Temperature Coefficient of Resistance:
Let R0 is resistance at any initial temperature t0 and Rt is the resistance at higher temperature t. Then increment in resistance (Rt - R0) is directly proportional to initial value of resistance R0 and increment in temperature (t - t0).
Rt - R0 = α0 R0 (t - t0)
Where α0 is the temperature coefficient of resistance referred to temperature t0
α0 = Rt - R0 / R0 (t - t0)
If initial temperature t0 = 0oC then α= Rt - R0 / R0 × t. Unit of temperature coefficient is per oC.
Resistance at any temperature is termed as
Rt = R0 (1 +α t ) (here t0 = 0o C)
The value of temperature coefficient of resistance (α) is not constant. Its value based upon the initial temperature on which the increment of resistance is based. If the value of α at t1oC is α1 then its value at t2oC shall be
α2 = 1/ ((1/ α1) + (t2 - t1))
The temperature coefficient of resistance 'α' is positive for metals and alloys. α is negative for electrolytes , semiconductors and insulators.