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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 statements(s) is(are) true.
A. The temperature distribution over the filament is uniform.
B. The resistance over small sections of the filament decreases with time
C. The filament emits more light at higher band of frequencies before it breaks up
D. The filament consumes less electrical power towards the end of the life of the bulb.

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Last updated date: 25th Jun 2024
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Answer
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Hint: The filament is observed to break at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten it means that temperature distribution in the filament is not uniform.

Complete answer:
Let's check each and every option

Option-A is incorrect because the filament is observed to break at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten it means that temperature distribution in the filament is not uniform.

Option-B is also incorrect as filament starts melting filament gets thinner or cross section area of the filament decreases so resistance of the filament must increase with time because resistance is inversely proportional to the cross section area

Option-C is correct because before the filament breaks up energy consumed by the filament is highest so higher band of frequencies emitted.

Option-D is also correct because when filament starts melting resistance of filament starts increasing but voltage source is constant it means power consumed by the filament towards the end of the life of the bulb is less( as power is inversely proportional to the resistance when voltage is constant.)

Therefore, Option-C & D are correct.

Additional information:
Black body radiation: An ideal blackbody is simply a closed cavity-like object which absorbs all incident radiation and re-emits radiation (energy) that is characteristic of the system irrespective of the type of the incident radiation when in thermal equilibrium. The radiated energy is called blackbody radiation and is produced by standing wave or resonant modes of the cavity which is radiating. The amount of radiation emitted in a given frequency range is proportional to the number of modes in that range. Classical Physics implies that all modes will have an equal chance of being produced and that the number of modes is proportional to the square of the frequency. This behavior is dubbed as Rayleigh Jeans Law which states that the spectral irradiance of electromagnetic radiation emitted by a blackbody at a fixed temperature.

Note: As filament starts melting the filament gets thinner or the cross section area of the filament decreases so resistance of the filament must increase with time because resistance is inversely proportional to the cross section area.