A coil of wire wrapped on a hollow tube and a light bulb are connected in series to an ac source. What happens to the brightness of the bulb when an iron rod is inserted in the tube?

An inductor is a passive two-terminal device that stores energy in a magnetic field when current passes through it. When an inductor is attached to an AC supply, the resistance produced by it is called inductive reactance (X_L).

Resistance is measure of opposition to the flow of current in a closed electrical circuit. It is measured in Ohm (Ω).

Impedance is defined as the effective resistance of an electric circuit to the flow of current due to the combined effect of resistance (offered by resistor) and reactance (offered by capacitor and inductor).

Power dissipated in the bulb is given by

$P=I_{rms}{R}^2$

By inserting a iron core means inductance will increase, and thus more energy will be stored in the inductor.

If Z is the impedance of the circuit, then current in the circuit is given by

$I_{rms}=V/Z$

As the inductance increase, the impedance increases and since the rms current is inversely proportional to impedance, the current consumed by bulb decreases which means the consumed power will decrease and thus bulb will be less bright.

Therefore, the brightness of the bulb decreases.