In the circuit shown, when a soft iron bar is quickly inserted into the inductor, the brightness of the bulb,

When the soft iron bar is being inserted, emf is induced in the circuit and according to Lenz's law, this induced emf will try to decrease the current and  proportional to current, brightness first decreases. When the relative motion between the soft iron becomes zero, induced emf also becomes zero and the brighness increases to its initial value.