Inductor
An inductor is a passive two terminal electrical component
which store energy in the form of magnetic field when an alternating electric current
passing through it. It offers inductive reactance to the circuit. An inductor
is nothing but a wire which reshaped as a coil around a central core. This
central core can be air (air core inductor) or ferromagnetic material (iron
core inductor). Voltage across an inductor is directly proportional to time
rate of change of current.
V α di/dt
V = Ldi/dt
L = inductance of a coil (Henry) (H)
Inductance
is the property of inductor by virtue of it, it oppose the flow of current
through it. It is represented by L. The Si unit of inductance is Henry (H).
As we know that an inductor is nothing but coil of wire, when alternating current passes through the wire (conductor) it generates magnetic field in a circular path around the wire. The strength of this magnetic flux is directly proportional to the electric current flow through it. The direction of magnetic field can be determined by Fleming’s Right Hand Thumb Rule.
Now if we reshaped a wire as a coil then it is assumed that
each turn has its own magnetic flux which links to other turns.
Flux linkages to the coil.
ψ = Nɸ
As the electric current passing though it is time varying
(alternating) then the flux produces by it is also time varying.
So according
to Faraday law of electromagnetic induction, if a time varying flux links to
the coil then an emf induced in the coil (statically induced emf).
If
flux is time unvarying in nature then for effective rate of change of flux
linkages relative motion between coils and flux required for effective rate of
change of flux linkages. Then in this case emf is dynamically induced emf.
The value of induced emf is directly proportional to the time
rate of change of flux linkages.
V
= dψ/dt = d(Nɸ)/dt
V
= Ndɸ/dt + ɸdn/dt
V
= Ndɸ/dt
ψ α ɸ
…………….. (2)
From
equation 1 and 2
ψ α i
ψ
= Li
L =
ψ/i = Nɸ/i
………………… (3)
Here
N is the number of turns provide to a wire to increasing its inductive effect.
R eactance of Inductor
XL
= wL
= 2Ï€fL
F
= Supply Frequency
L
= Inductance.
Some Specifications of Inductor
1. Inductor can be either linear or non linear
2. The average power dissipation in an ideal inductor is zero
3. For dc source inductor behave as short circuit.
4. An inductor does not allow sudden change in current because
for sudden change in current it requires infinite voltage which is practically
impossible
5. Practical impedance of an inductor contains inductive as well
as capacitive reactance and resistance.
Uses of Inductor
1. Inductors are used to design filters in analog circuits and
signal processing.
2. Inductors are used to design resonance circuit.
3. Inductors are used in electric power system to reduce
Ferranti Effect and to control reactive. In power system inductors are commonly
known as reactors.
4. Generally all practical load are inductive in nature.
Energy Stored in Inductor
Let v(t) is the voltage applied across the inductor and i(t)
current flow through it then
Power (p) = v(t). i(t)
Energy stored in inductor in
W = ∫P(t) dt
= ∫v(t). i(t) dt
= ∫(Ldi/dt) .i dt
Average power dissipated in inductor
Let v(t) is the voltage applied across the inductor and i(t)
current flow through it.
i(t) = Im
sin wt …….. (i)
v(t) = wL Im cos wt
v(t) = wL Im sin(wt+90) ……….(ii)
XL = wL
(inductive reactance)
From equation (i) and (ii) it is clear that voltage across an
ideal inductor is lead 900 from current flow through it.
Paverage =
1/T 0ʃT Vm cos wt . Im
sin wt dt
= Vm Im/2T 0ʃT sin2wt dt
= 0
So,
in an inductor average power dissipated in an ideal inductor is zero.
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# Nodal Analysis of an Electric Circuit
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