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Inductance





(1) Introduction


  • Before defining inductance first of all, we will define an inductor.
  • Like capacitor, inductor is another component commonly in electronic circuits.
  • An inductor consists of a coil wound on a core or former of a suitable material like solid or laminated iron. core or ferrites which are highly ferromagnetic substances.
  • when a current through an inductor changes am emf is induced in it which opposes this change of current in the inductor.
  • This property of inductor or coil due to which it opposes change of current through it called the inductance denoted by letter L.
  • Unit of inductance is henry(H).




(2) Self Inductance


  • Consider the figure given below


    Self Inductance

  • When we establish a current through an inductor or coil, it generates a magnetic field and this result in a magnetic flux passing through the coil as shown in figure 1(a).
  • If we vary the amount of current flowing in the coil with time, the magnetic flux associated with the coil also changes and an emf ξ is induced in the coil.
  • According to the Lenz’s law, the direction of induced emf is such that it opposes its cause i.e. it opposes the change in current or magnetic flux.
  • This phenomenon of production of opposing induced emf in inductor or coil itself due to time varying current in the coil is known as self induction.
  • If I is the amount of current flowing in the coil at any instant then emf induced in the coil is directly proportional to the change in current i.e.


    where L is a constant known as coefficient of self induction.
  • If (-dI/dt)=1 then ξ=L
    Hence the coefficient of self induction of a inductor or coil is numerically equal to the emf induced in the coil when rate of change of current in the coil is unity.
  • Now from the faraday's and Lenz’s laws induced emf is


    comparing equation 1 and 2 we have,

    or Φ=LI
  • Again for I=1, Φ=L
    hence the coefficient of self induction of coil is also numerically equal to the magnetic flux linked with the inductor carrying a current of one ampere
  • If the coil has N number of turn’s then total flux through the coil is
    Φtot=NΦ
    where Φ is the flux through single turn of the coil .So we have,
    Φtot=LI
    or L=NΦ/I
    for a coil of N turns
  • In the figure given below consider the inductor to be the part of a circuit and current flowing in the inductor from left to right


    Inductor as a part of circuit

  • Now when a inductor is used in a circuit, we can use Kirchhoff’s loop rule and this emf(Self induced emf) can be treated as if it is a potential drop with point A at higher potential and B at lower potential when current flows from a to b as shown in the figure
  • We thus have
    Vab=LdI/dt


(3) Self induction of a long solenoid


  • Consider a long solenoid of length l, area of cross-section A and having N closely wound turns.
  • If I is the amount of current flowing through the solenoid them magnetic field B inside the solenoid is given by,


  • Magnetic flux through each turn of the solenoid is,



(4) Energy in an inductor


  • Changing current in an inductor gives rise to self induced emf which opposes changes in the current flowing through the inductor.
  • This self inductance thus plays the role the inertia and it is electromagnetic analogue of mass in mechanics.
  • So a certain amount of work is required to be done against this self induced emf for establishing the current in the circuit.
  • In order to do so, the source supplying current in a circuit must maintain Potential difference between its terminals which is done by supplying energy to the inductor.
  • Power supplied to the inductor is given by relation
    P=ξI                      ---(4)
    where


    L is Self inductance and
    dI/dt is rate of change of current I in the circuit.
  • Energy dW supplied in time dt would be
    dW=Pdt
    =LI(dI/dt) dt
    =LIdI
    and total energy supplied while current I increases from o to a final value I is


  • Once the current reaches its final value and becomes steady ,the power input becomes zero.
  • The energy so far supplied to the inductor is stored in it as a form of potential energy as long as current is maintained.
  • When current in circuit becomes zero, the energy is returned to the circuit which supplies it.








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