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

Solution :
When a bulb of resistance $$R$$ is connected in series with a coil of self-inductance $$L,$$ then current in the circuit is given by
$$I = \frac{E}{{\sqrt {{\omega ^2}{L^2} + {R^2}} }},$$     where $$E$$ is the voltage of an $$AC$$  source
As $$L = \frac{{{\mu _0}{\mu _r}{N^2}A}}{l}$$
$$ \Rightarrow L \propto {\mu _r}$$
When iron rod is inserted, $$L$$ increases, therefore current $$I$$ decreases.