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Solved Problems-8

The circuit of the figure contains a voltage controlled voltage source. For this circuit, draw the oriented graph. By selecting a proper tree obtain the tie-set matrix and hence calculate the voltage, Vx.
Description: 2679.png
Since the controlled voltage source is not accompanied by any passive element, we will consider a resistance R1 in series with the controlled voltage source, and finally let R1 → 0.
Description: 2686.png
The graph of the network is shown with one tree.
The tie-set matrix is,
Description: 5120.png
The branch impedance matrix,
Description: 5126.png
∴ Description: 5132.png
Description: 5138.png
Now, Description: 5144.png
So, the loop equations become,
Description: 5150.png
With R1 → 0 and Vx = 4I2, the equations reduce to,
Description: 5156.png
Solving for I2,
Description: 5162.png
∴ Description: 5168.png 

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