What happens to the brightness of bulb 1, when bulb 2 burns out? (When a bulb burns out, its resistance becomes infinite.)

Pink: Bulb 1 gets brighter                      Green: Bulb 1 gets dimmer.

Yellow: It's brightness remains the same.

(Hint: What happens to the current from the battery when bulb 2 burns out.)

Answer: Green, Bulb 1 gets dimmer. When bulb 2 burns outs, the filament inside breaks and R₂ becomes infinitely large. The total equivalent resistance which the battery sees increases (since bulb 2 is gone, there are fewer paths for the current flow, so less flow, more total resistance.) Since the battery sees a larger R_tot, the current from the battery I_tot = V/R_tot is reduced. Less current from the battery means less current through bulb 1, less light.