# Solved Problems-13

Problems-13

For the network shown in the figure, draw the oriented graph, select a suitable tree and obtain the fundamental cutset matrix. Determine the node equations and find

*v*.Solution

The oriented graph of the network is shown in the figure. Since we have to find

*v*, we take branch (2) in the twig and a possible tree is selected.The fundamental cutsets are identified as

f-cutset-1: [1, 2, 3];

f-cutset-2: [3, 4];

The fundamental cutset matrix is given as,

The node equations are given as,

[

*Q*][*Y*][_{b}*Q*][^{T}*Vt*] = [*Q*] Ã— {[*Y*][_{b}*V*] â€“ [_{S}*I*]}_{S}Here,

Thus, the KCL equations are

Here,

*V*_{t}_{2}*=v*. Putting this in the KCL equations and solving we get,