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

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Physics

Ashleigh

23 April, 01:03

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

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Morse · Answer 1

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