Temperature Coefficient of Resistance:

Let R₀ is resistance at any initial temperature t₀ and R_t is the resistance at higher temperature t. Then increment in resistance (R_t - R₀) is directly proportional to initial value of resistance R₀ and increment in temperature (t - t₀).

i.e.

                                      R_t - R₀ = α₀ R₀ (t - t₀)

Where α₀ is the temperature coefficient of resistance referred to temperature t₀

α₀ = R_t - R₀ / R₀ (t - t₀)

If initial temperature t₀ = 0^oC then α= R_t - R₀ / R₀ × t. Unit of temperature coefficient is per ^oC.

Resistance at any temperature is termed as

R_t = R₀ (1 +α t )     (here t₀ = 0^o 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 t₁^oC is α₁ then its value at t₂^oC shall be

α₂ = 1/ ((1/ α_{1) +} (t₂ - t₁))

The temperature coefficient of resistance 'α' is positive for metals and alloys. α is negative for electrolytes , semiconductors and insulators.