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Mayurbhanj School Of Engineering, Baripada

Branch : Electrical Engineering�Semester : 3^rd

Subject : Circuit & Network Theory

Chapter : 03

Topic : Circuit Elements & Analysis

Faculty : Dr. Mrutyunjay Das

Contents

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• Different types of electrical elements
• Source Transformation Technique
• Mesh Analysis
• Super Mesh Analysis
• Nodal Analysis
• Super Node Analysis

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Types of electrical elements

• Passive Element: 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.

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• Active Element: The elements that supply energy to the circuit is called active element.

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Types of electrical elements

• Bilateral Element: Conduction of current in both directions in an element with same magnitude.

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• Unilateral Element: Conduction of current in one direction is termed as unilateral (example: Diode, Transistor) element.

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Terms Related to Electrical Circuits

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• Linear Circuit: Linear circuit is one whose parameters do not change with voltage or current i.e. which obeys Ohm’s law.

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• Non-Linear Circuit: Non-linear system is that whose parameters change with voltage or current.

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Terms Related to Electrical Circuits

• Node- A node in an electric circuit is a point where two or more components are connected together.

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• Branch- A branch is a conducting path between two nodes in a circuit containing the electric elements.

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Terms Related to Electrical Circuits

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• Loop- It is a closed path in an electric circuit i.e., a closed path or loop in a circuit is a continuous sequence of branches with starting and end points for tracing the path are, in effect, the same node and touches no other node more than once.

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• Mesh- A mesh is a special case of loop that does not have any other loops within it or in its interior.

Kirchhoff’s Current Law (KCL)

• At any node (junction) in a circuit, the algebraic sum of currents entering and leaving a node at any instant of time must be equal to zero.

Currents entering and currents leaving the node must be assigned opposite algebraic signs.

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Kirchhoff’s Voltage Law (KVL)

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• The algebraic sum of all source voltages must be equal to the algebraic sum of all the voltage drops.

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• For loop 1:

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• For loop 2:

Ideal and Practical Voltage Sources

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• An ideal voltage source is a device that produces a constant voltage across its terminals (V = E) no matter what current is drawn from it.

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• The practical voltage source is characterized by two parameters namely known as (i) Open circuit voltage (ii) Internal resistance in the source’s circuit model.

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Ideal and Practical Current Sources

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• An ideal current source is a device that delivers a constant current to any load resistance connected across it, no matter what the terminal voltage is developed across the load.

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• In practical current source the internal resistance of the source is represented by a resistance connected to current source in parallel.

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Conversion of Voltage Source to Current Source

• Series resistance in voltage source is connected in parallel with current source.

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Conversion of Current source to Voltage Source

• Parallel resistance in current source is connected in series with voltage source.

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Independent Sources

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• Independent Sources are the sources, whose output value does not depend upon the circuit parameters like voltage and current.

Dependent Sources

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• Dependent Sources are the sources whose output value depends upon the voltage or current at some other part of the circuit.

Mesh Analysis

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• It is used to find the current through any branch and voltage

across any branch by using Kirchoff’s voltage law.

Loop – 1:

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Loop – 2:

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Loop – 3:

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Super mesh Analysis

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• A supermesh forms when two meshes have a common current source dependent or independent).

Steps:

• Identify the total number

of meshes.

• Assign the mesh currents and

Check for supermesh in the

circuit.

• Develop the KVL equation for

the supermesh.

• Solve the equations to find the

mesh currents.

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Nodal Analysis

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In Nodal analysis, KCL is used at nodes at different nodes.

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Steps:

• Convert all voltage sources to current sources.
• Indicate one node as a reference node. This reference node is used as the common point in the network from which the node voltages are measured.
• At each node, except the reference node, apply the Kirchhoff’s current law (KCL)

Solve the set of simultaneous linear equations for the node voltages.

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Nodal Analysis

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Example:

KCL at Node 1:

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KCL at Node 2:

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Super node Analysis

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In two cases nodal analysis can be done with voltage sources.

Case 1: If the voltage source (dependent or independent) is connected between two non-reference nodes, the two non-reference nodes form a generalized node or supernode, we apply both KCL and KVL to determine the node voltages.

Case 2: if a voltage source is connected between the reference node and a non-reference node, we simply set the voltage at the non-reference node equal to the voltage of the voltage source.

• At supernode:

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Thank you

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