What is Branch?
A branch represents the single circuit elements like resistor, capacitor, inductor, voltage or current source.
For example, for the circuit shown in the figure 1, there are five branches. A 10 V voltage source, 2A current source, 4 Ω, 5 Ω and 3 Ω resistors.
What is Node ?
A node is the point in the circuit where two or more circuit elements (or branches) are connected. Figure. 2 ( Representation of Four Nodes in the Circuit)
For example, as shown in Figure 2, the above circuit contains the Four nodes. The node A, B, C and D.
What is Loop ?
Any closed path in the circuit is called as a loop.
A loop is a closed path formed by starting at a node, passing through a
set of nodes, and returning to the starting node without passing through
any node more than once.
Figure. 3 (Representation of Loop in the Circuit)
For example, as shown in the Figure.3, the circuit contains three loops.
The first is loop A-B-D-A, the second loop is B-C-D-B. And the third loop is A-B-C-D-A.
What is Mesh?
A mesh is a closed path in the circuit, which does not contain any other close path inside it.
For example, as shown in the Figure.3, the loop 1(A-B-D-A) and loop 2 (B-C-D-B) does not contain any other closed path within them. And they are the example of the Mesh.While loop 3 (A-B-C-D-A) contains loop 1 and loop 2 with in it. So, it can’t be called as a Mesh.
Note: All Mesh are loops but not all the loops are Mesh.
For more information, check this video: