Why does inductance increase with the iron core?

Hint: We know that the inductance is a property of an electrical conductor that opposes changes in current. Inductance increases with the iron core because the iron core provides a path of low resistance for the magnetic field. The iron core also amplifies the magnetic field, which increases the inductance.

Complete step by step solution:
Here, we can say that the magnetic permeability of a material is a measure of its ability to store magnetic flux. Iron has a high magnetic permeability, so it can easily store magnetic flux. This makes it an ideal material for use in inductors. When an iron core is used in an inductor, the inductance of the conductor is increased.

The number of turns in a conductor also affects the inductance. The more turns there are in a conductor, the greater the inductance. This is because the magnetic flux is increased when there are more turns in the conductor. The size of the conductor also affects the inductance.

A larger conductor has a greater surface area to store more magnetic flux. This increases the inductance of the conductor. Inductance increases with the addition of an iron core because iron has a high magnetic permeability. This means that it can easily store magnetic flux, which increases a conductor's inductance.

Note: The iron core also amplifies the magnetic field. This amplification increases the inductance because it increases the strength of the magnetic field.