# Solenoid vs transformer inductance

Discussion in 'General Electronics Chat' started by eigenvictor, Jan 23, 2015.

1. ### eigenvictor Thread Starter New Member

Jul 16, 2014
25
0
Why is the same formula used for both a long solenoid and a transformer coil inductance: L = μ * N^2 * A / ℓ

In case of an air core solenoid, it only gives a reasonable result for a single layer solenoid with the coil length ℓ >> D. However for multilayer coils with an arbitrary length to D ratio, mutual inductance between layers need to be accounted for, and basically different formulas are used, such as elliptic integrals and other numeric methods. For example, a more compact coil with shorter length but more layers will have higher inductance according to those formulas. Isn't this also the case for transformers? I just find this odd that the standard formula is so elegantly derived from the Ampere's law and the Faraday's law, and it contains the all important N^2, A, and ℓ that are all used in many other formulas. Yet it may not give an accurate result in a general case.