Temperature Coefficient of Electrical Resistivity

Over a narrow range of temperatures, the electrical resistivity, p, varies linearly with the temperature according to the equation below, where oris the temperature coefficient of the electrical resistivity expressed in Q.m.K  

The temperature coefficient of electrical resistivity is an algebraic physical quantity (i.e., negative for semiconductors and positive for metals and alloys) defined as follows  

It is important to note that in theory the temperature coefficient of the electrical resistivity is different from that of the electrical resistance, denoted a and defined as follows  

Actually, the electric resistance, as defined in the previous paragraph, also involves the length and the cross-sectional area of the conductor, so the dimensional change of the conductor due to the temperature change must also be taken into account. We know that both dimensional quantities vary with temperature according to their respective coefficient of linear thermal expansion (o ) and coefficient of surface thermal expansion ( ) in addition to that of electrical resistivity. Hence the exact equation giving the variation of the resistance versus temperature is given by  

However, in most practical cases, the two coefficients of thermal expansion are generally much smaller than the temperature coefficient of electrical resistivity. Therefore, if dimensional variations are negligible, values of the coefficient of electrical resistivity and that of electrical resistance can be assumed to be identical. 

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Resistivity. The temperature coefficient of electrical resistivity of commercial siUcon carbide at room temperature is negative. No data are given for refractory materials because resistivity is gready induenced by the manufacturing method and the amount and type of bond. Manufacturers should be consulted for specific product information. 

More importantly, such alloys also possess a very low temperature coefficient of electrical resistance (of the order of 220 idQ.IQ.rC, typical), which causes only a marginal change in its resistance value with variation in temperature. They can therefore ensure a near-consistent predefined performance of the motor for which the resistance grid is designed, even after frequent starts and stops. They are also capable of absorbing shocks and vibrations during stringent service conditions and are therefore suitable for heavy-duty drives, such as steel mill applications. 

The non-ferrous alloys include the misleadingly named nickel silver (or German silver) which contains 10-30% Ni, 55-65% Cu and the rest Zn when electroplated with silver (electroplated nickel silver) it is familiar as EPNS tableware. Monel (68% Ni, 32% Cu, traces of Mn and Fe) is used in apparatus for handling corrosive materials such as F2 cupro-nickels (up to 80% Cu) are used for silver coinage Nichrome (60% Ni, 40% Cr), which has a very small temperature coefficient of electrical resistance, and Invar, which has a very small coefficient of expansion are other well-known Ni alloys. Electroplated nickel is an ideal undercoat for electroplated chromium, and smaller amounts of nickel are used as catalysts in the hydrogenation of unsaturated vegetable oils and in storage batteries such as the Ni/Fe batteries. 

This type of gauge, like the Pirani gauge, uses a filament with a high temperature coefficient of electrical resistance exposed to the gases in the vacuum system. The temperature of the filament, as measured by a small thermocouple connected to a sensitive millivoltmeter and attached to the heated filament, indicates the gas pressure. The range is 0.5 toiT to 0.001 torr. 

The electrical resistance of ductile molybdenum at 25° is 5.6 microhms per cubic centimeter for hard drawn wire and 4.8 microhms for annealed wire. The temperature coefficient of electrical resistance between 0° and 170° C. is 0.005. The specific heat is 0.072. 

The most frequently used source of infrared light for infrared spectrometers is so called the Nemst stick. This stick is about two to four centimeters long and one to three millimeters thick, and is made from zirconium oxide with additions of yttrium oxide and oxides of other metals. This mixture of oxides has a negative temperature coefficient of electrical resistance. This means that its electrical conductivity increases with an increase in temperature. At room temperature, the Nemst stick is a non-conductor. Thus, an auxiliary heating is necessary for ignition of the Nernst stick. Even if the Nernst stick is red-hot, it can be heated further by electricity. The normal operating temperature of this infrared light source is approximately 1900 K. 

Thermistors are usually made from ceramic metal oxide semiconductors, which have a large negative temperature coefficient of electrical resistance. Thermistor is a contraction of thermal-sensitive-resistor. The recommended temperature range of operation is from -55 to 300°C. The popularity of this device has grown rapidly in recent years. Special thermistors for cryogenic applications are also available [12]. 

These can be used over a very wide range. Their principle of operation is based on the large temperature coefficient of electrical resistance of Pt and Ni (for example, the resistance of Pt changes by 0.4% per degree). These thermometers are among the most accurate temperature measuring instruments. It is not difficult to make a resistance thermometer in the laboratory, but the commercial instruments are preferable. The high-temperature type consists of a mica cross inserted in a thin-wall quartz tube. A fine double Pt filament is wound around the mica cross. 

Material Density (g/cm ) Melting point (interval) (°C) Electrical conductivity (m/Sl mm ) Temperature coefficient of electrical resistance (10 K ) Modulus of elasticity (kN/mm )... 

Therefore the relationship existing between the temperature coefficient of electrical resistivity and the coefficient of temperature is given below ... 

In a TCD detector, two sets of filaments are mounted in a Wheatstone bridge circuit, one set is immersed in the pure carrier gas stream (reference) while the other in the stream exiting from the reactor (measure). The filaments are made of suitable metals (i.e. tungsten or gold) having high temperature coefficient of electrical resistance ... 

Here, Rp is the electrical resistance of the tip at reference temperature TpQ and Up is the temperature coefficient of electrical resistivity. 

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