31. Consider a light bulb with a filament made from tungsten (with a resistivity

Question

31. Consider a light bulb with a filament made from tungsten (with a resistivity temperature coefficient of 4.5E-3/K). Suppose the bulb is off, and at a temperature of 23 degrees C. Then let the bulb be switched on. For the first instant, while the temperature has not yet had a chance to increase, the current in the bulb is 2.07 A. Then the current decreases with time. A minute later, the current is only 0.69 A. What is the temperature T (in degrees C) of the filament at that time? The voltage driving the lightbulb filament stays the same as the filament heats.

Explanation / Answer

Temperature Change in Resistance
Rt = Ro(1 + α∆T)
α is temperature coef in / ºC

(V/0.58) = (V/2.45)(1 + 4.5e-3∆T)
divide by V
(1/0.58) = (1/2.45)(1 + 4.5e-3∆T)
4.22 = 1 + 4.5e-3∆T
4.5e-3∆T = 3.22
∆T = 716 ºC
T = 716+23 = 739 ºC

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