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?

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Infinity Learn · Accepted Answer

The  filament will be a conductor of non uniform $$crossectionA)$$ For any element of length dx in equilibrium   $$I2R=Pradiated$$ ⇒$$I2$$ρdx$$π$$$$r2=$$σ$$2$$$$π$$$$rdxT4$$  ⇒$$T4=I2$$ρ$$2$$$$π$$$$2$$σ$$r3$$ ⇒T∝$$1r3/4T$$ will be non uniform as r is non $$uniformB)$$  $$R=$$ρdx$$π$$$$r2$$ ⇒R∝$$1r2Due$$ to evaporation, r of every element decreases with time ⇒  ‘R’ increases with $$timeC)$$ λ$$T=$$  constant Tf  $$=constant$$ ⇒ Tαf   from (A) ,  Tα$$1r3/4$$∴fα$$1r3/4$$  ‘r’  decrease with time ⇒'f'  increases with time i.e. it emits bond of higher frequencies before it breaks  up if I is taken as constant. $$D)$$  $$P=V2R$$ Due to evaporation, ‘R’ increases with  time as radius of cross section decreases for every element  ⇒'P' decrease with time

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