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Solved Problems-8

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
Solution
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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