Inductance / Inductor

Inductance

Inductance or Inductor indicated by letter ‘L’ is a passive circuit element that stores energy in the form of magnetic field. Inductors are the coils generally wounded over a permeable medium. The windings in electrical machines and transformers
are examples of Inductors. An ideal Inductor never dissipates power, but practically due to internal resistance of the coils there will be a small power dissipation.

Inductor

An inductor opposes sudden changes in magnitude or direction of electric current passing through it.

Unit of Inductance

Inductance is measured in Henry (H) , given by the Faraday’s law of electromagnetic induction.
Inductance of a circuit is said one henry when current is varying at one ampere per second resulting in an electromotive force of one volt.

Inductance of a coil of length l and area of cross section, A having N number of turns is given be by,

L= (μ₀μ_rAN²)/l

Voltage and Current relation for Inductor

The Voltage developed across an inductor is given as \[v=-L\frac{di}{dt}\]
Hence the current through an inductor is i = \[\frac{1}{L}\]∫v(t)dt

From the above equations it can be observed that an inductor needs rate of change of current for voltage to appear across it.

i. If a constant DC is applied for an inductor there will not be any rate of change of current. Hence di/dt=0 ⇒ V=0. Thus an inductor behaves as a short circuit in pure DC.

ii. If a time varying wave form such as i=sin(ωt) is applied, then the voltage across it is given by
v=L(di/dt)= L\[\frac{d}{dt}\]sin(ωt)=Lcos(ωt)

iii. If a sudden change of current is applied then di/dt will become infinity and thus the voltage, which is not practically possible. So an inductor opposes sudden changes in current.

Energy Stored in an Inductor

Power absorbed by an inductor is given by
P=vi=Li\[\frac{di}{dt}\]

Energy stored is given by,
\[\int_{0}^{t}P.dt\] = \[\int_{0}^{t}Li\frac{di}{dt}\] = \[\frac{1}{2}Li^{2}\]