GATE 2014 EE (EE1) – Question 39
A lamp is rated 40 W, 240 V. Its resistance at 26°C is 120 Ω and temperature coefficient is $4.5\times10^{-3}$ per °C. Find approximate ON-state filament temperature (°C).
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Correct answer: 2470 to 2471
Explanation
Rated hot resistance is V²/P=240²/40=1440Ω. Relative to120Ωat26°C, the resistance ratio is12. Use R=R26[1+α(T−26)]with α=0.0045/°C:12=1+0.0045(T−26). Thus **T=2470.444°C**. This is the stated constant-temperature-coefficient approximation over a very large temperature range.