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Solved Problems-19

In the following circuit, determine the voltages V2 and V3 using cutset analysis. Select the circuit elements (1), (2) and (3) in the tree.
Description: 3376.png
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 R1 and R2 in series with the voltage source and in parallel with the current source, respectively. Finally, we will let R1 → 0, R2 → ∝.
Description: 1976.png
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][Yb][QT][Vt] = [Q] × {[Yb][VS] – [IS]}
Description: 5718.png 
Description: 5724.png
Description: 5737.png
Thus, the KCL equations are
Description: 5747.png 
When R1 → 0, R2 → ∝, the equations reduce to the form as given below.
Description: 5754.png
Description: 5760.png
Solving the last two equations, Description: 5786.png
Description: 5777.png

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