As the electric current in a lightbulb is slowly increased the filament glows kore and more brightly. Why does this happen

For just a second, think of the light bulb as just a resistance.

The power dissipated any any resistance is (current) ² x (resistance).

You can see that if you increase the current through any resistance,

then it dissipates more power.

The light bulb dissipates power in the form of heat and light. If you

increase the current through it, then both of those will increase.