Tripling the number of turns in an inductor increases the inductance by how many times?

The inductance of an inductor is proportional to the square of the number of turns of wire wrapped around its core. This relationship is derived from the formula for inductance, which can be expressed as L = k * N², where L is the inductance, k is a constant that depends on the core material and geometry, and N is the number of turns.

When you triple the number of turns (N becomes 3N), the inductance is proportional to (3N)², which expands to 9N². Since the original inductance is proportional to N², tripling the number of turns results in an inductance that is nine times greater than the original value.

This fundamental principle in electromagnetism underlines the significant impact that the number of turns has on inductance, demonstrating why the correct answer reflects a multiplication of the original inductance by nine times.