# Coil Inductance Formulas

Inductance is defined as the property of a conductor by which it opposes the flow of current.

where

L = Inductance of inductor (coil)

µ = Absolute permeability of core material

N = Number of turns in coil

A = Area of coil

W = Energy

l = average length

### How to calculate the inductance of coil

The inductance of any coil depends on four factors. It is directly related to magnetic permeability, the number of coil turns and area of the coil. However, it is inversely related to the length of the coil.

L = µN^{2}A/I

Example # 1: An iron core inductor has 7 number of turns. The radius of the core is 0.1 cm^{2}. The length of coil is 0.1 cm. Find the inductance of coil created by 2 A current.

Solution: Area = πr^{2 }= 3.14 * 10^{-6}

The magnetic permeability of iron is 6.3×10^{−3}. So µ = 6.3×10^{−3}

L = [ 6.3×10^{−3 }* 49 * 3.14 * 10^{-6}] / 2 A = 461 nF

### Energy stored in coil

The energy stored in an inductor (coil) is half the inductance times square of the current. Mathematically

W = [L * I^{2}] /2

From above equation, the inductance can be defined as twice the energy to current.

L = 2 W/I^{2}

Example 2: The inductor coil stores 20 J energy when a steady current of 2 amps current flows through it. Find the inductance of the coil.

Solution: L = 2 W/I^{2} = {2 * 20 J} / 4 amps = 10

### In terms of EMF

We can also define inductance as the change which is generated to oppose the current flow. In that case, we can mathematically write. EMF = -LΔI/Δt^{2}