Circuit Theory Tutorial

Circuit Theory, also known as Network Theory, is a fundamental subject in electrical engineering and related engineering domains. Circuit theory provides knowledge and tools to design, analyze, and understand electric circuits and their behavior. This subject builds the foundational understanding required to study how electricity is produced, transmitted, and consumed through an interconnected electrical network. It provides theoretical explanation of various electrical components like resistor, inductor, capacitor, energy sources, etc.

In general, circuit theory has two main parts namely, Circuit Analysis and Circuit Synthesis.

• Circuit Analysis − This part of circuit theory involves the study of finding either response or excitation where the circuit is already given. Thus, in circuit analysis part, the circuit is known and we need to determine either response or excitation.
• Circuit Synthesis − This part provides the study of designing electrical circuit for a given set of excitation and response. Thus, in synthesis part, we need to determine the circuit for a set of known excitation and response.

This tutorial is primarily focused on circuit analysis part. Hence, in this tutorial, we will learn about mathematical tools, physical laws, and various analysis techniques that we can use to determine or estimate the behavior or performance of an electric circuit.

What is a Circuit?

A Circuit or Electric Circuit is a closed loop/path consisting of various electrical components such as wires, resistors, inductors, capacitors, lights, and more, providing a continuous path for the flow of electric current.

A typical electric circuit consists of two main types of electrical components as given below −

• Active Elements − Those electrical components that can supply electrical energy to the circuit are called active elements. These components are also known as source elements. Examples include voltage sources, current sources, batteries, generators, etc.
• Passive Elements − Those components that only consume electrical energy in the circuit and do not produce are known as passive elements. These circuit elements are also called as load components. Examples of passive elements include resistors, inductors, capacitors, transformers, lamps, etc.

Hence, from this discussion, we can state that an electric circuit has following three important characteristics −

• It must contain an active element.
• It must contain a passive element.
• It must have a closed path.

What is Circuit Theory?

Circuit Theory or Network Theory can be defined as a branch of electrical engineering that deals with the study of design and analysis of electrical circuits. Circuit theory provides a set of tools such as electrical laws, principles, and techniques to design circuits or determine excitation and response of circuits.

Hence, we can simply state that circuit theory is a tool which helps electrical and electronics engineers to answers the questions like given below −

• How much current flowing through the load?
• How much electric power is consumed by a device?
• How much voltage drops across a circuit component? Etc.

Why Circuit Theory is Important?

In the field of electrical and electronics engineering, circuit theory serves as a foundational subject and provides laws, principles, and techniques essential for designing, analyzing, and optimizing electrical circuits and systems.

Some of the key reasons highlighting the significance and importance of circuit theory are listed below −

• Circuit theory builds the foundational understanding for electrical engineering and similar domains.
• Circuit theory provides a large set of mathematical models and techniques to design and analyze electrical circuits and determine their behavior.
• It also explains how electronic components to be interconnected and how they interact with each other.
• In power system engineering, circuit theory allows to design, analyze, and optimize transmission and distribution lines for efficient power transportation.
• Circuit theory also allows engineers to understand energy flow, power consumption, energy storage, power dissipation, etc. in electrical systems.
• Various engineering software like MATLAB, PSpice, etc. used for designing practical systems are based on the principles of circuit theory.

Applications of Circuit Theory

Circuit theory plays a vital role in all fields of electrical and electronics engineering. Some major examples of applications of circuit theory are listed below −

• Circuit theory is widely used in power system engineering to determine voltage, current, and power in transmission and distribution networks.
• In analog and digital circuits, circuit theory is used to design and analyze electronic circuits such as amplifiers, oscillators, modulators, logic circuits, signal processors, and more.
• Circuit theory serves as a backbone of control system and instrumentation, as it allows for measuring and controlling physical quantities.
• Circuit theory is also used in renewable energy and smart grid systems to analyze system's operation and performance.

Important Circuit Theory Terminology

This section defines some of the key terms related to circuit theory or network theory. These terms will be very helpful in studying this circuit theory tutorial.

Node

In an electric circuit, node is a point where two or more circuit elements join each other.

Junction

A junction is nothing but a node where three or more branches connect together.

Branch

In an electric circuit, a path between two nodes containing circuit elements is known as a branch.

Loop

Any closed path in an electric circuit is known as a loop.

Mesh

The most elementary loop which does not enclose any other loop is called a mesh.

Ohm's Law

Ohm's law is a fundamental circuit law which provides relationship between voltage across and current through a conductor. According to Ohm's law,

$$\mathrm{V \propto I}$$

Kirchhoff's Current Law (KCL)

KCL is a basic circuit analysis tool which states that the algebraic sum of electric currents entering a node in an electric circuit equals to the algebraic sum of electric currents leaving the node.

$$\mathrm{\displaystyle\sum I_{in} = \displaystyle\sum I_{out}}$$

Kirchhoff's Voltage Law (KVL)

KVL is also a circuit analysis tool which is applied to a closed loop in a circuit. This law states that the algebraic sum of voltages, i.e. voltage drops and voltage rises, around the loop is zero.

$$\mathrm{\sum V_{drops} + V_{rises} = 0}$$

Series Connection

In electric circuits, when circuit elements are arranged in a manner where the same electric current flows through each one, then this is called series connection.

Parallel Connection

When circuit elements in an electric circuit are connected in a way that there will be the same voltage across them, it is known as parallel connection.

Impedance

Impedance can be defined as the combined opposition offered by resistive and reactive components in the flow of alternating current (AC).

Transient Response

The response that an electric circuit shows when initial condition or switching causes it to change from one state to another before achieving the steady state.

Steady State Response

The stable response that the circuit shows after complete elimination of all transients is called steady-state response of the circuit.

Open Circuit

When there is a break or gap in a part of a circuit which interrupts the flow of electric current and offers an infinite resistance is called an open circuit. An open circuit results in no current flow through it.

Short Circuit

An unwanted path of very low resistance that bypasses the intended circuit elements is called as a short circuit. A short circuit results in excessive current to flow through it.

Who Should Learn Circuit Theory?

As Circuit Theory is a foundational subject in the field of electrical and electronics engineering and acts as a foundation for understanding simple electronic devices to complex power system networks. Hence, circuit theory has a wide range of audience.

This tutorial on circuit theory is designed in a manner that it can be used by any of the following –

• Electrical engineering students and working professionals
• Electronics and communication engineering students and professionals
• Instrumentation engineering students and professionals
• Technicians working in electrical maintenance departments
• Higher study students
• Aspirants preparing for technical exams and interviews like GATE, ESE, PSUs, technical job interviews, etc.

Prerequisites to Learn Circuit Theory

In engineering domains, circuit theory is the point of beginning. But it requires a prior knowledge of fundamental concepts of mathematics, physics, and chemistry along with logical reasoning skills. These prerequisites are important to ensure smooth understanding of concepts like mathematical models, equations, etc. explained here.

What You Will Learn in This Circuit Theory Tutorial?

This circuit theory tutorial is designed in an absolute beginner friendly style and all topics are organized in a chronological order. The topics covered in the tutorial and overview is provided in the following table −

FAQs on Circuit Theory

In this section, we have collected some of the most Frequently Asked Questions (FAQs) on Circuit Theory followed by their brief answers −

1. What is Circuit Theory in Electrical Engineering?

Circuit theory is a foundational course in electrical engineering and it deals with the study of designing and analyzing circuits to determine excitation or response. It uses various tools such as Ohm's law, KCL, KVL, nodal and mesh analysis, and various theorems.

2. What is the difference between Circuit Theory and Network Theory?

Circuit theory and network theory seems different at first sight, but they are synonyms for each other.

3. Why is Circuit Theory important for engineering students?

Circuit theory is important for engineering students, especially from electrical and electronic domain. It plays a key role in developing foundational understanding about circuit components, their interconnection and behavior.

4. What are the basic laws used in Circuit Theory and Network Theory?

The following three basic laws are most widely used in circuit theory or network theory −

• Ohm's Law − It provides relationship between voltage across and current through a circuit element.
• Kirchhoff's Current Law − KCL states that sum of currents entering a node equals to sum of currents leaving the node.
• Kirchhoff's Voltage Law − KVL states that algebraic sum of voltage drops and rises in a loop is equal to zero.

5. What are the main types of electrical networks?

Depending upon the basis of classification, electrical networks can be of various types. A typical classification of electrical network is given below −

• Active and passive networks
• Unilateral and bilateral networks
• Linear and non-linear networks
• Lumped and distributed networks

6. What are the main methods of circuit and network analysis?

The following are main methods widely used for circuit and network analysis −

• Nodal analysis
• Mesh analysis
• Source transformation
• Network theorems (Thevenin's theorem, Norton's theorem, superposition theorem, maximum power transfer theorem)

7. What is a two-port network in Network Theory?

A two port network is an electrical network having a pair of two terminals, where current enters through one terminal and leaves through another terminal.

8. What is Ohm's Law and its formula?

Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it, provided the physical conditions remain constant.

$$\mathrm{V \propto I}$$

$$\mathrm{V = R I}$$

Where, R is the resistance of the conductor.

9. What is the condition for maximum power transfer in a circuit?

In an electric circuit if the internal resistance of the circuit seen from the load terminals becomes equal to the load resistance, then maximum power will be delivered to the load from the source. Hence, the condition for maximum power transfer in a circuit is,

$$\mathrm{R_{internal} = R_{load}}$$

10. What is the difference between a loop and a mesh in circuit analysis?

In circuit analysis, loop is a closed path containing one or more circuit elements, while a mesh is a smallest loop that does not enclose any other loop within it.