Current Electricity 3 Question 13
12. 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 Adv.)
(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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Solution:
- Because of non-uniform evaporation at different section, area of cross-section would be different at different sections.
Region of highest evaporation rate would have rapidly reduced area and would become break up cross-section.
Resistance of the wire as whole increases with time.
Overall resistance increases hence power decreases.
$p=\frac{V^{2}}{R}$ or $p \propto \frac{1}{R}$ as $V$ is constant .
At break up junction temperature would be highest, thus light of highest band frequency would be emitted at those cross-section.
