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Introduction of Electric Circuit 1

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Objectives • • • • • • • • • Familiarity with and understanding of the basic elements encountered in electric networks. To learn the fundamental differences between linear and nonlinear circuits. To understand the Kirchhoff’s voltage and current laws and their applications to circuits. Meaning of circuit ground and the voltages referenced to ground. Understanding the basic principles of voltage dividers and current dividers. Potentiometer and loading effects. To understand the fundamental differences between ideal and practical voltage and current sources and their mathematical models to represent these source models in electric circuits. Distinguish between independent and dependent sources those encountered in electric circuits. Meaning of delivering and absorbing power by the source. L.3.1 Introduction The interconnection of various electric elements in a prescribed manner comprises as an electric circuit in order to perform a desired function. The electric elements include controlled and uncontrolled source of energy, resistors, capacitors, inductors, etc. Analysis of electric circuits refers to computations required to determine the unknown quantities such as voltage, current and power associated with one or more elements in the circuit. To contribute to the solution of engineering problems one must acquire the basic knowledge of electric circuit analysis and laws. Many other systems, like mechanical, hydraulic, thermal, magnetic and power system are easy to analyze and model by a circuit. To learn how to analyze the models of these systems, first one needs to learn the techniques of circuit analysis. We shall discuss briefly some of the basic circuit elements and the laws that will help us to develop the background of subject. L-3.1.1 Basic Elements & Introductory Concepts Electrical Network: A combination of various electric elements (Resistor, Inductor, Capacitor, Voltage source, Current source) connected in any manner what so ever is called an electrical network. We may classify circuit elements in two categories, passive and active elements. Passive Element: The element which receives energy (or absorbs energy) and then either converts it into heat (R) or stored it in an electric (C) or magnetic (L ) field is called passive element. Active Element: The elements that supply energy to the circuit is called active element. Examples of active elements include voltage and current sources, generators, and electronic devices that require power supplies. A transistor is an active circuit element, meaning that it can amplify power of a signal. On the other hand, transformer is not an active element because it does not amplify the power level and power remains same both 2

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in primary and secondary sides. Transformer is an example of passive element. Bilateral Element: Conduction of current in both directions in an element (example: Resistance; Inductance; Capacitance) with same magnitude is termed as bilateral element. Unilateral Element: Conduction of current in one direction is termed as unilateral (example: Diode, Transistor) element. Meaning of Response: An application of input signal to the system will produce an output signal, the behavior of output signal with time is known as the response of the system. L-3.2 Linear and Nonlinear Circuits Linear Circuit: Roughly speaking, a linear circuit is one whose parameters do not change with voltage or current. More specifically, a linear system is one that satisfies (i) homogeneity property [response of α u (t ) equals α times the response of u (t ) , S (α u (t )) = α S (u (t )) for all α ; and u (t ) ] (ii) additive property [that is the response of system due to an input ( α1 u1 (t ) + α 2 u2 (t ) ) equals the sum of the response of input α1 u1 (t ) and the response of input α 2 u2 (t ) , S (α1 u1 (t ) + α 2 u2 (t)) = α1 S (u1 (t )) + α 2 S (u2 (t )) .] When an input u1 (t ) or u2 (t ) is applied to a system “ S ”, the corresponding output response of the system is observed as S (u1 (t )) = y1 (t ) or S (u2 (t )) = y2 (t ) respectively. Fig. 3.1 explains the meaning of homogeneity and additive properties of a system. 3

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Non-Linear Circuit: Roughly speaking, a non-linear system is that whose parameters change with voltage or current. More specifically, non-linear circuit does not obey the homogeneity and additive properties. Volt-ampere characteristics of linear and non-linear elements are shown in figs. 3.2 - 3.3. In fact, a circuit is linear if and only if its input and output can be related by a straight line passing through the origin as shown in fig.3.2. Otherwise, it is a nonlinear system. Potential Energy Difference: The voltage or potential energy difference between two points in an electric circuit is the amount of energy required to move a unit charge between the two points. 4

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