An inductor L of inductance X_L is connected in series with a bulb B and an ac source.

How would brightness of the bulb change when (i) number of turn in the inductor is reduced, (ii) an iron rod is inserted in the inductor and (iii) a capacitor of reactance X_C = X_L  is inserted in series in the circuit. Justify your answer in each case.   

i) Net resistance in the circuit is given by, 

Inductance is given by, 

As number of turns decreases, L decreases.

Inductance is given by, 
Therefore,  will also decrease thereby, reducing the net resistance in the circuit. Thus, current increases and brightness of the bulb is increased.

ii) When a soft iron rod is inserted in the circuit, L increases. Therefore, inductive reactance also increases. Net resistance increases and flow of current in the circuit decreases. Thus, the brightness of the bulb will decrease.

iii) When a capacitor of reactance X_L = X_C is connected in series with the circuit net resistance becomes,
 ; where R is the resistance of the bulb.
Here, we will have Z= R which is the condition of resonance.
At resonance, maximum current will flow through the circuit. Therefore, the brightness of the bulb will increase.