ELECTRICAL ENGINEERING REFERENCE INFORMATION
ELECTRICITY AND MAGNETISM BASICS, CIRCUIT THEOREMS AND EQUATIONS
Electrical engineering
(EE) 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 (see below). 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.
Electrical formulas and impedance calculations;
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MAXWELL'S EQUATIONS IN FREE SPACE (in SI units) |
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| LAW | DIFFERENTIAL FORM | INTEGRAL FORM |
| Gauss law for electricity Gauss law for magnetism Faraday's law of induction Ampere's law |
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| NOTES:
E - electric field, ρ - charge density, ε0 ≈
8.85×10-12 - 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, µ0 = 4π×10-7 - magnetic permeability of free space, 
- del operator (if V
is a vector function, then .V is divergence of V,
×V is the curl of V). |
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BASIC ELECTRICAL THEOREMS AND CIRCUIT ANALYSIS LAWS |
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| THE LAW | DEFINITION | RELATIONSHIP TO OTHER LAWS |
| Ohm's Law extended for AC circuits with single frequency sinusoidal signals | V=Z×Ĩ,
where V and Ĩ - voltage and current phasors, Z - complex impedance (for resistive circuits: Z=R and V=R×I ) |
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 |
You can download a reference sheet with these and other equations in a pdf file.
ELECTRICAL NETWORK THEOREMS FOR AC CIRCUITS |
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| THE THEOREM | DEFINITION | CALCULATION |
Thevenin's 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 |
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 a adjustable 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 |
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 |
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) |