Physics Lesson 15.5.1 - Junctions, Nodes, Paths, Branches and Loops

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Welcome to our Physics lesson on Junctions, Nodes, Paths, Branches and Loops, this is the first lesson of our suite of physics lessons covering the topic of Kirchhoff Laws, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Junctions, Nodes, Paths, Branches and Loops

First, we must explain some terms used when dealing with the Kirchhoff Laws.

a. A junction is a point in which two or more conducting wires converge.

Some examples of junctions are shown in the figure below.

The points A, B and C are all junctions as they connect two or more conducting wires. The wires that form a junction may or may not have circuit components connected in them.

b. A node is a point where two or more circuit elements' terminals are connected together.

A node can be any point between two circuit elements such as the point N shown in the figure below.

Node is represented by a dot in a circuit. The point N in the above figure represents a simple node as it connects two elements of the circuit that are in the same conducting wire. On the other hand, when the node is located in the junction of two or more wires, it is called a principal node. In the figure above, the points A and B represent principal nodes as they are located in junctions while the point N represent a simple node as it is located in a single wire.

We have encountered examples of nodes when explaining the parallel combination of resistors or cells in the previous tutorials. In those examples, there was an input (I_total) and two outputs (I₁ and I₂) or two inputs (I₁ and I₂) and one output (I_total) for the currents flowing in the two nodes.

If a short circuit (a conducting wire with no circuit components connected in it) connects two principal nodes, then these two principal nodes form a single simple node. Thus, for example if we connect the points A and B in the figure above with a conducting wire, the points A and B forms a single simple node as the current flows only in the direction AB (a short circuit is obtained), bypassing the two resistors R₁ and R₂. In this case, the new simple node is a point in the longest path that connects the ammeter and the cell, while the other simple node N is in the shortest path that connects these two components.

All points of a node have the same potential difference as the resistance of wire is not considered.

c. A path is the set of wires, components and nodes through which the current flows, where all the above elements are counted only once.

For example, the flow of current following the direction

represents a path, while

represents another path for the circuit above.

d. A branch is the path between one node and another node.

Thus, in the figure above, the paths A ― R₁ ― B and A ― R₂ ― B are examples of branches.

In more scientific terms, the path between two nodes which can absorb or deliver energy is a branch of an electric circuit. Therefore, the path A ― emf ― B in the above figure is also a branch.

Now that we gave the definition of branch, we can also provide an alternative definition for node based on the meaning of branch. Thus, a node is the point of connection between two or more branches.

e. A loop is any closed path in a circuit.

In other words, a loop is a closed path starting from a node passing through a set of nodes and returning to the starting node without passing the same node more than once.

It is easy to confuse loops and paths, so let's illustrate the difference through an example from the circuits above. Thus,

is a path as discussed earlier, while

is a loop (a closed path). Therefore, loop is an extension of the concept of path.

Example 3

Identify the junctions, nodes, paths, branches and loops in the circuit shown in the figure.

Solution 3

1. There are two junctions in the circuit. They are at the points where two wires meet, aside the resistor R₂ at the points A and B in the figure below.
2. There are four nodes in the given circuit. Two of them are principal and two are simple nodes. The principal nodes are at the junctions, i.e. at the points A and B, while one simple node is between the source and ammeter and the other is between the ammeter and the resistor R₁.
3. There are two paths in this circuit:
   1. source ― SN1 ― ammeter ― SN2 ― R₁ ― principal node A ― R₂ ― principal node B
   2. source ― SN1 ― ammeter ― SN2 ― R₁ ― principal node A ― R₃ ― principal node B
4. There are five branches in this circuit. They are:
   1. SN1 ― ammeter ― SN2
   2. SN2 ― R₁ ― principal node A
   3. principal node A ― R₂ ― principal node B
   4. principal node A ― R₃ ― principal node B
   5. principal node B ― source ― SN1
5. There are two loops in the circuit. Loops are extension of paths as unlike paths, a loop ends at the starting point. Thus, we have
   1. source ― SN1 ― ammeter ― SN2 ― R₁ ― principal node A ― R₂ ― principal node B ― source
   2. source ― SN1 ― ammeter ― SN2 ― R₁ ― principal node A ― R₃ ― principal node B ― source

You have reached the end of Physics lesson 15.5.1 Junctions, Nodes, Paths, Branches and Loops. There are 4 lessons in this physics tutorial covering Kirchhoff Laws, you can access all the lessons from this tutorial below.

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