A coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decreases when:

${\mathrm{V}}_{\mathrm{L}}={\mathrm{iX}}_{\mathrm{L}}; {\mathrm{X}}_{\mathrm{L}},$when iron rod is inserted in the coil, inductance is increased and voltage drop across inductance increase.

Due to increase in voltage drop across inductance, voltage drop across bulb decreases and hence brightness of bulb is reduced.