What is Inductor | How Inductor Works

What is an Inductor ?

A wire of finite length when twisted into a coil makes simplest inductor. 

Lets see how inductor works ? As soon as a current I flows  through a coil, an electromagnetic field is formed. Thus a magnetic flux Φ is created. 
However, with any change in direction or magnitude of current  the magnetic flux changes to induce an emf e in the coil. This phenomenon is called self-induction.

The emf induced is given by,  e=-(dΦ/dt)=-L(dI/dt)

Now,

(1) If current remains constant  i.e dI/dt is zero , the voltage induced across the inductor will be zero ,showing that an inductor behaves as a short circuit in steady state when conncted to a dc source.

(2) If current tries to change abruptly  i.e dI/dt  tending to infinity , a emf of infinite magnitude will be induced across the inductor, but, infinite magnitude voltage is physically not possible, showing that current cannot change abruptly in an inductor.

An inductor thus behaves as an open-circuit just after switching across a dc voltage.

(3) No matter how good conductor you use to make an inductor, it will always have some resistance. So, practical inductors will dissipate energy on account of this resistance but ideally the resistance will be zero, therefore, an ideal inductor does not dissipate energy but only stores it.

Power absorbed by the inductor is given by,

P = voltage across inductor × current through inductor
   = eI= IL(dI/dt) watt

And energy absorbed is given by,

E=∫^t₀Pdt = LI² / 2

How does an Inductor work in AC circuit 

Let a pure inductor (zero resistance) of inductance L be supplied by an ac source V_s as shown.

Using inductor  equation

e =-L(dI/dt) = V_s

simplifying and taking integration limits :-

dI= (V_sdt/L) 

take integration  :-

∫^I₀dI= (1/L)∫^t₀ V_s dt

Solving integration :-

I = (1/L)∫^t₀ V_m sinwt dt

  = - (V_m coswt/wL)

  =  {V_m sin(wt-90⁰)} / wL                ∵   -coswt = sin(wt-90⁰)

Comparing above equation with standard current equation i.e

 I = (V/R) = {V_m sin(wt-90⁰)} / wL

We get,

(1) R= wL  , is the opposition offered to flow of current and it is given a special name ,inductive reactance. Inductive reactance is represented by X_{L .}

i.e  X_L =wL= 2 πfL   

Its clear from inductive reactance formula that it depends on source frequency f.

The inductive reactance plays the same role for inductors as the resistance plays for resistors i.e to oppose the current flow.

(2) The voltage has phase  wt  while current has (wt-90⁰).

i.e current flowing  through the inductor lags  the voltage across it by 90⁰

Current and voltage waveforms would appear as shown.

Closely related concepts :-

     (1) Inductance of a coil | Concept of Self Induction | Solenoid