3 Easy Definitions of Nodes, Branches, and Loops and Example

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Branches, Nodes, and Loops are essential for electric circuit analysis. Electric circuit elements can be connected to each other in various ways. Because of it, we need to understand the basic knowledge behind an electric circuit such as network topology and circuit. Even though they sound like the same thing, both network and circuit are different things.

• A network is an interconnection of devices or elements.
• A circuit is a network consisting of one or more closed paths.

In network topology analysis, we will find various ways of electric elements interconnection and configuration. The connection between circuit elements will form branches, nodes, and loops. What are they? We will learn them in this post, read this until the end.

What is a Branch in Electric Circuit

A branch is a path between two nodes. What is a node? We will learn it after this. If you haven’t known what a node is, we will learn a branch with easier explanation.

With simple explanation, a branch is generally a two-terminal element we use to build an electric circuit. Every time we use a circuit element, the electric circuit will connect to both of its terminals forming a closed path.

Just as mentioned above, circuit elements are connected between two nodes of the circuit. The path formed between two nodes is called a branch. Using a more advanced term, a branch is a path between two nodes which is able to absorb or deliver energy in an electric circuit.

But more thing to remember, a branch without any element or short circuit is still a branch.

In conclusion:

A branch is a circuit element such as voltage or current source or a resistor, capacitor, inductor.

For a better understanding, you can observe the circuit example below:

The circuit above we can see that we have five branches:

1. The 10V voltage source
2. The 5Ω resistor
3. The 2Ω resistor
4. The 3Ω resistor
5. The 2A current source

What is a Node in Electric Circuit

We have already mentioned what is node above and we’ll understand it completely now. If a branch is a path between two nodes or a circuit element, then a node is a point through a circuit element. If we use circuit element terms, a node is a point where two or more elements’ terminals are connected together.

In conclusion:

A node is the point where two or more branches are connected together.

Node is represented by a dot in an electric circuit. Understand that if a short circuit (a plain conducting wire) is connected to two nodes, these two nodes form a single node. Observe the example circuit below:

In the circuit above we can list three nodes that exist inside it: nodes a, b, and c. The three nodes connected to a single wire form a single node b.

Just as node b, we can also treat node c as the same. After understand a bit about node, we can redraw the circuit above into circuit below:

Don’t worry, both circuits are identical.

What is a Loop in Electric Circuit

In a short explanation, a loop is formed from a node passing through a set of nodes and returning to the starting point or node without passing the same node twice or more.

We can call a loop independent if the loop contains at least one branch which is not a part of another independent loop.

In conclusion:

A loop is a closed path inside an electric circuit.

Observe the circuit below:

It is a common thing to find an independent loop where it doesn’t contain such a branch. In the circuit above we list the independent loop:

1. The path abca with 2Ω resistor.
2. The path bcb with 3Ω resistor and current source.
3. The path with 3Ω resistor and 2Ω resistor in parallel.

Conclusion of Branches, Nodes, and Loops

After learning about branches, nodes, and loops we can draw some conclusions to close our study here. Assume that we have a network consists of:

• b branches
• n nodes
• l loops

These three numbers will satisfy the basic theorem of network topology:

The equation above will help us greatly on studying voltage and current in an electric circuit. The term node can be used to distinguish between series and parallel circuits.

A series circuit is when two or more circuit elements share a single node and carry the same amount of current.

A parallel circuit is when two or more circuit elements are connected to the same two nodes and carry the same voltage across them.

Nodes, Branches, and Loops Examples

For better understanding let us review the examples below:

Observe the circuit below and count the number of branches and nodes. Also identify which parts are in series or parallel.

The circuit above has four element, thus it has four branches:

• 10V voltage source,
• 5Ω resistor,
• 6Ω resistor, and
• 2A current source

It has three nodes as shown the circuit below:

The series connection is formed from a 10V voltage source and 5Ω resistor. The parallel connection is formed from a 6Ω resistor and 2A current source connected to nodes 2 and 3.

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