Test: Graph Theory
10 Questions MCQ Test Network Theory (Electric Circuits) | Test: Graph Theory
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The circuit 1 and 2 are redrawn as below. 3 and 4 can not be redrawn on a plane without crossing other branch.
Other three circuits can be drawn on plane without crossing
A graph of an electrical network has 4 nodes and 7 branches. The number of links l, with respect to the chosen tree, would be
l = b - ( n - 1) = 4.
There are 4 node and 6 branches.
t = n - 1 = 3, l = b - n + 1 = 3
From fig. it can be seen that afhg is a tree of given graph
Branch current and loop current relation are expressed in matrix form as
where ij represent branch current and Ik loop current. The number of independent node equation are
Number of branch = 8
Number of link = 4
Number of twigs = 8 - 4 = 4
Number of twigs =number of independent node equation.
If the number of branch in a network is b, the number of nodes is n and the number of dependent loop is l, then the number of independent node equations will be
The number of independent node equation are n - 1.
Branch current and loop current relation are expressed in matrix form as
where ij represent branch current and Ik loop current.
Q. The rank of incidence matrix is
Number of branch b=8
Number of link l = 4
Number of twigs t = b - l = 4
rank of matrix = n - 1 = t = 4
Branch current and loop current relation are expressed in matrix form as
where ij represent branch current and Ik loop current.
Q. The directed graph will be
We know the branch current and loop current are related as
f-loop 1 include branch (2, 4, 6, 7) and direction of branch–2 is opposite to other (B only).
A network has 8 nodes and 5 independent loops.The number of branches in the network is
Independent loops = link
l = b - ( n - 1)
⇒ 5= b - 7, b = 12
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