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A network has 8 branches and 4 independent loops. How many nodes are there in the network ? 

A network has 8 branches and 4 independent loops. How many nodes are there in the network ?  Correct Answer 5

Concept:

Mesh Analysis:

Mesh analysis is a method of analyzing networks with the help of KVL equations.

For a network having N nodes and B branches, the number of simultaneous equations to be solved to get the unknowns

= Number of KVL equations

= number of independent loop equations

= B - N + 1

Where, B = no of the branch, N = No of node

Nodal Analysis:

Nodal analysis is a method of analyzing networks with the help of KCL equations.

For a network of N nodes, the number of simultaneous equations to be solved to get the unknowns

= Number of KCL equations

= N - 1

Calculation:

Given that,

Let the number of nodes = N

Number of independent loops (L) = 4

Number of branches B = 8

We know that,

L = B – N + 1

⇒ 4 = 8 – N + 1 ⇒ N = 5

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