Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics, and electromagnetism. This field first became an identifiable occupation in the latter half of the 19th century after commercialization of the electric telegraph, the telephone, and electric power distribution and use. It now covers a wide range of subfields including electronics, digital computers, power engineering, telecommunications, control systems, RF engineering, and signal processing.
Electrical engineering may include electronic engineering. Where a distinction is made, usually outside of the United States, electrical engineering is considered to deal with the problems associated with systems such as electric power transmission and electrical machines, whereas electronic engineering deals with the study of electronic systems including computers, communication systems, integrated circuits, and radar.
In arithmetic and number theory, the least common multiple (also called the lowest common multiple or smallest common multiple) of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a,0) for all a, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility.
The LCM is familiar from grade-school arithmetic as the "least common denominator" (LCD) that must be determined before fractions can be added, subtracted or compared.
Electronics engineering, or electronic engineering, is an engineering discipline where non-linear and active electrical components such as electron tubes, and semiconductor devices, especially transistors, diodes and integrated circuits, are utilized to design electronic circuits, devices and systems, typically also including passive electrical components and based on printed circuit boards. The term denotes a broad engineering field that covers important subfields such as analog electronics, digital electronics, consumer electronics, embedded systems and power electronics. Electronics engineering deals with implementation of applications, principles and algorithms developed within many related fields, for example solid-state physics, radio engineering, telecommunications, control systems, signal processing, systems engineering, computer engineering, instrumentation engineering, electric power control, robotics, and many others.]verification needed[
The Institute of Electrical and Electronics Engineers (IEEE) is one of the most important and influential organizations for electronics engineers.
An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, voltage sources, current sources and switches. An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Linear electrical networks, a special type consisting only of sources (voltage or current), linear lumped elements (resistors, capacitors, inductors), and linear distributed elements (transmission lines), have the property that signals are linearly superimposable. They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms, to determine DC response, AC response, and transient response.
A resistive circuit is a circuit containing only resistors and ideal current and voltage sources. Analysis of resistive circuits is less complicated than analysis of circuits containing capacitors and inductors. If the sources are constant (DC) sources, the result is a DC circuit.
A voltage multiplier is an electrical circuit that converts AC electrical power from a lower voltage to a higher DC voltage, typically using a network of capacitors and diodes.
Voltage multipliers can be used to generate a few volts for electronic appliances, to millions of volts for purposes such as high-energy physics experiments and lightning safety testing. The most common type of voltage multiplier is the half-wave series multiplier, also called the Villard cascade (but actually invented by Heinrich Greinacher).
In monetary economics, a money multiplier is one of various closely related ratios of commercial bank money to central bank money under a fractional-reserve banking system. Most often, it measures the maximum amount of commercial bank money that can be created by a given unit of central bank money. That is, in a fractional-reserve banking system, the total amount of loans that commercial banks are allowed to extend (the commercial bank money that they can legally create) is a multiple of reserves; this multiple is the reciprocal of the reserve ratio, and it is an economic multiplier.
In equations, writing M for commercial bank money (loans), R for reserves (central bank money), and RR for the reserve ratio, the reserve ratio requirement is that the fraction of reserves must be at least the reserve ratio. Taking the reciprocal, which yields meaning that commercial bank money is at most reserves times the latter being the multiplier.
Elementary arithmetic is the simplified portion of arithmetic which includes the operations of addition, subtraction, multiplication, and division.
Elementary arithmetic starts with the natural numbers and the written symbols (digits) which represent them. The process for combining a pair of these numbers with the four basic operations traditionally relies on memorized results for small values of numbers, including the contents of a multiplication table to assist with multiplication and division.