A coil is wound on a core of rectangular cross-section. If all the linear dimensions of core are increased by a factor 3 and number of turns per unit length of coil remains same, the self-inductance increases by a factor

Step-by-step solution

The self-inductance of a solenoid is given by L = n^2 A l , where denotes permeability of the core material, n the number of turns per unit length, A the cross-sectional area, and l the length of the solenoid. All linear dimensions of the core's cross-section increase by a factor of 3. Since A scales with the square of linear dimensions, the new area becomes A' = (3)^2 A = 9A . The length l remains constant, as this scaling applies only to cross-sectional dimensions. Substituting into the inductance formula yields