- Network Theory - Home
- Network Theory - Overview
- Example Problems
- Network Theory - Active Elements
- Network Theory - Passive Elements
- Network Theory - Kirchhoff’s Laws
- Electrical Quantity Division Principles
- Network Theory - Nodal Analysis
- Network Theory - Mesh Analysis
- Network Theory - Equivalent Circuits
- Equivalent Circuits Example Problem
- Delta to Star Conversion
- Star to Delta Conversion
- Network Theory - Network Topology
- Network Topology Matrices
- Superposition Theorem
- Thevenin’s Theorem
- Network Theory - Norton’s Theorem
- Maximum Power Transfer Theorem
- Response of DC Circuits
- Response of AC Circuits
- Network Theory - Series Resonance
- Parallel Resonance
- Network Theory - Coupled Circuits
- Two-Port Networks
- Two-Port Parameter Conversions
- Network Theory - Filters
Network Theory Tutorial
Network Theory Tutorial
Network Theory, also referred to as Circuit Theory, is one of the fundamental subjects in electrical and electronics engineering discipline. Network theory provides basic definitions of electrical quantities, laws and methods for analyzing electric circuits. You can use this tutorial as your guide to learn the principles of network theory or circuit theory.
This tutorial covers topics such as the concepts of electric charge, current, voltage, EMF, Ohms law, Kirchhoffs laws, Nortons theorem, Thevenins theorem, nodal and mesh analysis, AC circuits, three-phase circuits, electric power, two-port network, and many more.
The knowledge of circuit theory is essential for designing, analyzing, and troubleshooting a variety of electric circuits and systems. This tutorial provides both theoretical and practical knowledge of electric circuits. This tutorial can be considered a very useful resource for students who want to understand the fundamental concepts required for studying electrical and electronics engineering.
Introduction to Circuit Theory
Circuit Theory is the most elementary subject in electrical and electronics engineering that deals with the design, analysis, and study of electric circuits and networks. It is also referred by some other names like Network Theory, Network Analysis, Circuit Analysis, Fundamentals of Electric Circuits, etc.
Circuit theory provides laws, principles, and methods required for synthesizing and analyzing electric circuits for a variety of applications like electrical machines, power electronics, power systems, communication systems, signal processing, etc.
What is a Network in Electrical?
In electrical engineering, a network is nothing but an interconnected arrangement of electrical components like resistors, inductors, capacitors, wires, batteries, etc.
If an electric network has a source of energy and a closed path for the flow of electric current is referred to as an electric circuit.
The following figure depicts a typical electrical network and a circuit −
What is Network Analysis?
Network Analysis or Circuit Analysis is a process of determining electrical excitation or response in an electric circuit.
In other words, network analysis is the process of determining the voltages across and the currents through, various components of an electric circuit.
In circuit theory, there are several laws and methods available for analyzing electric circuits such as Ohms law, KCL, KVL, Thevenins theorem, Nortons theorem, superposition theorem, and more.
Important Definitions in Network Theory
The following are some of the key definitions that play a vital role in network theory −
Circuit Component
An electric device having two or more terminals and allows the flow of electric current through, is referred to as a circuit component. It is also called as circuit element.
Node
In an electric circuit, a point where two or more components join each other is known as a node. The node with a ground potential is considered as a reference node in the circuit and it is used for circuit analysis purpose.
Junction
A node in an electric circuit where three or more components are joined together is called a junction.
Branch
The part of an electric circuit between two junction is referred to as a branch.
Loop and Mesh
A closed path of electrical components is called as a loop. A mesh is an elementary loop which does not contain any other loop inside it.
Port
The input and output terminals of an electrical circuit are termed as ports. For example, the two terminals of a battery are its output ports.
Transfer Function
Transfer function is a mathematical expression that represents a relationship between input and output of an electric circuit.
Component Transfer Function
For an electric circuit having two-terminals only, i.e., one-port component, the transfer function is calculated in the units of impedance or admittance, and it is referred to as component transfer function.
Equivalent Circuit
A reduced or simplified version of a complex electrical circuit or network that has the same input and output is known as an equivalent circuit. Two circuits are said to be equivalent to each other with respect to a pair of terminals if both circuits have the same relationship between voltage across the terminals and current through the terminals.
Resistive Circuit
An electric circuit which has only resistors as energy consumption components and current or voltage sources as energy delivering components is known as a resistive circuit.
Why Circuit Theory is Important?
Circuit theory is an important subject in the field of electrical and electronics engineering, because of the following key reasons −
- It provides laws, principles, methods for easily analyzing electric circuits.
- It allows engineers to design and synthesize circuits for devices and systems that we use in everyday life.
- It also provides analysis tools for electric circuits to make them more reliable and efficient.
- It builds the foundation for understanding complex concepts in electrical engineering like power systems, power electronics, analog electronics, electrical machines and drives, etc.
- It provides tools for troubleshooting and optimizing electrical systems.
Advantages and Disadvantages of Circuit Theory
Circuit theory provides a scientific framework to deal with a variety of electrical circuits and systems. However, it has both advantages and limitations, which are highlighted in the following table −
| Advantages of Circuit Theory | Disadvantages of Circuit Theory |
|---|---|
| Circuit theory provides a comprehensive knowledge about circuit laws, theorems, and principles. | Circuit theory mainly assumes that circuit components like R, L, C, etc. are lumped and linear. It has some limitations when dealing with distributed and non-linear elements. |
| Circuit theory provides various effective methods for reducing complex circuits into their simpler versions. | With non-linear circuits, circuit analysis theories become more complex and require additional methods. |
| Circuit theory has versatile applications, ranging from elementary physics to modern day power systems and robotics. | Circuit theory becomes ineffective where electromagnetic fields are dominating like in antenna design. |
| Circuit theory provides analysis techniques for both AC (Alternating Current) and DC (Direct Current) circuits. | Circuit theory has many concepts which are based on ideal assumptions and introduce imperfections in real-world applications. |
| Circuit theory also provides a number tools and techniques to design and synthesis of efficient electric circuits and systems. | Circuit theory sometimes becomes incapable in modelling some specific types of power losses and noise like dielectric losses, radiation losses, etc. |
Applications of Circuit Theory
Circuit Theory is the backbone of entire electrical and electronics engineering, and it has a wide range of applications. Some of the major applications of circuit theory in various fields are listed below −
- Power Systems − Circuit theory in power systems helps designing and implementing reliable and efficient electrical network for power transmission and distribution.
- Electronics − Circuit theory plays a vital role in analog and digital electronics, as it allows for designing efficient electronic circuits like amplifiers, rectifiers, clippers, filters, oscillators, etc.
- Signals and Systems − Circuit theory is also useful in signals and systems for analyzing and manipulating signals.
- Consumer Electronics − Circuit theory is used for designing circuits for electronic devices like computers, laptops, mobiles, TVs, etc. It is also used to analyze and troubleshoot these devices.
- Telecommunication Systems − Circuit theory helps developing circuits like amplifiers, transmitters, receivers, filters, etc. used in telecommunication systems.
These examples of circuit theory applications demonstrate its versatility in the field of electrical and electronics engineering.
What You Will Learn in Network Theory Tutorial?
This comprehensive tutorial on Network Theory covers a number of important topics required for developing foundation in electric circuits and mastering other advanced concepts in electrical and electronics engineering. A basic overview of each chapter covered in this tutorial is given in the following table −
| Chapter | Description |
|---|---|
| Network Theory Overview | This chapter introduces basic concepts in network theory like concept of circuit and network, basic electrical quantities, types of circuit elements, etc. |
| Active Elements in Network Theory | In this chapter, you will understand what active elements are in electric circuits? and you will also learn about independent and dependent sources. |
| Passive Elements in Network Theory | In this section, we will have a detailed discussion on three key passive elements in electric circuits namely, resistor, inductor, and capacitor. |
| Kirchhoffs Laws | This chapter explains two most fundamental laws in network theory known as KCL (Kirchhoffs Current Law) and KVL (Kirchhoffs Voltage Law). |
| Electrical Quantity Division Principles | In this chapter, you will learn about two principles of electric circuits namely, voltage division rule and current division rule. |
| Nodal Analysis | This section provides a detailed explanation on how to solve electric circuits using nodal analysis method. |
| Mesh Analysis | In this chapter, you will understand the procedure and application of mesh analysis method to solve electric circuits. |
| Equivalent Circuits | This chapter demonstrates the method for simplifying complex series and parallel circuits to their simplest form. |
| Delta to Star Conversion | This chapter explains the process of representing a delta network in its equivalent star network. |
| Star to Delta Conversion | This section demonstrates the conversion of a start network into its equivalent delta network. |
| Network Topology | In this chapter, you will learn about the concept of network topology (graph theory), basic terminology of graph theory, and different types of network graphs. |
| Network Topology Matrices | This chapter discusses the Network Topology Matrices which are useful for solving any electric circuit or network problem by using their equivalent graphs. |
| Superposition Theorem | In this chapter, you will find a detailed explanation on circuit solution using superposition theorem. |
| Thevenins Theorem | This chapter provides a step-by-step explanation on Thevenins theorem to solve circuits. |
| Nortons Theorem | This chapter explains circuit solution using Nortons theorem with the help solved examples. |
| Maximum Power Transfer Theorem | This chapter describes the statement of maximum power transfer theorem along with the condition for maximum power transfer and efficiency at maximum power transfer. |
| Response of DC Circuits | In this chapter, you will understand the transient and steady state response of DC circuits and will learn to find the response of series RL circuit. |
| Response of AC Circuits | This chapter describes the process of finding the AC response of series RL circuit. |
| Series Resonance | This chapter defines resonance and provides a study of series resonant circuit. |
| Parallel Resonance | In this chapter, you will study the circuit diagram and electrical quantities in a parallel resonant circuit. |
| Coupled Circuits | This section provides an overview of coupled circuits and types of couplings in electric circuits. |
| Two Port Networks | This chapter describes two-port networks and different types of two-port network parameters. |
| Two-Port Parameter Conversions | In this chapter, you will study the procedure to convert two-port network parameters. |
| Filters | This section provides a description of different types of filters in electric circuits. |
FAQs on Network Theory
In this section, we have collected some of the most Frequently Asked Questions (FAQs) on Network Theory followed by their answers.
In electrical engineering, network theory is a core subject that deals with the study of electric circuits using mathematical principles to determine their behavior. It helps analyzing electric circuits containing resistors, capacitors, inductors, and energy sources.
Superposition theorem is the fundamental theorem used for analyzing electric circuits containing multiple independent sources. In this theorem, the response of the circuit for each independent source is determined separately, and the final response of the circuit is determined by adding response of each source.
Kirchhoff stated two fundamental laws for circuit analysis known as Kirchhoffs Current Law (KCL) and Kirchhoffs Voltage Law (KVL). KCL provides a way for calculating total currents entering and leaving a node in the circuit, whereas KVL states the method for finding total voltage around a closed path.
The primary difference between nodal and mesh analysis is that nodal analysis is based on KCL (Kirchhoffs Current Law) and the mesh analysis is KVL (Kirchhoffs Voltage Law).
Both Thevenins and Nortons Theorems help reducing complex linear electric networks into their simplest form for analysis. Where, Thevenins theorem reduces a complex circuit to an equivalent simplified circuit containing a voltage source and a resistor in series with it. On the other hand, Nortons theorem reduces a complex circuit to equivalent simplified circuit containing a current source and a resistor in parallel with it.
In a series circuit, if there are N numbers of resistors connected, then the total resistance of the series circuit is calculated by using the following relation −
$$\mathrm{R_t = R_1 + R_2 + R_3 + \dots + R_N}$$
Similarly, in a parallel circuit consisting of N numbers of resistors, the total resistance is calculated by using the following expression −
$$\mathrm{\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_N}}$$
There is a special case in parallel circuits, when there are only two resistors connected in parallel, then the total resistance is calculated as follows −
$$\mathrm{R_t = \frac{R_1 R_2}{R_1 + R_2}}$$
In an RLC circuit, resonance is a condition that occurs at a specific frequency, called resonance frequency, where the inductive reactance becomes equal and opposite to the capacitive reactance and hence cancelling the effect of each other. Under resonance condition, the RLC circuit behave as a purely resistive circuit.
Laplace Transform (LT) is a mathematical technique used in electric circuit analysis for converting time-domain differential equations into simple algebraic equations in the s-domain. It is mainly used for analyzing transient behavior of circuits containing capacitors and inductors.
Capacitors and inductors in AC and DC circuits behave as follows −
- In DC circuits, capacitors block the direct current after charging, while inductors allow the flow of direct current.
- In AC circuits, capacitors allow the flow of alternating current, while inductors try to block the changes in alternating current.
Sometimes while working with electrical circuits, we find connections which are not in series or parallel. Instead, they are connected in either delta (Δ) or star (Y) configurations.
For simplifying the analysis of circuits containing delta (Δ) and star (Y) connections, we need to interchange either delta to star or star to delta. These methods are referred to as delta-star transformation and star-delta transformation.