A light bulb and an inductor coil are connected to an ac source...

We know that the formula of impedance for $L - R$ circuit, $Z = \sqrt{{R}^{2} + {X}_{L}^{2}}$, here, $R =$resistance and ${X}_{L} = \omegaL$, where, $L$ is the inductance when we insert the iron rod in inductor then the value of $L$ increased and then the value of impedance also increased, and due to constant voltage current will be decreased across the bulb and the glow of the bulb will decrease.