Temperature Coefficient of Resistance

As we discussed in the page under title resistance variation with temperature that electrical resistance of every substance changes with change in its temperature.
Temperature coefficient of resistance is the measure of change in electrical resistance of any substance per degree of temperature rise.
Temperature Coefficient of Resistance Let a conductor having a resistance of R0 at 0oC and Rt at toC respectively.

From the equation of resistance variation with temperature we get  This αo is called temperature coefficient of resistance of that substance at 0oC.
From the above equation, it is clear that the change in electrical resistance of any substance due to temperature rise mainly depends upon three factors-

  1. The value of resistance at initial temperature,
  2. Rise of temperature and
  3. the αo.
This αo is different for different materials, so effect on resistance at different temperature are different in different materials.

So the temperature coefficient of resistance at 0oC of any substance is the reciprocal of the inferred zero resistance temperature of that substance.

So far we have discussed about the materials that resistance increases with increase in temperature, but there are many materials electrical resistance of which decreases with decrease in temperature. Actually in metal if temperature is increased, the random motion of charged particles and inter atomic vibration inside the materials increases which result to more collisions. More collision resist smooth flow of electrons through the metal, hence the resistance of the metal increases with the increase in temperature. So, temperature coefficient of resistance is considered as positive for metal.
But in case of semiconductor or other non-metal, the number of free electrons increases with increase in temperature. Because at higher temperature, due to sufficient heat energy supplied to the crystal, more numbers of covalent bonds are broken and hence more free electrons are created. That means if temperature increases, more number of electrons comes to the conduction bands from valance band by crossing the forbidden energy gap. As the number of free electrons increases, the resistance of this type of non-metallic substance decreases with increase of temperature. Hence temperature coefficient of resistance is negative for non-metallic substances and semiconductors.
If there is approximately no change in resistance with temperature, the value of this coefficient is considered as zero. Such as alloys like constantan and manganin have temperature coefficient of resistance nearly zero.
The value of this coefficient is not constant, it depends on the initial temperature on which the increment of resistance is based. When the increment is based on initial temperature of 0oC, the value of this coefficient is αo - which is nothing but the reciprocal of the respective inferred zero resistance temperature of the substance. But at any other temperature, temperature coefficient of electrical resistance is not same as this αo. Actually for any material, the value of this coefficient is maximum at 0oC temperature. Say the value of this coefficient of any material at any toC is αt, then its value can be determined by the following equation,  The value of this coefficient at a temperature of t2oC in the term of the same at t1oC is given as,

Review the Concept of Temperature Coefficient of Resistance

The electrical resistance of conductors such as silver, copper, gold, aluminum etc., depends upon collision process of electrons with in material. As the temperature increase, this electron collision process becomes faster, which results in increased resistance with rise in temperature of conductor. The resistance of conductors generally rise with rise in temperature.
If a conductor is having R1 resistance at t1oC and after raising the temperature, its resistance becomes R2 at t2oC. This rise in resistance (R2 - R1) with rise in temperature (t2 - t1) depends on following things – By combining above effects, Where, α is the temperature coefficient of resistance of material at t1oC.
From Equation (1) If at a particular temperature, we know the resistance and temperature coefficient of resistance of material, we can find out the resistance of material at other temperatures by using equation (2).
The Temperature Coefficient of Resistance of some Materials or Substances
The temperature coefficient of resistance of some materials/substances at 20oC are listed below-
Sl. No.Material/SubstancesChemical Symbol/Chemical compositionTemperature coefficient of resistance /oC (at 20oC)
3GoldAu 0.0034
4AluminumAl 0.00429
8ManganinCu = 84% + Mn = 12% + Ni = 4%0.000002
9Mercury Hg0.0009
10NichromeNi = 60% + Cr = 15% + Fe = 25%0.0004
11ConstantanCu = 55% + Ni = 45%0.00003
12Carbon C- 0.0005
13Germanium Ge- 0.05
14SiliconSi- 0.07
15BrassCu = 50 - 65% + Zn = 50 - 35%0.0015
Effect of Temperature on Temperature Coefficient of Resistance of a Material
The temperature coefficient of resistance of a material is also changes with temperature.
If αo is the temperature coefficient of resistance of material at 0oC, then from equation (2), the resistance of material at toC, Where, R0 is the Resistance of material at 0oC
Similarly, if the temperature coefficient of resistance of material at toC is αt, then the resistance of the material at 0oC, from equation (2) Where, Rt is the Resistance of material at to C
From equation (3) and (4) Where, α1and α2 the temperature coefficient of resistance of material at t1oC and t2oC respectively.
Hence, if we know the temperature coefficient of resistance of a material at a particular temperature, we may find out the temperature coefficient of material at any other temperature by using equation (6).
The conducting material are having large and positive temperature coefficient of resistance. Therefore, the resistance of conducting material (metals) rise with rise of temperature. The semiconductors and insulating material are having negative temperature coefficient of resistance. Therefore, the resistance of semiconductors and insulators decrease with rise in temperature.
Alloys, such as manganin, constantan etc. are having very low and positive temperature coefficient of resistance. Therefore, the resistance of alloys increase with rise in temperature but this rise in resistance is very low (almost negligible) as compare to metals, which makes these alloys suitable for using in measuring instruments.


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