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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
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