Where $r_{0}$ is the radius of the earth and $\sigma$ is Stefan's constant.

($A$) 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