Table of contents | |
Basic Terminology | |
1. Electric Circuit | |
2. Electric Network | |
3. Current | |
4. Voltage | |
5. Power | |
Types of Network Elements | |
Examples |
Network theory is the study of solving the problems of electric circuits or electric networks. In this introductory EduRev document, let us first discuss the basic terminology of electric circuits and the types of network elements.
In Network Theory, we will frequently come across the following terms:
So, it is imperative that we gather some basic knowledge on these terms before proceeding further. Let’s start with Electric Circuit.
An electric circuit contains a closed path for providing a flow of electrons from a voltage source or current source. The elements present in an electric circuit will be in series connection, parallel connection, or in any combination of series and parallel connections.
An electric network need not contain a closed path for providing a flow of electrons from a voltage source or current source. Hence, we can conclude that "all electric circuits are electric networks" but the converse need not be true.
The current "I" flowing through a conductor is nothing but the time rate of flow of charge. Mathematically, it can be written as
I = dQ/dt
Where,
As an analogy, electric current can be thought of as the flow of water through a pipe. Current is measured in terms of Ampere.
In general, Electron current flows from negative terminal of source to positive terminal, whereas, Conventional current flows from positive terminal of source to negative terminal.
Electron current is obtained due to the movement of free electrons, whereas, Conventional current is obtained due to the movement of free positive charges. Both of these are called as electric current.
The voltage "V" is nothing but an electromotive force that causes the charge (electrons) to flow. Mathematically, it can be written as
V = dW/dQ
Where,
As an analogy, Voltage can be thought of as the pressure of water that causes the water to flow through a pipe. It is measured in terms of Volt.
The power "P" is nothing but the time rate of flow of electrical energy. Mathematically, it can be written as
P = dW/dt
Where,
We can re-write the above equation as
Therefore, power is nothing but the product of voltage V and current I. Its unit is Watt.
We can classify the Network elements into various types based on some parameters. Following are the types of Network elements:
Elements We can classify the Network elements into either active or passive based on the ability of delivering power.
Examples: Voltage sources and current sources.
Examples: Resistors, Inductors, and capacitors.
We can classify the network elements as linear or non-linear based on their characteristic to obey the property of linearity.
Examples: Resistors, Inductors, and capacitors.
Examples: Voltage sources and current sources.
Network elements can also be classified as either bilateral or unilateral based on the direction of current flows through the network elements.
(a) Bilateral Elements are the elements that allow the current in both directions and offer the same impedance in either direction of current flow. Examples: Resistors, Inductors and capacitors.
The concept of Bilateral elements is illustrated in the following figures.
In the above figure, the current (I) is flowing from terminals A to B through a passive element having impedance of Z Ω. It is the ratio of voltage (V) across that element between terminals A & B and current (I).
In the above figure, the current (I) is flowing from terminals B to A through a passive element having impedance of Z Ω. That means the current (–I) is flowing from terminals A to B. In this case too, we will get the same impedance value, since both the current and voltage having negative signs with respect to terminals A & B.
(b) Unilateral Elements are those that allow the current in only one direction. Hence, they offer different impedances in both directions.
We discussed the types of network elements in the previous chapter. Now, let us identify the nature of network elements from the V-I characteristics given in the following examples.
Step 1 − Verifying the network element as linear or non-linear.
From the above figure, the V-I characteristics of a network element is a straight line passing through the origin. Hence, it is a Linear element.
Step 2 − Verifying the network element as active or passive.
The given V-I characteristics of a network element lies in the first and third quadrants.
Since, the given V-I characteristics offer positive impedance values, the network element is a Passive element.
Step 3 − Verifying the network element as bilateral or unilateral.
For every point (I, V) on the characteristics, there exists a corresponding point (-I, -V) on the given characteristics. Hence, the network element is a Bilateral element.
Therefore, the given V-I characteristics show that the network element is a Linear, Passive, and Bilateral element.
The V-I characteristics of a network element is shown below.
Step 1 − Verifying the network element as linear or non-linear.
From the above figure, the V-I characteristics of a network element is a straight line only between the points (-3A, -3V) and (5A, 5V). Beyond these points, the V-I characteristics are not following the linear relation. Hence, it is a Non-linear element.
Step 2 − Verifying the network element as active or passive.
The given V-I characteristics of a network element lies in the first and third quadrants. In these two quadrants, the ratios of voltage (V) and current (I) produce positive impedance values. Hence, the network element is a Passive element.
Step 3 − Verifying the network element as bilateral or unilateral.
Consider the point (5A, 5V) on the characteristics. The corresponding point (-5A, -3V) exists on the given characteristics instead of (-5A, -5V). Hence, the network element is a Unilateral element.
Therefore, the given V-I characteristics show that the network element is a Non-linear, Passive, and Unilateral element.
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1. What is network theory in electrical engineering? |
2. What are the types of network elements in network theory? |
3. How does network theory benefit electrical engineering? |
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