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THEORY ( IN SOMEWHAT DETAIL )
THE REAL REASON WHY COMPLEX NUMBERS OCCUR IN ELECTRONICS
|||| Complex numbers seep into electronics whenever a single force divides or branches out into two component forces.
|||| .In majority of the cases in real life....the real reason for this splitting is the tilting or rotating of the object or force. Whenever anything gets
|||| .Out of these component forces,.....the force which is in alignment is known as the cos component. It is also for some mysterious reason called as the real-part.
|||| .And the other component which is which is perpendicular is called as the imaginary-part or the ixsin() component.
|||| .Toll give you an analogy......imagine that you throw a knife at a target.....initially lets say the knife was moving sharply horizontally....then it has only the Cos() component. But after it tilts,....now it has a vertical component also...an imaginary component ....Sin().(trust me its not imaginary at all).
|||| .Now....the question that we need to ask ourselves is that.....is tilting the only reason.....the only agent which can make a single force divide into two?
|||| . Initially....I used to think so. But thanks to being an Electronics and Telecommunication student,....I knew one thing for sure that complex numbers was finding its way into electronics as well.
|||| .The moment a capacitor or an inductor comes into the path of an electric current......complex numbers also make their unwelcomed entry.
|||| .Naturally there was more to complex numbers than just expressing tilting and rotation.
|||| . I then had to turn my attention towards what is common between a tilted object and a capacitor? Strange question,....right? and maybe irrelevant too. But the answer lied somewhere there.
|||| . Eventually....it dawned to me that both of them were responsible for making an otherwise single....and unified force into two daughter forces.
|||| . When a capacitor is not put in a circuit.....the electrons have a joyride in the circuit.
|||| . The only thing they may have to face is some resistance of the conductor itself.
|||| . This resistance acts along the line of motion of the electrons....so basically....now there is only a Cos() component or a Real part.
|||| . But after the capacitor is put....the capacitor not only resists the motion of the electrons with its own internal resistance. Trust me ....the internal resistance of a capacitance is very small and that is not the real reason why we put it there.
|||| . The real reason why we put it there is because of its ability to store electrons temporarily. Yes,....the capacitor acts like a temporary dam. It does not allow the electrons to flow as they are. It stops them intially........makes them accumulate.
|||| .As they accumulate......the voltage on one side of the capacitor keeps on increasing.
|||| .Now after a certain threshold voltage is reached....the capacitor now discharges electrons.
|||| . So in a way....the electrons eventually do flow....but they surely get delayed by the capacitor.
|||| . The capacitor acts like an unneccessary traffic police halting.....creating a traffic jam upto a certain level and only then leaving them.
|||| .So thus...now the electrons have to go through two forces......thanks to the electrons.
1] The resistance caused by the internal resistance of the capacitor.
2] The delay caused by the capacitance of the capacitor.
|||| . This storage or accumulation of electrons as if goes up vertically.....perpendicular to their normal flow into the circuit. Hence it is known as the imaginary of the sin() component.
|||| . As I have mentioned in the post of trigonometry....sin() comes in maths whenever something is going perpendicular.
|||| .This is the reason why complex numbers come into the world of electronics also. Actually.....whenever you see complex numbers...just ask yourself whether any force or anything is branching out into two.
|||| . I am glad to post this post....especially because countless Electronics students might benefit from it.
|||| . If time permits .....I would love to explain the working of an inductor also.
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