A network has 8 nodes and 5 independent loops.The number of branches i...
Independent loops = link
l = b - ( n - 1)
⇒ 5= b - 7, b = 12
A network has 8 nodes and 5 independent loops.The number of branches i...
Given Information:
- The network has 8 nodes.
- There are 5 independent loops in the network.
Number of branches in the network:
To find the number of branches in the network, we need to understand what a branch is. In electrical network analysis, a branch refers to a single element or a combination of elements (such as resistors, capacitors, inductors, etc.) that are connected between two nodes.
Counting branches:
To count the number of branches, we can start by considering the simplest case where there are no loops. In this case, each branch connects two different nodes, so the total number of branches is equal to the number of nodes minus 1.
In the given network, we have 8 nodes. Therefore, in the absence of loops, the number of branches would be 8 - 1 = 7.
However, the given network has 5 independent loops. Each loop introduces an additional branch. So, we need to add the number of independent loops to the previously calculated number of branches.
Calculating the number of branches:
Number of branches = Number of nodes - 1 + Number of independent loops
Number of branches = 8 - 1 + 5 = 12
Therefore, the correct answer is option 'B', 12 branches.
Summary:
- The number of branches in a network can be calculated by adding the number of nodes minus 1 with the number of independent loops in the network.
- In the given network, there are 8 nodes and 5 independent loops, resulting in a total of 12 branches.