# Solved Problems-19

Problems-19

In the following circuit, determine the voltages

*V*_{2}and*V*_{3}using cutset analysis. Select the circuit elements (1), (2) and (3) in the tree.Solution

The graph and tree are shown in the figure. Hence, there is no series impedance with voltage source and parallel admittance with current source. We consider two resistances

*R*_{1}and*R*_{2}in series with the voltage source and in parallel with the current source, respectively. Finally, we will let*R*_{1}→ 0,*R*_{2}→ ∝.Three fundamental cutsets are:

f-cutset-1: [1, 4, 5, 6];

f-cutset-2: [2, 4, 6];

f-cutset-3: [3, 5, 6]

The fundamental cutset matrix is given as,

The node equations are given as,

[

*Q*][*Y*][_{b}*Q*][^{T}*Vt*] = [*Q*] × {[*Y*][_{b}*V*] – [_{S}*I*]}_{S}Here,

Thus, the KCL equations are

When

*R*_{1}→ 0,*R*_{2}→ ∝, the equations reduce to the form as given below.Solving the last two equations,

Therefore,