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?
(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
(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
- (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✓ Correct
- (D)The filament consumes less electrical power towards the end of the life of the bulb✓ Correct
Answer: (C), (D)
Solution
As tungsten evaporates non-uniformly, the filament's cross-section decreases at certain points, increasing local resistance and temperature at those points. The temperature distribution becomes non-uniform. (A) is incorrect.
As the cross-section decreases, resistance increases (not decreases). (B) is incorrect.
Higher local temperatures before breakup shift the black-body spectrum to higher frequencies (Wien's law: ), so more light is emitted at higher frequencies. (C) is correct.
At constant voltage, power . As resistance increases, power consumption decreases toward the end of the bulb's life. (D) is correct.
As the cross-section decreases, resistance increases (not decreases). (B) is incorrect.
Higher local temperatures before breakup shift the black-body spectrum to higher frequencies (Wien's law: ), so more light is emitted at higher frequencies. (C) is correct.
At constant voltage, power . As resistance increases, power consumption decreases toward the end of the bulb's life. (D) is correct.
JEE Advanced · 2016 · 22 May 2016 · Paper 1 · One or more correct options