ELECTRICAL ENGINEERING REFERENCE INFORMATION



ELECTRICITY AND MAGNETISM BASICS, CIRCUIT THEOREMS AND EQUATIONS

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This page provides a concise introduction to electrical engineering (EE) as well as basic formulas and theorems. Electrical engineering is a discipline that deals with electricity, magnetism and their applications. EE applications include electronics, power conversion, data communications, computer science, information technologies, and other. The term EE usually encompasses electronic engineering or electronics. Electronics involves the design and analysis of electronic circuits.


In academia and electronic industry, the terms electrical and electronics engineer often are used interchangeably. In other industries, the term electrical engineer may refer to those who deal with utility and industrial power systems and other electric equipment. In any case, both disciplines are overlapping.

The theoretical foundation for EE is electromagnetism. The theory of classical electromagnetism is based on Maxwell's equations. They provide a unified description of the behavior of electric and magnetic fields as well as their interactions with matter. In practice however, Maxwell's equations are rarely used in an electrical design. The circuit designers normally use simplified equations of electricity and magnetism and theorems that use circuit theory terms, such as Ohm's law modified for AC circuits, voltage and current Kirchoff's laws, as well as power relationships (see below).

This webpage is for those who have already learned EE and need a quick reference information. Here you will find electricity and magnetism basics, electronics reference as well as the career related information online.

Also see:
Electrical formulas and impedance calculations;
Distance learning: engineering degree online from accredited schools and salary surveys.




BASIC ELECTRICAL THEOREMS AND CIRCUIT ANALYSIS LAWS

THE LAW DEFINITION RELATIONSHIP TO OTHER LAWS
Ohm's Law extended for AC circuits with single frequency sinusoidal signals V=ZĨ, where V and Ĩ - voltage and current phasors, Z - complex impedance
(for resistive circuits: Z=R and V=RI )
Lorentz force law and Drude model for resistors
Kirchhoff's Current Law (KCL) The sum of electric currents which flow into any junction in a circuit is equal to the sum of currents which flow out Conservation of electric charge
Kirchhoff's Voltage Law (KVL) The sum of the voltages around a closed circuit must be zero Conservation of energy
Note that Kirchhoff's laws can be derived from Maxwell's equations under static conditions, although historically they preceded Maxwell's equations.
You can download a printable reference sheet with these and other equations in a pdf file.

MAXWELL'S EQUATIONS IN FREE SPACE (in SI units)

LAW DIFFERENTIAL FORM INTEGRAL FORM
Gauss law for electricity


Gauss law for magnetism


Faraday's law of induction


Ampere's law

Maxwell equations
NOTES: E - electric field, ρ - charge density, ε0 ≈ 8.8510-12 - electric permittivity of free space, π ≈ 3.14159,
k - Boltzmann's constant, q - charge, B - magnetic induction, Φ - magnetic flux, J - current density, i - electric current,
c ≈ 299 792 458 m/s - the speed of light, 0 = 4π10-7 - magnetic permeability of free space, Del operator - del operator (if V is a vector function, then Del operator.V is divergence of V, Del operatorV is the curl of V).

ELECTRICAL NETWORK THEOREMS FOR AC CIRCUITS

THE THEOREM DEFINITION CALCULATION
Thevenin's Theorem
Thevenin theorem
Any combination of a single frequency sinusoidal AC sources and impedances with two terminals can be replaced by a single voltage source V in series with an impedance Z. V - open-circuit voltage phasor of the original circuit;
Z - impedance between the two terminals with all voltage sources shorted and all current sources opened.
Norton's Theorem
Norton theorem
Any combination of a single frequency sinusoidal AC sources and impedances with two terminals A and B can be replaced by a single current source I in parallel with an impedance Z. I - short-circuit current phasor of the original circuit;
Z - impedance between the two terminals with all voltage sources shorted and all current sources opened.
Superposition Theorem The current (voltage) phasor in any part of a linear circuit equals the algebraic sum of the current (voltage) phasors produced by each source separately. To find an individual current (voltage) from each source, short all other voltage sources and open all other current sources.
Maximum Power Transfer Theorem A voltage source delivers maximum power to an adjustable load when the source and the load impedances are complex conjugates of each other Active components of the source and load impedances should be equal, and reactive components should have equal magnitude but opposite sign.
Delta to Wye Transformation
Delta to Wye diagram
A delta network of three impedances can be transformed into a star (Y) network of three impedances Za = ZcaZab / (Zab+Zbc+Zca)
Zb = ZabZbc / (Zab+Zbc+Zca)
Zc = ZbcZca / (Zab+Zbc+Zca)
Star-Delta Transformation
Star-delta transform diagram
A star (Y) network of three impedances can be transformed into a delta network of three impedances
Zab = Za + Zb + (ZaZb / Zc)
Zbc = Zb + Zc + (ZbZc / Za)
Zca = Zc + Za + (ZcZa / Zb)

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