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?

Towards the end of the life, the filament will become thinner. Resistance will increase because resistance is inversely proportional to the cross-sectional area of the filament (R = ρL/A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area). Since the voltage is constant (V = IR, where V is voltage, I is current, and R is resistance), an increase in resistance leads to a decrease in current. Power consumed is given by P = IV = V²/R. Since the voltage is constant and the resistance increases, the power consumed (P) will decrease. The filament will emit less light because less power is being consumed. The temperature distribution will be non-uniform because thinner sections will have higher resistance and thus higher power dissipation per unit length, leading to higher temperatures in those regions. At the position where the temperature is maximum, the filament will break due to evaporation. The black body radiation curve will shift towards lower intensity as the power decreases, but the peak will still be at higher frequencies. Therefore, statements C and D are true. Answer is C and D.