Circuito RC y Leyes de Kirchhoff

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Universidad del Atlántico

 Circuito RC y Leyes de Kirchhoff

Presentado por: Andres Felipe Pertuz

Docente: Oscar Martínez

INGENIERA INDUSTRIAL

An electrical circuit is the set of electrical elements connected to each other to generate, transport and use electrical energy. Electrical circuits are part of everyday life, street lighting, connecting our homes, appliances, etc. All this reflects their importance in the daily development of society. RC circuits are very important in the development of the modern world, because their use leads to the introduction of technologies of high relevance, such as the design of networks, electrical and electronic wiring, adapted to specific needs.

During the development of this text we will also talk about Kirchhoff’s laws which, like Ohm’s law are another of the fundamental rules for electronics. These laws allow you to analyze the voltage and current in a node, something essential to know aspects of the circuits. It also describes the behavior of the current in a node and the voltage around a mesh.

RC circuit

A RC circuit (resistor-capacitor) is a type of circuit that, as its name indicates, is formed by resistors and capacitors that can be connected in different topologies: seriously or in parallel.

The operation of these circuits is also thanks to the inclusion in them of elements such as capacitors that, depending on their location in the circuit and design, perform a specific function, such as allowing the passage of current for a period of time, either in all or a part of the system analyzed, reason why circuits like these are used in various applications, where time becomes a fundamental factor to allow or not the passage of the current.

To understand how it affects the incursion of these devices, one must start from the laws of Kirchhoff. They say that in any union the sum of the currents must be equal to zero and the sum of the potential differences across all the elements around any spiral of a closed loop must be equal to zero.[pic 2]

Taking into account the above and by means of the statement of differential equations, it is theoretically obtained that the charge in the capacitor and the current through the circuit, in the process of charge of the capacitor, are represented by the following equations:

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Where it clears and leaves us:

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Obtaining at the end: [pic 5]

By the above considerations, deriving the above equation you have to:[pic 6]

[pic 7]

Under the same loading procedure, you have to:

[pic 8]

Where I(t) is the current at a time t through the circuit, q(t) the capacitor charge, Q the maximum charge of the capacitor and e the potential difference of the source.

Kirchhoff Laws

In 1846 the engineer Gustav Kirchhoff presented a couple of laws on which the conservation of energy and the charging of electrical circuits was based, these laws were called Kirchhoff Laws in honor of their creator. They are the basis and fundamental part for the study of electricity and electronics. These allow determine the tensions and currents in any part of an electrical circuit.

Kirchhoff Current Law (KCL)

Since the load entering a node must exit, and no load is destroyed on the nodes, the net load entering a node is equal to the load leaving the node. From the above can be deduced the following laws for current.

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