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How to Find the Number of Nodes, Branches, Loops and Meshes in a Circuit?

What is Node, Branch, Loop & Mesh in Electric Circuit?

Solving and analyzing electrical circuits and networks, we must know about Nodes, Branches, Loops, and Meshes in an electric circuit and network. First, we have to know about Node, Branch, Loop and Mesh and their role in an electrical circuit. We may determine the exact number of branches, nodes, loops, and meshes then.

For this purpose, will find all these terms one by one with the following simple steps.

Consider the following simple electric circuit in fig 1 which contains on 7 components or elements.

What are Nodes, Branches, Loops & Mesh in Electric Circuits?
Fig 1: What are Nodes, Branches, Loops & Mesh in Electric Circuits?

Node

A point or junction where two or more circuit’s elements (resistor, capacitor, inductor etc) meet is called Node. In other words, a point of connection between two or more branches is known as a Node.

Finding Nodes in Electric Circuits

After redrawing the above circuit, it becomes as below equivalent circuit. Now you can easily find the total number of Nodes as shown in fig 2 below which has 6 Nodes.

Finding Nodes in Electric Circuits
Fig 2: Finding Nodes in Electric Circuits

Branch

That part or section of a circuit which locate between two junctions is called the branch. In a branch, one or more elements can be connected and they have two terminals. It may any two terminals single component such as a voltage source, current source, resistor etc.

Finding Branches in Electric Circuits

The circuit in Figure 3 has seven branches, namely, a “V” voltage source and the sex resistors.

Finding Branches in Electric Circuits
Fig 3: Finding Branches in Electric Circuits

Loop

A closed path in a circuit where more than two meshes can occur is known as Loop i.e. there may be many meshes in a loop, but a mesh does not contain on one loop. In simple words, It is a closed path in a circuit.

Finding Loops in Electric Circuits

Loops can be found by the following fundamental theorem of circuit and network topology

l = b – n + 1

Therefore, in fig 4, there is 3 number of Loops.

Finding Loops in Electric Circuits
Fig 4: Finding Loops in Electric Circuits

Mesh

A closed loop which contains no other loop within it or a path which does not contain on other paths is called Mesh

Finding Meshes in Electric circuits

Finding Meshes in Electric circuits
Fig 5: Finding Meshes in Electric circuits
In Fig 5, there is two number of meshes.

Good to Know: A Loop can be Mesh, but Mesh can’t be Loop.

Overall circuit with 6 Nodes, 7 Branches, 3 Loops and, 2 Meshes shown in fig 6.

A circuit with 6 Nodes, 7 Branches, 3 Loops, and 2 Meshes
Fig 6: A circuit with 6 Nodes, 7 Branches, 3 Loops and, 2 Meshes

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