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?

detailed solution

Correct option is C

The  filament will be a conductor of non uniform crossectionA) For any element of length dx in equilibrium   I2R=Pradiated ⇒I2ρdxπr2=σ2πrdxT4  ⇒T4=I2ρ2π2σr3 ⇒T∝1r3/4T will be non uniform as r is non uniformB)  R=ρdxπr2 ⇒R∝1r2Due to evaporation, r of every element decreases with time ⇒  ‘R’ increases with timeC) λT=  constant Tf  =constant ⇒ Tαf   from (A) ,  Tα1r3/4∴fα1r3/4  ‘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