# Electrical element

An electrical component or circuit component or electrical element is a conceptual abstraction that ideally represents real elementary electrical devices such as resistors, capacitors, and inductors for the theoretical analysis of electrical circuits. Any electrical circuit can be represented and analyzed in the form of connections between multiple components; if the component also roughly corresponds to the actual physical device, the representation constitutes a concentrated parameter wiring diagram. In other cases, such as modeling transmission lines, the components represent infinitesimal elements (distributed parameter diagram).

Ideal components, while representing real devices, do not have a true physical equivalent since their properties are assumed to be ideal, while real components also have non-ideal aspects, tolerances to nominal value and certain degrees of non-linearity. For this reason, in order to model and approximate the operation of a real component taking into account its non-ideal aspects, it may be necessary to represent it by combining several different ideal components together. For example, an ideal inductor is characterized only by inductance and has neither resistance nor capacitance, but a real physical inductor, such as a coil, also has a resistance value, so its representation in an ideal component scheme is an ideal inductor connected in series to an ideal resistor in order to take into account the effects of both characteristics.

Circuit analysis based on ideal components is useful for understanding how real electrical circuits work in practice: by analyzing and combining the resulting effects generated by the ideal components, it is possible to estimate the actual real behavior.

Every electrical element has at least two terminals: an area of an electrical component that can receive the electric current or let it out. Simple electrical components, called also dipoles, have only one input terminal and one output terminal. A terminal is also used to make connections, which means connecting an electrical component to another electrical component. Examples of dipoles are batteries, bulbs, switches, and so on. Some complex electrical components can have multiple input terminals and multiple output terminals (such as transistors or operational amplifiers).

## Types and classification

Components can be classified in different categories; one of these is based on the number of terminals available for connection with other components and distinguishes between

• bipolar components, called bipoles are the simplest because they present for connection only two terminals that constitute the electrical port. Examples are resistors, capacitors, inductors and diodes
• multipolar components, called multipoles are connected to other devices through pairs of terminals and each pair constitutes an electrical port. For example, a three-winding transformer has six terminals and is ideally represented as a three-port element, each consisting of a pair of terminals. The most common elements of this type are two-port components, characterized by two pairs of terminals.

Components can also be subdivided into:

• active components or generators, capable of generating electrical power, such as voltage generators or current generators. Typically they are used to model batteries and power supplies. To this category belong the controlled generators in which the voltage or current generated is proportional to the voltage or current applied to another pair of terminals. They are used to model amplifiers such as transistors, thermionic valves and operational amplifiers;
• passive components that are not capable of generating their own power, such as resistors, capacitances and inductances.

A further classification is related to the relationship between electrical quantities and allows to distinguish between:

• linear components in which the relationship between voltage and current is a linear function and the principle of superposition of effects can be applied. Examples of linear components are resistors, capacitances, inductances and linear controlled generators. Circuits composed of only linear components, also called linear circuits, do not exhibit phenomena such as intermodulation and can be analyzed using powerful mathematical techniques such as the Laplace transform;
• non-linear components in which the relationship between voltage and current can be expressed through a non-linear function. An example is the diode, in which the current is an exponential function of the voltage. Circuits that include nonlinear components are more complex to analyze and design, and simulation software programs are often required.

All physical circuit components are actually nonlinear and can only be approximated by linear components up to a limited point. To represent passive components more correctly, a constitutive relation is used rather than the simpler proportional relations. Starting from any two quantities six constitutive relations can be defined and to complete the description this has led to theorize a fourth passive component, the memristor. This component is a non-linear time-variable element that under linear and time-invariant conditions is reduced to an ordinary resistor and for this reason it is not used in linear time-invariant circuit models.

## Application examples

These are some examples of how real physical devices can be represented by electrical components:

• A battery can be represented as a voltage generator. A more accurate model involves adding a series-connected resistor to represent the internal resistance of the battery (which is what causes it to heat up and drop in voltage during operation) and a current generator connected in parallel to represent the current loss, which over time causes the battery to run down.
• A resistor can be represented with a resistance. A more accurate model also involves a series-connected inductance that represents the inductance of the conductor, and a parallel capacitance that models the capacitive effects associated with the proximity of the terminals to each other.
• A wire can be represented as a low value resistor (possibly even with some inductance and capacitance).
• Current generators are often used to represent semiconductors: for example, to a first approximation a bipolar transistor can be represented as a variable current generator controlled by the input current.
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