A certain lightbulb has a tungsten filament with a resistance of 26 Ω when cold and 170 Ω when hot. If the equation R = R0 [1 + α ∆T] can be used over the large temperature range involved here, find the temperature of the filament when it is hot. Assume that α , the temperature coefficient of resistivity of tungsten, is 0.0045 (◦C)−1 and that the temperature of the cold filament is 40◦C. Answer in units of ◦C

Explanation: The equation that relates resistance of tungsten at different temperatures is as follows

R = R₀ [1 + α ∆T]  , R₀ is resistance at lower temperature , R is resistance at higher temperature . α is temperature coefficient of resistivity and ∆T is rise in temperature .

Putting the values

170 = 26 [1 + .0045 ∆T]

∆T = 1230.75

lower temperature = 40◦C

higher temperature = 1230 + 40

= 1270◦C

magnitude and direction

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