Determine the resistance and temperature-coefficient:

A platinum coil has a resistance of 3.146 Ω at 40^oC and 3.767 Ω at 100^oC. Determine the resistance at 0^oC and the temperature-coefficient of resistance at 40^oC.

Solution

R_t  = R₀  + α₀  R₀  (t - t₀ )

Take t0 = initial temperature = 0^o.

R_t  = R₀  + α₀  t R₀

= R₀ (1 + α₀ t )

R₁₀₀ = R₀ (1 + 100 α₀) at          t = 100 C          ------- (i)

And        R₄₀ = R₀ (1 + 40 α₀ )         at  t = 40^oC           ----------  (ii)

From Eqs. (i) and (ii)

3.767 /3.146    = 1 + 100 α₀/1 + 40 α₀   ⇒ α = 0.00379 per^o C

From Eq. (i)

∴ 3.767 = R₀  (1 + 100 × 0.00379)

R₀ = 2.732,

α₄₀ =   1/( (1/ α₀) + (t₂  - t₁ ) =1/ (1/0.00379) + (40 - 0) = 1/304 per  ^o C