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The variation in electrical resistance of a component with regard to each degree change in temperature is known as the temperature coefficient of resistance.
When we consider the electrical resistance of a conductor be it gold, silver, copper and aluminium, we must consider the process of electron collision within the substance. The action of electron collision occurs rapidly as the temperature rises. As a result, as the conductor’s temperature rises, the resistance rises with it.
Relation Between the Resistance And The Temperature
Consider a conductor with a resistance of R0 at 0°C and a resistance at the temperature T°C is RT. The relationship between resistance and the temperature R0 and RT is roughly described as
RT = R0 [1+ α (T-T0)]
that is
RT = R0 [1+ α (∆T)].
As a result of the aforementioned equation, it is obvious that the change in electrical resistance of any material owing to temperature is primarily determined by three factors –
- The resistance value at a given temperature.
- The rising temperature.
- The temperature coefficient of resistance.
Depending on the type of material, the value might change. When the temperature of a metal rises, the electrons get more kinetic energy and consequently higher speed, allowing them to collide more frequently. We know that any substance’s resistivity is determined by
ρ is equal to (m/n)q2 τ
As a result, the resistivity is proportional to the no. of carrier of the charge per unit volumes n as well as the relaxation time τ between the collisions. The average velocity of the current carriers, i.e. the electrons, increases as the temperature of the metal rises, resulting in more collisions.
The average duration between successive collisions falls as a result of this. However, the effect of temperature on the value of n is insignificant, implying that the value of resistivity is now solely dependent on the change in τ.
Kinds of TCR
- Temperature Coefficient of Resistance is Positive when as a result of the drop in τ, the material’s resistivity and resistance rise. As a result, the temperature coefficient of metal has a positive value.
A PTC is a term used to describe materials that increase in electrical resistance as their temperature rises. The materials with a higher coefficient rise quickly as the temperature rises. A PTC material is designed to achieve the highest temperature possible for a given i/p voltage because as the temperature rises, the electrical resistance rises as well. Unlike NTC materials or linear resistance heating, the positive temperature coefficient of resistance materials is naturally self-limiting. Some materials, such as PTC rubber, have a temperature coefficient that rises exponentially.
- Temperature Coefficient of Resistance is Negative when the number of charge carriers per unit volume in semiconductors and insulators increases as the temperature rises. Because the increase in n more than compensates for the decrease in τ, the value of resistivity and resistance falls as temperature rises.
An NTC is a type of material that experiences a decrease in electrical resistance as its temperature rises. The materials with a lower coefficient diminish quickly as the temperature rises. Temperature sensors, Current limiters and thermistors are all made with NTC materials.
As a result, in insulators and semiconductors, the temperature coefficient of resistivity is negative.
Methods of Measurement of TCR
A resistor’s TCR is measured by finding the resistance values across a specified temperature range. The averaged slope of the resistance value over all this interval is used to determine the TCR. Because the TCR is constant at all temperatures, this is accurate for linear relationships. Many materials, however, have a nonlinear coefficient. Nichrome, for example, a popular resistor alloy, exhibits a nonlinear relationship between the temperature and TCR. Because the TCR is calculated as an average slope, specifying the TCR as well as the temperature interval is critical. MIL-STD-202 Method 304 specifies how TCR should be measured. TCR is computed using this method for the temperature ranges of -55°C to 25°C and 25°C to 125°C. Because TCR is defined as the highest measured value, this method frequently leads to over-specifying a resistor for less demand applications.
Temperature Coefficient Of Resistance Table For Different Substances
SUBSTANCE | TEMPERATURE COEFFICIENT | |
Aluminium | 43 x 10-4 | |
Antimony | 40 x 10-4 | |
Bismuth | 42 x 10-4 | |
Brass | ~10 x 10-4 | |
Cadmium | 40 x 10-4 | |
Cobalt | 7 x 10-5 | |
Constantan (Alloy) | 33 x 10-4 | |
Copper | 40 x 10-4 | |
Gold | 34 x 10-4 | |
Carbon (Graphite) | -5.6 x 10 -4 | |
Germanium | -4.8 x 10-2 | |
Iron | 56 x 10-4 | |
Lead | 39 x 10-4 | |
Manganin | ~2 x 10-5 | |
Molybdenum | 46 x 10-4 | |
Nichrome | 1.7 x 10-4 | |
Nickel | 59 x 10-4 | |
Platinum | 38 x 10-4 | |
Silicon | -7.5 x 1024 | |
Silver | 40 x 10-4 | |
Tantalum | 33 x 10-4 | |
Tin | 45 x 10-4 | |
Tungsten | 45 x 10-4 | |
Zinc | 36 x 10-4 | |
Conclusion
Except for semiconductors, which have a TCR of around 30 to 50 x 10-4, most materials, but not those frequently utilised in the electrical and electronics industry, have a temperature coefficient of resistance of around 30 to 50 x 10-4.
