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

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node branch loop

Because the electric circuit’s elements can be interconnected in some ways, we need to understand some basic concepts of network topology.

To make a difference between circuit and network, we may assume a network is an interconnection of elements or devices.

A circuit is a network providing one or more closed paths.

Make sure to read what is dc circuit first.

In network topology, we study the placement element properties in the network and the geometric configuration of the network. Such elements include branches, nodes, and loops

Branch of Electric Circuit

Generally, we use the two-terminal element to build an electric circuit. If we connect a circuit element, the circuit will connect to its both terminal, creating a closed path.

Circuit elements are connected between two nodes of the circuit. When this element exists, the path between one node to another node is called a branch.

For more scientific explanation, the path between two nodes which can absorb or deliver energy is a branch of an electric circuit.

Further to say, a conducting wire without an element or short circuit; is considered as a branch.

A branch represents a single element such as voltage source or a resistor.
electric circuit branches
Figure 1. Electric circuit branches

For better understanding, a branch represents any two-terminal element. The circuit in Figure.(1) has five branches: the 10 V voltage source, the 2 A current source, and the three resistors.

Nodes of Electric Circuit

Just as stated above, we can conclude that a node is a point through a circuit element.

For better words, a node is a point where two or more circuit elements’ terminal are connected together.

A node is the point of connection between two or more branches.

Node is usually represented by a dot in a circuit. If a short circuit (a connecting wire) connects two nodes, the two nodes form a single node.

In Figure.(1) has three nodes a, b, and c. Take a note on three connecting wire that form node b is assumed a single node.

The same concept also happens for node c. After knowing how to determine the number of nodes, we can redraw the Figure.(1) to simplify it in Figure.(2).

The two circuits in Figure.(1) and Figure.(2) are still identical.

electric circuit branches
Figure 2. Electric circuit identical energy

Loops in Electric Circuit

A loop is a closed path formed starting from a node passing through a set of nodes and returning to the starting node without passing the same node more than once.

A loop is called to be independent if it contains at least one branch that is not a part of another independent loop.

A loop is any closed path in a circuit.
 

It is possible to form an independent set of loops where one of the loops does not contain such a branch. In Figure.(2), abca with 2Ω is independent.

The second loop with a 3Ω resistor and the current source is independent. A third loop could be the one with a 3Ω resistor in parallel with 2Ω resistor. This one is an independent set of loops.

A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology :

branches nodes loop theorem
(1)
 

The circuit topology is a great material to study voltages and currents in an electric circuit.

Two or more elements are in series if they exclusively share a single node and consequently carry the same current.

Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

It is called a series when the elements are chain-connected or connected sequentially, end to end. Two elements are in series if they share one common node and no other element is connected to that common node.

It is also called a series when the elements carry the same value of current.

Example: Figure.(1), voltage source and the 5Ω resistor are in series.

It is called parallel when the elements are connected to the same pair of the terminal. It is also called parallel when the elements carry the same value of voltage.

Example: Figure.(1), the 2Ω resistor, the 3Ω resistor, and the current source are in parallel.

Nodes, Branches, and Loops Examples

For better understanding let us review the example below :

1. Determine the number of branches and nodes in Figure.(3). Identify which are in series and parallel.

electric circuit example
Figure 3
 
Solution :
  • The circuit has four elements, thus it has four branches: 10 V, 5 Ω, 6 Ω, and 2 A.
  • The circuit has three nodes: Figure.(4).
electric circuit example
Figure 4
  • Series connection: 5 Ω and 10 V.
  • Parallel connection: 6 Ω, 2 A, connected together to nodes 2 and 3.

Frequently Asked Questions:

What is node branch and loop in a circuit?

A node is the point of connection between two or more branches. A branch represents a single element such as a voltage source or a resistor. A loop is any closed path in a circuit.

What is a node in a circuit?

We can conclude that a node is a point through a circuit element. For better words, a node is a point where two or more circuit elements’ terminal are connected together.

How do you count nodes in a circuit?

A node is the point of connection between two or more branches. Node is usually represented by a dot in a circuit.

What is the difference between node and branch?

A node is a point where two or more circuit elements’ terminal are connected together. Circuit elements are connected between two nodes of the circuit. When this element exists, the path between one node to another node is called a branch.

How do you find current in a loop?

We can use Kirchhoff’s Current Law to find current in a loop. The more advanced method is mesh analysis which is using meshes to analyze a circuit.

What is difference between node and Junction?

While a node is a point where two or more branches are connected together, a junction is a point where three or more electric circuit’s paths are connected together.

Have you understood what is nodes, branches, and loops?
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Happy learning!

Reference:  Fundamentals of electric circuits by Charles K. Alexander and Matthew N. O. Sadiku

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