BASIC ELECTRICAL and ELECTRONICS ENGINEERING FORMULAS
EE REFERENCE, THEOREMS, CIRCUIT DESIGN AND ANALYSIS,
ELECTRIC CALCULATIONS
<>
Let's start with quick definitions.
Electronics involves the design and analysis of
electronic circuits. Originally, this subject was referred to as
radio engineering. The term "circuit" refers to a collection of components through which electrical current can flow or which use electromagnetic fields in their operation.
Basic circuit design and analysis rests primarily on two
Kirchoff's laws,
Ohm's law modified for AC circuits, and power relationships (see below). There are also a number of network theorems and methods (such as Thevenin, Norton, Superposition, YDelta transform) that are consequences of these three laws.
In order to simplify calculations in AC circuits, sinusoidal voltages and currents are usually represented as complexvalued functions called
phasors. With phasors we need to solve algebraic equations instead of differential equations (see below). In general, practical
circuit design and analysis requires an understanding of semiconductor devices, integrated circuits, magnetics, DSP, and feedback control.
Here you will find electricity and magnetism reference, basic electrical engineering formulas, calculators, and other related information.
Also see:
Electrical engineering
reference: electric network laws and theorems;
Free tech
ebooks and white papers;
The guide to accredited
online schools, distance learning programs and courses.
FORMULAS FOR THE BASIC CIRCUIT COMPONENTS

CIRCUIT
ELEMENT 
IMPEDANCE 
VOLTAMP EQUATIONS 
ENERGY
(dissipated on R or stored in L, C) 
absolute value 
complex
form 
instantaneous
values 
RMS values for sinusoidal signals

RESISTANCE 
R 
R 
v=i×R 
Vrms=Irms×R 
E=Irms^{2}R×t 
INDUCTANCE 
2πfL

jωL 
v=L×di/dt 
Vrms=Irms×2πfL 
E=Li^{2}/2 
CAPACITANCE 
1/(2πfC) 
1/jωC 
i=C×dv/dt 
Vrms=Irms/(2πfC) 
E=Cv^{2}/2 
Notes:
R resistance in ohms, L inductance in henrys, C capacitance in farads, f  frequency in hertz, t time in seconds, π≈3.14159;
ω=2πf  angular frequency;
j  imaginary unit ( j^{2}=1 )
Euler's formula: e^{jx}=cosx+jsinx


EQUATIONS FOR SERIES AND PARALLEL CONNECTIONS

CIRCUIT
ELEMENT 
SERIES
CONNECTION 
PARALLEL
CONNECTION 
RESISTORS 

Rseries=
R1+R2+... 

Rparallel=
1/
(1/R1+1/R2+...) 
INDUCTORS

Lseries=
L1+L2+... 
Lparallel=
1/(1/L1+1/L2+...) 
CAPACITORS 
Cseries=
1/
(1/C1+1/C2+...) 
Cparallel=
C1+C2+... 
CALCULATIONS OF EQUIVALENT RLC IMPEDANCES

CIRCUIT CONNECTION 
COMPLEX FORM 
ABSOLUTE VALUE 
Series 
Z=R+jωL+1/jωC 

Parallel 
Z=
1/(1/R+1/jωL+jωC) 

Note: you can download a reference "cheat sheet" with these and other formulas in pdf file.

TRANSISTORS AND DIODES: THE BASICS
The properties of semiconductor devices are studied in college courses. The introduction to the circuits including operation of diodes and transistors and basic formulas can be found in various textbooks or handbooks, such as
The Art of Electronics. Below are just some highlights.
The IV characteristic of a
diode is approximated by the Shockley equation:
I=Is×(e^{nVd/Vt}1),
where Is  the reverse bias saturation current (~10
^{−15} to 10
^{−12} A for Silicon); Vd  voltage drop in volts; Vt  the thermal voltage (~0.026V at room temperature), n  the "ideality factor" (from 1 to 2).
At a fixed current I, forward voltage drop changes by about 2 mV/
^{o}C.
In a
bipolar transistor collector current Ic in a linear mode is related to the baseemitter
voltage by the same Shockley (also called EbersMoll) equation, except for n=1. The collector current relates to the base current I
_{B} by
Ic=I_{B}×h_{21}, where h
_{21}  static current gain (typically 201000). When Ic reaches a limit determined by the supply voltage and the net external impedance in the collector circuit, the transistor is saturated.
MOSFET behavior varies with the gate voltage Vg. When Vg<Vth, where Vth  gate threshold voltage, the MOSFET is in OFF state with drain current Id≈0. When Vg>Vth and the external load is such that Vd>VgVth, the MOSFET is in an active region, in which Id is proportional to the (VgVth)
^{2} and practically does not depend on the Vd. Once Id reaches certain limit determined by an external circuit, MOSFET start acting as a nearly constant resistance. In this mode
Vds≈Id×Rdson, where Rdson  the ONstate channel's resistance specified in data sheets as a function primarily of temperature and gate voltage. Power MOSFETs are usually used as switching devices which operate in either ON or OFF state.