How does the Final Current affect the Surge Current Time in a Filament Bulb? (Physics EE)

When a filament bulb is first switched on, its metal filament is cold and so has a relatively low resistance. This leads to a large surge current until the filament heats sufficiently to glow white hot with a steady electrical current. This essay investigates the research question: “How does the final current affect the surge current time in a filament bulb?” The surge current time is the time interval between switching the bulb on and when the final steady current is first reached.