Doubling the number of turns on a coil will:

Doubling the number of turns on a coil will increase the inductance by a factor of four, which is a fundamental principle in the design of inductors. The inductance (L) of a coil is given by the formula:

[ L = \frac{N^2 \cdot \mu \cdot A}{l} ]

where ( N ) is the number of turns, ( \mu ) is the permeability of the core material, ( A ) is the cross-sectional area of the coil, and ( l ) is the length of the coil.

From this formula, it can be observed that inductance is proportional to the square of the number of turns. Therefore, if the number of turns is doubled (from ( N ) to ( 2N )), the inductance becomes:

[ L' = \frac{(2N)^2 \cdot \mu \cdot A}{l} = \frac{4N^2 \cdot \mu \cdot A}{l} = 4L ]

This shows that the inductance increases by a factor of four when the number of turns is doubled. Factors such as the type of core material and geometry remain