance, or more specifically with the actual weight and specific heat of the resistance alloy used. Calculation is based on the assumption that all of the heat generated in the pulse goes to raise the temperature of the resistance wire. When a resistors must operate for a period of time (una tantum) shorter than the time required to attain its thermic balance, it can be overloaded. The shorter is the loading time, the higher will be the overloading, provided that the maximum voltage achieved does not exceed the limiting voltage. It should be kept in mind, however, that it is not enough not to exceed the maximum permissible surface temperature of the resistor at the end of the loading time, It is also important that not too fast heating occurs to avoid that any mechanical stress deriving from fast thermic changes among the various materials of the resistor reaches the failure point or, in any case, such a value that, in the long run, could jeopardize the good performance of the resistor. Therefore, it is advisable to establish a limit for the overload coefficients. These will be different for each type of resistors and will depend on various factors not easy to evaluate. Also here experience is the only and essential assistance. In this case only the tests and experiments performed in Fairfild laboratories can supply the data required for practical applications. In repeated pulse loading operation a coefficient "m" can be applied if the following conditions occur: that is, the average dissipated power in the T2 time must not exceed the rated power P. However, the overload coefficient under these conditions will be such that mPn<nPn and will be in function of the full-empty ratio of the train of pulses. In fact this condition is necessary but is not sufficient because the limiting considerations described above with regard to the fact that resistors cannot stand too fast temperature rises is applicable also here. In addition, it must be checked that the maximum applicable voltage does not exceed the limiting voltage. Due to the complexity of the matter it is advisable to consult Fairfild technical personnel every time special operating conditions are to be faced.

Forced Cooling

Resistors can dissipate considerably higher power than the nominal rating provided they are properly cooled. Forced ventilation and liquid cooling are the most common methods used. In the former case the efficiency of the cooling action depends on the temperature, the speed and the direction of the air flow, while in the latter case it depends on the temperature and thermic conductivity of the liquid. In the most favourable cases the increased coefficient of the power than can be dissipated achieves the value from 3 to 4.

Limited Temperature Rise

It is sometimes desirable to operate a resistor at a fraction of the Rated Power in order to keep the temperature rise low. This may be to protect adjacent heat sensitive apparatus, to hold the resistance value very precisely both with changing load and over long periods of time and to insure maximum life.

## 5. Other Considerations

High Resistance

High resistance units, which require the use of very small diameter wire, generally should operate at reduced temperature for maximum reliability.

High Voltage

A maximum voltage gradient of 200 volts R.M.S. (705 volts peak) per cm of winding length is recommended under normal conditions. For higher gradients in pulse applications or for other special conditions, consult factory.

High Frequency

Non-inductively wound resistors are generally required for use at high frequencies.