Inductance Formula

Inductance, in Physics, is one of the most important features of electromagnetism. There are various concepts and formulas that are associated with inductance like the mutual inductance formula, formula for induced EMF, inductance of a coil, and so on. Each of these inductance formulas is very important and has several applications. Here, we will discuss all the formulas one after another along with their applications but before that, let us first revise what inductance is, in brief. 

Inductance

• When electricity passes through a conductor - like a copper wire - an electromagnetic field is produced around it and it is proportional to the value of the electricity passing through it.

• Now if we wind the wire around any cylindrical object, we make the wire spiral-shaped. This is called an inductor. 

• When we pass electricity through one end of the wire, it goes through the spirals producing an electromagnetic field. This spiral tends to keep this electromagnetic field stable. So if we increase the current, the spiral will try to block the current - producing a stronger electromagnetic field. 

• This tendency to stop is what we call Electromotive Force. And this force is known as Inductance. 

• You will see this Inductance even when you try to lower the flow of current. In this case, the inductor will lose its electromagnetism to try to supply the same amount of electron that was flowing earlier because of the electric current. 

Based on the above explanation, the formal definition of Inductance is - An electromotive force produced in a conductor to try and resist the change in the flow of the current is called Inductance. 

Inductance of a Coil Formula

The main formula for calculating Inductance is -

L = N²μA / l

Here, 

L = Symbol of Inductance, measured in Henry unit.

N = Number of times the wire is turned on the coil

µ = Absolute Permeability

A = Area covered by the coil (typically measured with the help of radius using Pi)

l  = Length of the coil.

Calculating the Inductor Voltage

V= L.di/dt

V = Voltage

L = Inductance

di/dt = Rate of change of the current = ampere/second

Inductive Reactance Formula

X=2πfL

X = Reactance measured in Ohm

F = Frequency

L = Inductance

Self Inductance Formula

When the change in the rate of the electric current results in the self-induced creation of EMF in the coil we call that Self Inductance. It is measured as the ratio between the EMF and the change in the current flow.

The Self Inductance Formula is -

E = -L.di/dt

Here,

E = Induced EMF formula

L = Induction

di/dt = rate of current change = amps/second

Inductive EMF Formula

When the Electromagnetic flux in the coil changes, we see the production of Voltage. This is called EMF induction. 

Inductive EMF Formula 

e = N × dΦdt

Here,

e = Voltage Produced

N = Number of windings the coil has

Φ = Magnetic flux

T = Time

Calculating the Total Inductance of a Series of Inductors

When inductors are connected one after the other, we measure each of the inductor’s inductance and add the figures. That sum is the Total Inductance

Total Inductance = L = L1 + L2 + L3 + …. + Ln

Solved Questions

1. Why is there a Minus Symbol in the Self Inductance Formula?

Ans. In Self Inductance, the EMF pushes the Voltage in the opposite direction to oppose it. This opposing nature of the force is depicted as the minus symbol.

2. What is Lenz’s Law?

Ans. Lenz’s Law states that when a voltage is induced in the circuit because of a change in the magnetic flux, that induced voltage in turn creates another magnetic flux which negates the initial magnetic flux.