Self-inductance varies the number of turns in the coil as _.

Explanation

Self-inductance is defined as the property of a coil by which a changing current through it induces an electromotive force (EMF) in the same coil. The value of the self-inductance of a coil depends on various factors like the number of turns in the coil, the cross-sectional area of the coil, the length of the coil, and the nature of the material of the core. Mathematically, the self-inductance L of a coil is given by: L = (μ₀ N² A) / l Where, μ₀ is the permeability of free space N is the number of turns in the coil A is the cross-sectional area of the coil l is the length of the coil From the above formula, it is clear that the self-inductance is directly proportional to the square of the number of turns in the coil (N²). Therefore, if the number of turns in the coil is doubled, the self-inductance becomes four times greater. Similarly, if the number of turns is halved, the self-inductance becomes one-fourth of its original value.