# A network has 8 branches and 3 independent loops. How many nodes are there in the network?

A network has 8 branches and 3 independent loops. How many nodes are there in the network?

### Right Answer is:

6

#### SOLUTION

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) = 3

Number of branches (b) = 8

In any network, the number of independent loops,

l = b – n + 1

⇒ 3 = 8 – n + 1

**⇒ n = 6**