Consider a light bulb with a filament made from tungsten (with a resistivity tem

Question

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 1.76 A. Then the current decreases with time. A minute later, the current is only 0.81 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

Initial resistance = V/1.76

final R = V/0.81

Temperature Change in Resistance

Rt = Ro(1 + alpha (delta T))

(V/0.81) = (V/1.76)(1 + 4.5 * 10-3(delta T))

(1/0.81) = (1/1.76)(1 + 4.5 * 10-3(delta T))

2.17 = (1 + 4.5 * 10-3(delta T))

4.5 * 10-3(delta T) = 1.17

(delta T) = 260 deg C

T = 260+23 = 283 deg C

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