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A network has 12 branches and 8 independent loops. How many nodes are there in the network?

A network has 12 branches and 8 independent loops. How many nodes are there in the network? Correct Answer 5

Concept:

Nodal Analysis:

Nodal analysis is a method of analyzing network 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

Mesh Analysis:

Mesh analysis is a method of analyzing network 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

Calculation:

Given that, number of loops (l) = 8

Number of branches (b) = 12

In any network, number of independent loops,

l = b – n + 1

⇒ 8 = 12 – n + 1

⇒ n = 5

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