a solenoid with a n loops of wire tightly wrapped around the iron core is carrying an electric current i if the current through the solenoid is reduced to half then what change would you expect in inductance L of the solenoid

Dear student
Inductance of solenoid = μ​​​​​​0​​​​​N²A/length.
That's independent of current value.
So it will not change when you change current value.
Hope it helps you

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