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Can anyone explain me the meaning of lumped element and lumped circuit abstraction in detail. What does lumping or discretizing matter mean?

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Two theories (really one!)

There are basically two ways of looking at an electrical circuit: electromagnetic theory (Maxwell's equations) and the theory of lumped elements.

In fact the theory of lumped parameter circuits, is a simplification of electromagnetic theory, since the latter involves a hard mathematical work for analysis or design of an electrical circuit.

The simplifications.

In the lumped parameter theory, it is assumed that all conductors interconnecting the circuit components are ideal (zero resistance). Another simplification is that all actions of magnetic induction, can be represented by an ideal element, called Inductor. By element called resistor, all energy exchanges that occur irreversibly are represented. Finally, the element called capacitor, represents interactions where electric energy is stored as potential energy.

Ideal components

Obviously, the ideal components do not exist, but while taking into account the condition of the working frequency; a coil, for example, can be modeled with good approximation by an inductor. As the operating frequency increases, the capacitive effect on the coil, due to proximity of the conductors from each other, are made much more noticeable. This capacity is not a capacitor connected to the coil (as concentrated element) but it is distributed on the coil.

When I can apply the theory of lumped parameter?

This theory represents a very good approximation when the physical dimensions of the circuit are much smaller than the shortest wavelength is expected to process. That is, when the higher frequency (shorter wavelength), this theory begins to fail, if the circuit dimensions are comparable with the wavelength. In this case, use the electromagnetic theory.
When the physical size of the circuit, is comparable with the wavelength effects start appearing, such as induced currents, to the full extent of the circuit, and also vary with the distances of the conductors that connect the components. In this case, it can not be considered to all effects of magnetic induction can be represented by a single component (i.e., an inductor), but the inductor, is distributed throughout the circuit. A similar analysis can be plotted for the case of a capacitor.

Summary.

Concentrated Parameters Theory, is a simplification of electromagnetic theory, which applies when the physical dimensions of the circuit are much smaller than the shortest wavelength of work. Three ideal elements are defined to represent the exchange of energy between the electromagnetic field and the medium: resistor, inductor and capacitor. These elements are considered physically implemented by an object (lumped!) And are connected by ideal conductors.

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