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-
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,
|Sl. No.||Material/Substances||Chemical Symbol/Chemical composition||Temperature coefficient of resistance /oC (at 20oC)|
|8||Manganin||Cu = 84% + Mn = 12% + Ni = 4%||0.000002|
|10||Nichrome||Ni = 60% + Cr = 15% + Fe = 25%||0.0004|
|11||Constantan||Cu = 55% + Ni = 45%||0.00003|
|15||Brass||Cu = 50 - 65% + Zn = 50 - 35%||0.0015|