The temperature coefficient of a resistance wire is 0.00125 per degree. The resistance at 300 K is 1 Ω. At what temperature its resistance will be 2Ω?

Options

(a) 1154 K
(b) 1127 K
(c) 600 K
(d) 1400 K

Correct Answer:

1127 K

Explanation:

Temperature = 300 K = 300 – 273 = 27°C

R₂₇ = R₀ (1 + 27 α) ⇒ 1 = R₀ (1 + 27 α)

Rt = R₀ (1 + αt) ⇒ 2 = R₀ (1 + αt)

2 / 1 = (1 + αt) / (1 + 27 α) ⇒ 1 + αt = 2 + 54α

⇒ αt = 1 +| 54 α ⇒ 0.00125t = 1 + 54 × 0.00125

⇒ t = 854°C = 854 + 273 = 1127 K