Explanation: An inductor's ability to store energy in a magnetic field, known as inductance, is directly proportional to the magnetic permeability of its core material. Magnetic permeability ($\mu$) is a measure of how easily a material can support the formation of a magnetic field within itself. Air has a magnetic permeability very close to that of a vacuum. Ferromagnetic materials like iron have a significantly higher magnetic permeability—hundreds to thousands of times greater than air. When an iron core is inserted into an air-core inductance, it provides a much more efficient path for the magnetic field lines. This concentrates and strengthens the magnetic flux passing through the coil for a given current, effectively increasing the coil's ability to store magnetic energy. Consequently, the inductance of the coil increases. Therefore, option A is correct. Options B and C are incorrect because changing the core material from air to iron fundamentally alters the magnetic field characteristics and thus the inductance. Option D describes parasitic oscillations, which are typically caused by unwanted capacitance or resistance within the component or circuit, not by simply adding a core to an inductor. While core losses can occur, the primary effect on the *inductance value* itself is an increase.