INDUCTOR:
Basic concept:
The overall concept of an inductor is that of a resistance but the general concept of an inductor is in some seperation of relation to the resistance. The fundamentality of an inductor is in so called by reactance, something that does the job like resistance without being the resistance specifically. Now its interesting in knowing from where all these nature is coming and how they resemble in such an orientation.
Inductor is a device(lets take it ideally just as if a device which will later be known just by a component or element) that restricts the flow of current as do resistors without exerting the effect of resistance. To view it basically it's a coil of several turns of wire that forms the electromagnetism when current flows through it. Now it's important to realise the mystery behind the reactive nature of such a simple device.
Working of an inductor:
As the name inductor suggests that there is somehow some situation of induction in it. Now to visualise this one can estimate that there is some electromagnetic induction that prevails as current flows through the coil and that's dominating when there is variation of current leading to variaton of magnetic flux which tries to compensate the change in supplied current by inducing some reverse magnetic flux by itself as well as an reverse emf as well as some reverse current.
Image result for faradays law imageInductor working is based on the two famous laws:
1] Faraday's Law: A changing magnetic field causes an emf induced in a conductor under that magnetic field.
Image result for Lenz's law2] Lenz's Law: Current induced in a circuit due to a change or a motion in magnetic field is so directed as to oppose the change that's producing it.
Inductive Reactance:
The property that an inductor exerts is inductive reactance.
Image result for Sinusoidal voltage current through inductorTo get more familiar with this term it's necessary to observe its effect on the varying supply voltage and current which are considered for the instance to be sinusoidal in nature.
In the figure as shown, the current lags the voltage by a phase difference of 90 degree. This is because the change in supply voltage as well as the change in supply current induces some varying magnetic flux
that neither allows the rise in current neither allows the fall of current.Thus it always beholds back the current from its normal nature and maintains a phase difference between supplied voltage and the current. Whereas in case of resistor both voltage and current appears as well as diminishes sinusoidally without any lagging or phase difference.
Mathematical Analysis: 
Let the supplied voltage be represented as V=Vm*sin(wt)
Then current through an inductor is given as 
I=Im*sin(wt-90degree).
Inductive reactance X=2*pi*f*l. where f=frequency, 
l=self inductance.
Equation of voltage or emf induced is given as E=l*(di/dt)
where di/dt is the rate of change of current. 
Application of inductor : 
Inductors are highly applicable in electrical power quality maintanance.
Inductors are preferred over resistance or capacitance to compensate in between active and reactive power thus to improve power factor. 
In dc electric motors inductance plays a majr role in current lagging and thus in dc motor drives inductors are used to make the current as well as torque continuous. 

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