For small section of filament

R = r ℓ / A and A is decreasing due to breakup hence R is increasing with time

For total power consumption

$\mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}}$

since V is constant

hence P is inversely proportional to R and due to breakup resistance of different section of the filament increases hence total resistance increases hence total power consumption decreases.

For different section of filament has different resistance due to breakup and i²R = eA σ T⁴ hence temperature will be different for different section

Just before breakup in the small section of the tungsten filament

eAσT⁴ = i²R

$\mathrm{R}\underset{}{\overset{}{\to }}\infty$

$\mathrm{T}\underset{}{\overset{}{\to }}\infty$

and λ_mT = b hence the filament emits more light at higher band of frequencies before it breaks up.