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Determine the resistance and temperature-coefficient:
A platinum coil has a resistance of 3.146 Ω at 40oC and 3.767 Ω at 100oC. Determine the resistance at 0oC and the temperature-coefficient of resistance at 40oC.
Solution
Rt = R0 + α0 R0 (t - t0 )
Take t0 = initial temperature = 0o.
Rt = 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 = 40oC ---------- (ii)
From Eqs. (i) and (ii)
3.767 /3.146 = 1 + 100 α0/1 + 40 α0 ⇒ α = 0.00379 pero 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
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