Network Theory Introduction and Terminology

Electrical Network

Any arrangement of electrical  sources, resistances and other circuit elements is called an electrical network. The term network is also called circuit in electrical literature.

Example of an electrical circuit is shown below in Fig.1

Fig.1

Network Terminology

In network theory, while discussing network theorems and techniques, we often comes across the following terms :

(1) Active Element :

An active element provides or supplies electrical energy to the electrical circuit. For example: Voltage sources, current sources.

In Fig.1, E1 and E2 are the active elements as they supply energy to the circuit.

(2) Passive Element :

A passive element is one which receives electrical energy and then either converts it into heat (resistance) or stores it in an electric field (capacitance) or magnetic field (inductance). For example : Resistors, capacitors, inductors. They can not deliver energy to other electrical elements.

In Fig.1 there are three passive elements, R1, R2 and R3. These passive elements(i.e. resistances) receives energy from the active elements (i.e. E1 and E2) and converts it into heat.

Mostly resistive elements are used in DC networks, whereas AC networks are usually connected with resistive, inductive as well as capacitive elements.

(3) Node

A node of a network is an equipotential surface at which two or more circuit elements are joined.

In Fig.1, circuit elements R1 and E1 are joined at A and hence A is a node. Similarly B, C and D are also nodes.

Node A – Source E1 and Resistor R1 are joined together

Node B – Resistor R1, R2 and R3 are joined together

Node C – Source E2 and Resistor R3 are joined together

Node D – Source E1, E2 and Resistor R2 are joined together

(4) Junction

A junction is that point in a network where three or more circuit elements are joined.

In Fig.1, there are only two junction points B and D.

At junction B, three circuit elements R1, R2 and R3 are joined.

Similarly at D, three circuit elements R2, E1 and E2 are joined.

(5) Branch

A branch is that part of a network which lies between two junction points.

In Fig.1, there are three branches in total. They are, BAD, BCD and BD.

branch BAD consists of R1 and E1

Branch BCD consists of R3 and E2

Branch BD consists of only R2

(6) Loop

A loop is any closed path of a network.

Thus, in Fig.1, ABDA, BCDB and ABCDA are the loops.

(7) Mesh

A mesh is the most elementary form of a loop and can not be further divided into other loops.

In Fig.1, both loops ABDA and BCDB qualify as meshes because they can not be further divided into other loops.

However, the loop ABCDA can not be called a mesh as it encloses two loops ABDA and BCDB.