## Monday, 4 August 2014

WHY DO COMPLEX NUMBERS COME IN ELECTRONICS..???

Firstly you may want to know why and where complex numbers come in Maths...and what they denote.

NOW...... THE WORKING OF A CAPACITOR

WHAT ARE THE REAL AND THE IMAGINARY PARTS OF CAPACITANCE ???

INDUCTORS ARE IN CONSTRUCTION...............

ELECTRONICS.GURUKULAM.COM ( Finally a good site on electronics...its rare to find)

CIRCUIT-FANTASIA.COM A Cluttered site...but awesome analogies present. An ocean of analogies literally

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THE ABOVE IS A EXCERPT FROM A BOOK AVAILABLE FOR PURCHASE (5\$) AT THE FOLLOWING LINK

AVAILABLE FOR PURCHASE FOR 5\$ (INR 300) HERE (PDF)

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I hardly understood Math in school. In fact was on the verge of dropping the subject I loved the most because as much as I loved the theory of it, I could not understand the math involved in it. However I loved the subject too much to be able to live without. Hopelessly, I was continuing my love-affair with it.

Then one day....a miracle happened,....while applying a certain formula again and again.....I came to know its significance. Slowly and steadily....other equations also started clicking. I got to see a strong relationship between Maths and the Physics it was pointing towards. They both were the same. Maths was just an easy language to express a physical phenomenon. And a bit more to that in the sense that it could even predict the behaviour of a certain physical phenomenon. Equations now as if came to life.

Every equation now had as if something to say. A burning urge to share these things with the world aflamed within me. So that no one has to give up the subject that he or she loves the most.
The book on visualizing maths thus got written as a sprout of inspiration. The blog followed. Both these are dedicated to you and all such similar minds searching for answers.

Visualizing Math & Physics is a blog dedicated to you and all such similar minds searching for answers.

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CONTACT
binnoypanicker@gmail.com

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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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THE ABOVE IS A EXCERPT FROM A BOOK AVAILABLE FOR PURCHASE (5\$) AT THE FOLLOWING LINK

AVAILABLE FOR PURCHASE FOR 5\$ (INR 300) HERE (PDF)

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