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 R 1 resistance at t 1 o C and after raising the temperature, its resistance becomes R 2 at t 2 o C. This rise in resistance (R 2 - R 1 ) with rise in temperature (t 2 - t 1 ) depends on following things –
By combining above effects,
Where, α is the temperature coefficient of resistance of material at t 1 o C.

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 20 o C are listed below-

Sl. No. Material/Substances Chemical Symbol/Chemical composition Temperature coefficient of resistance / o C (at 20 o C)
1 Silver Ag
2 Copper Cu
3 Gold Au
4 Aluminum Al
5 Tungsten W
6 Iron Fe
7 Platinum Pt
8 Manganin Cu = 84% + Mn = 12% + Ni = 4%
9 Mercury Hg
10 Nichrome Ni = 60% + Cr = 15% + Fe = 25%
11 Constantan Cu = 55% + Ni = 45%
12 Carbon C -
13 Germanium Ge -
14 Silicon Si -
15 Brass Cu = 50 - 65% + Zn = 50 - 35%
16 Nickel Ni
17 Tin Sn
18 Zinc Zn
19 Manganese Mn
20 Tantalum Ta
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 α o is the temperature coefficient of resistance of material at 0 o C, then from equation (2), the resistance of material at t o C,
Where, R 0 is the Resistance of material at 0 o C

Similarly, if the temperature coefficient of resistance of material at t o C is αt, then the resistance of the material at 0 o C, from equation (2)
Where, R t is the Resistance of material at t o C

From equation (3) and (4)
Where, α 1 and α 2 the temperature coefficient of resistance of material at t 1 o C and t 2 o C 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 .

The temperature coefficient of resistance for a resistor is determined by measuring the resistances values over an appropriate temperature range. The TCR is calculated as the average slope of the resistance value over this interval. This is accurate for linear relations, since the TCR is constant at every temperature. However, many materials have a non linear coefficient. For Nichrome for example, a popular alloy for resistors, the relation between temperature and TCR is not linear. Because the TCR is calculated as average slope, it is therefore very important to specify the TCR as well as the temperature interval. The way to measure TCR is standardized in MIL-STD-202 Method 304. With this method, TCR is calculated for the range between -55°C and 25°C and between 25°C and 125°C. Because the highest measured value is defined as TCR, this method often results in over specifying a resistor for less demanding applications.