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# electrical theory for dummies

From Wikipedia

Circuit theory

Circuit theory is the theory of accomplishing work by means of routing matter through a loop. The types of matter used are:

## Parts of a circuit

Every circuit consists of three basic components:

A gun, a rocket and an internal combustion engine all use compressed gas to do work, but the spent gas is vented to the atmosphere and is not reused in the system, so these are not examples of pneumatic circuits. Refrigeration systems do, however, recycle the compressed gases they use, but are not typically thought of as circuits.

Gears, levers, linkages, pulleys/ropes and sprockets/chains transmit work energy from one location to another, but there is no loop, so these are not examples of circuits.

## Circuit vs. network

An electrical circuit is a collection of electrical components which accomplish a specific task such as heating, lighting or running a motor. This collection may or may not form a complete topological loop, depending on whether it is presently connected to power, integrated into a larger device or circuit, or damaged. Sometimes, it is convenient to speak of an electrical circuit as a network, de-emphasizing the return path. Return paths are sometimes omitted from circuit diagrams, making the resulting graphic visually resemble a network topology rather than some sort of loop topology. See circuit diagram and schematic.

## Open circuit vs. closed circuit

A fundamental part of circuit analysis is determining whether the matter has a return path to the power source. If the matter is blocked from returning to the power source, either wholly or partially, the entire assemblage will be prevented from accomplishing work. In an electrical circuit, an open circuit is caused intentionally when a user opens a switch or unintentionally when vibration or mechanical damage severs a wire. In a pneumatic or hydraulic circuit, this occurs when a valve is closed or there is a leak in one of the lines or components.

In electrical circuits, closing a switch creates a closed loop for the electrons to flow through. This is sometimes referred to as "completing the circuit."

## Short circuit

In an electrical or electronic circuit, sometimes an unintended connection is made, such as when insulation is broken, frayed, melted or chewed by rodents, or a technician inserts a metal tool into a live device. When this happens, current bypasses some or all of the components in the circuit, taking a "shorter" path back to the power source. This can lead to excessive current drain, which in turn generates excessive heat, damaging or destroying sensitive parts of the system such as transistors and ICs.

## Loops

In Graph theory, an edge whose two ends meet is called a loop, which is an entirely different usage of the word. In any kind of circuit, such a loop has no distinct function. An argument can be made that redundant lines for transmission of power do have a function, even if it is only a backup function.

## Types

There are three basic types of circuit currently used in industry:

The following is a rough list of the types of components which make up each type of circuit.

### Hydraulic circuit

Unified field theory

In physics, a unified field theory (occasionally referred to as a "uniform" field theory) is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a single field. There is no accepted unified field theory. It remains an open line of research. The term was coined by Einstein, who attempted to unify the general theory of relativity with electromagnetism, hoping to recover an approximation for quantum theory. A "theory of everything" is closely related to unified field theory, but differs by not requiring the basis of nature to be fields, and also attempts to explain all physical constants of nature.

This article describes unified field theory as it is currently understood in connection with quantum theory. Earlier attempts based on classical physics are described in the article on classical unified field theories.

There may be no a priori reason why the correct description of nature has to be a unified field theory; however, this goal has led to a great deal of progress in modern theoretical physics and continues to motivate research. Unified field theory is only one possible approach to unification of physics.

## Introduction

According to the current understanding of physics, forces between objects (e.g. gravitation) are not transmitted directly between the two objects, but instead go through intermediary entities called fields. All four of the known fundamental forces are mediated by fields, which in the Standard Model of particle physics result from exchange of bosons (integer-spin particles). Specifically the four interactions to be unified are (from strongest to weakest):

Modern unified field theory attempts to bring these four force-mediating fields together into a single framework. Quantum theory seems to limit any deterministic theory's descriptive power (in simple terms, no theory can predict events more accurately than allowed by the Planck constant).

## History

The first successful (classical) unified field theory was developed by James Clerk Maxwell. In 1820 Hans Christian Ã˜rsted discovered that electric currents exerted forces on magnets, while in 1831, Michael Faraday made the observation that time-varying magnetic fields could induce electric currents. Until then, electricity and magnetism had been thought of as unrelated phenomena. In 1864, Maxwell published his famous paper on a dynamical theory of the electromagnetic field. This was the first example of a theory that was able to encompass previous separate field theories (namely electricity and magnetism) to provide a unifying theory of electromagnetism. Later, in his theory of special relativity, Albert Einstein was able to explain the unity of electricity and magnetism as a consequence of the unification of space and time into an entity we now call spacetime.

In 1921 Theodor Kaluza extended General Relativity to five dimensions and in 1926 Oscar Klein proposed that the fourth spatial dimension be curled up (or compactified) into a small, unobserved circle. This was dubbed Kaluza-Klein theory. It was quickly noticed that this extra spatial direction gave rise to an additional force similar to electricity and magnetism. This was pursued as the basis for some of Albert Einstein's later unsuccessful attempts at a unified fi

Electrical network

An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current. Electrical networks that consist only of sources (voltage or current), linear lumped elements (resistors, capacitors, inductors), and linear distributed elements (transmission lines) can be analyzed by algebraic and transform methods to determine DC response, AC response, and transient response.

A network that contains activeelectronic components is known as an electronic circuit. Such networks are generally nonlinear and require more complex design and analysis tools.

## Design methods

To design any electrical circuit, either analog or digital, electrical engineers need to be able to predict the voltages and currents at all places within the circuit. Linear circuits, that is, circuits with the same input and output frequency, can be analyzed by hand using complex number theory. Other circuits can only be analyzed with specialized software programs or estimation techniques such as the piecewise-linear model.

Circuit simulation software, such as VHDL and HSPICE, allows engineers to design circuits without the time, cost and risk of error involved in building circuit prototypes.

## Electrical laws

A number of electrical laws apply to all electrical networks. These include:

• Kirchhoff's current law: The sum of all currents entering a node is equal to the sum of all currents leaving the node.
• Kirchhoff's voltage law: The directed sum of the electrical potential differences around a loop must be zero.
• Ohm's law: The voltage across a resistor is equal to the product of the resistance and the current flowing through it (at constant temperature).
• Norton's theorem: Any network of voltage and/or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
• ThÃ©venin's theorem: Any network of voltage and/or current sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.

Other more complex laws may be needed if the network contains nonlinear or reactive components. Non-linear self-regenerative heterodyning systems can be approximated. Applying these laws results in a set of simultaneous equations that can be solved either by hand or by a computer.

## Network simulation software

More complex circuits can be analyzed numerically with software such as SPICE or GNUCAP, or symbolically using software such as SapWin.

### Linearization around operating point

When faced with a new circuit, the software first tries to find a steady state solution, that is, one where all nodes conform to Kirchhoff's Current Law and the voltages across and through each element of the circuit conform to the voltage/current equations governing that element.

Once the steady state solution is found, the operating points of each element in the circuit are known. For a small signal analysis, every non-linear element can be linearized around its operation point to obtain the small-signal estimate of the voltages and currents. This is an application of Ohm's Law. The resulting linear circuit matrix can be solved with Gaussian elimination.

### Piecewise-linear approximation

Software such as the PLECS interface to Simulink uses piecewise-linear approximation of the equations governing the elements of a circuit. The circuit is treated as a completely linear network of ideal diodes. Every time a diode switches from on to off or vice versa, the configuration of the linear network changes. Adding more detail to the approximation of equations increases the accuracy of the simulation, but also increases its running time.