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Electrical and electronics basics

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Electrical and Electronics engineering is a branch of engineering science. It involves two subject areas related to circuits which control high voltage and circuits which control low voltage. The high voltage study is basically electrical engineering and the low voltage study is electronic engineering. The above definition may be unconventional but to my view electrical and electronics engineering is all about circuits. Nicola Tesla greatly contributed to ac machinery development. He is one of the greatest inventors and scientists of all the time. Then the inventor of radio , Guglielmo Marconi must be considered a pioneer in the development of wireless communication. Electrical engineering heavily relies on the application of mathematics like rest of the engineering disciplines. Subjects of it are now diverse and unique. Energy is the most important issue now a days and electrical engineers are trying their best to make the power generation and distribution most efficient. Electricity has conquered darkness when Tomas Alva Edison had invented the first electrically powered lamp. Then other electrical machinery began to be developed. They replaced old fashioned engines in many power systems. Before going into more details, we need to know that electricity can be of two forms : one is static electricity and the other is moving or dynamic electricity. There is an intermediate form which may be called quasi-static electricity. Many dynamic electrical phenomena can be modeled with quasi-static electricity postulates. In quasi-static case the time varying part is negligible compared to spatially varying part.

Quasi satic maxwell

Electrical systems have been an integral part of all the applications of modern engineering science. Just because without electricity no rocket would fly, no industry would run, not even internet. Electrical engineering not only involves developing new machinery but also controlling them. Control system engineering is a sub field of electrical engineering. It gives stability to electrical system like running generator, electrical motor driven machines and many other electrical things. Robots are also controlled machines. Control system designing and analysis must be explained in details to understand how it works. Technological innovation are being made by the help of fruitful research in electrical and electronics engineering. More and more people are pursuing their career in EEE engineering. But we must not forget all the mathematical theorems and physical laws that have brought light to this prestigious branch of engineering. One of the most important theorems is Fourier analysis. Consequently Fourier analysis has become an indispensable mathematical tool in telecommunication system modelling.

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Synchronous machines

Synchronous Machine constitutes of both synchronous motors as well as synchronous generators. An AC system has some benifits over DC system. Therefore, the AC system is exclusively used for generation, transmission and distribution of electric power. The machine which transforms mechanical power into AC electrical power is called as Synchronous Generator or Alternator. However, if the same machine can be operated as a motor is known as Synchronous Motor.
A synchronous machine is an AC machine whose satisfactory operation depends upon the maintenance of the following relationship.
synchronous motor
Where,
Ns is the synchronous speed in revolution per minute (r.p.m)
f is the supply frequency
P is the number of poles of the machine.
Motor speed can be regulated using the above equation. For example if we increase the supply frequency we can increase its speed. Other methods of increasing the speed is :
b) increasing the torque of the motor. It will involve changing the voltage. c) changing the number of poles. c) by controlling current to the rotor Law of Electro-Magnetic Induction This law is also called as Faraday’s First Law of Electromagnetic Induction. This law relates to the production of emf, i.e.; emf is induced in a conductor whenever it cuts across the magnetic field as shown below.
electromagnetic induction

Law of Interaction

This law relates the production of torque due to electromagnetic induction. When a current carrying wire is placed inside a magnetic field the interaction between magnetic field produced by the wire and the main magnetic field produes a torque which try to rotate the conductor or the wire.
law of interaction

Zero Power Factor Characteristic (ZPFC)

Zero Power Factor Characteristic (ZPFC) of a generator is a curve of the armature terminal voltage and the field current. The machine is run with constantly rated armature current at synchronous speed and zero lagging power factor. The Zero Power Factor Characteristic is also called as Potier Characteristic.
zero power factor characterstics
In the phasor diagram shown above, the terminal voltage V is taken as the ideal phasor. At zero power factor lagging, the armature current Ia lags behind V by 90 degrees. IaRa is drawn parallel to Ia and IaXaL perpendicular to Ia.
zero power factor characterstics
Eg is the generated voltage per phase.
The phasor diagram at ZPF lagging with the armature resistance Ra neglected is shown below.
zero power factor characterstics
Where,
Far is the armature reaction MMF. It is in phase with the armature current Ia.
Ff is the MMF of the main field winding (field MMF).
Fr is the resultant MMF.
The field MMF Ff is obtained by subtracting Far from Fr so that F_r = F_f + F_ar
From the above phasor diagram, it is seen that the terminal voltage V, the reactance voltage drop IaXaL and the generated voltage Eg all are in phase. Therefore, V is practically equal to the arithmetical difference between Eg and IaXaL.
V = E - I_aX_al The three MMF phasor Ff, Fr and Far are in phase. Their magnitudes are related by the equation shown below F_f = F_r + F_ar .
Therefore
zero power factor characterstics

Atomic physics all formula

Einstein discovered famous formula E=mc^2 which works almost everywhere. It is a consequence of special theory of relativity.
special theory of relativity
General theory of relativity was a great leap in the history of physics. It was a natural extension of special theory of relativity. The idea is quite simple although the equations turned out to be somewhat convoluted and complex.
general theory of relativity
Theory of relativity radically changed the way we see our universe. Universe is not what it seems. Einstein became a superstar after discovering his theory of relativity. But he was never awarded Noble prize for his discovery of theory of relativity. However atomic physics is the modern physics without which the sun would not shine. The nuclear reactor would not work. Even we could not think. In my perspective our mind is a natural quantum computer where the calculation is being made with quantum superposition. The comparison of hamiltonian of one particle and many particle system can be made with a table.
hamiltonian quantum system
The hydrogen atom can be explained by applying and analyzing Schrodinger's equation.
hamiltonian hydrogen atom

Ansatz is an the assumption of a function in order to faciliate the solution of a problem.
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