An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. [2016]

Question

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true? [2016]

Smart Achievers · Accepted Answer

(3, 4)

With the use of filament and the evaporation involved, the filament will become thinner, thereby decreasing the area of cross-section and increasing the resistance. Therefore, the filament will consume less power towards the end of its life.

As power, $P = \frac{V^{2}}{R}$ or, $P \propto \frac{1}{R}$ $(∵ V = constant)$

As the evaporation is non-uniform, the area of cross-section will be different at different cross-sections. Therefore temperature distribution will be non-uniform. The filament will break at the point where the temperature is maximum.

When the filament temperature is higher $(λ_{n} \propto \frac{1}{T}),$ it emits light of lower wavelength or higher band of frequencies.

Solution

1 The temperature distribution over the filament is uniform

2 The resistance over small sections of the filament decreases with time

3 The filament emits more light at higher band of frequencies before it breaks up

4 The filament consumes less electrical power towards the end of the life of the bulb

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