Nodes, Branches and Loops

Posted on Thursday, 3 May 2012 by Matal Hawa


When we discuss network topology we have to understand certain terms. Among these terms node, branch or loops are used most of the time. Let’s see what they mean.

Branch: A single element with its terminals is usually called a branch. For example a voltage source or a resistor is a branch.

Node: When two or more branches are connected at a point then that point is called a node.
Loop: A closed path in a circuit is called a loop.

Mesh: Mesh is a kind of loop which has no loop inside it. But you have to remember that all meshes are also loops. But all loops are not meshes. 

For example let’s have look at the following figure:


In a network or circuit, number of loop, nodes and branches has to satisfy the following fundamental relationship:
                b=l+n-1
where, b = number of branches,
l = number of loops and
n = number of nodes.

There is another important thing to remember in circuit analysis. 

01.   In a series connection two or more elements are connected sequentially, so they carry the same current I , that is in a series connection current will always remain constant where as voltage will have a drop after each element.
02.   In a parallel connection, all the branches are connected at two common nodes. So, they apparently have the same voltage at each node but the current is divided according to ohm’s law.

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8 Responses to Nodes, Branches and Loops

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  2. Electrical Technology27 December 2013 at 05:37

    Good one...Also check this article
    How to determine the number of Nodes, Branches, Loops and Meshes in a Circuit?

    ReplyDelete
  3. DreamLegend13 September 2018 at 20:48

    Can you please explain how the fundamental relationship(branches= loops+nodes-1) is derived?? Please give a clear picture of that. It seems wrong in many circuits.

    Here is the circuit that seemed to not be fit to the fundamental relationship


    https://www.electricaltechnology.org/2013/12/determine-the-number-of-Nodes-Branches-Loops-and-Meshes-in-Circuit.html

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