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Solved Problems-15

Using topological method, obtain node equations and node voltages in s domain for the network shown in the figure, when
Description: 5441.png
where, u(t) is unit step function and δ(t) is the unit impulse function.
Description: 3028.png
The graph of the network is shown in the figure.
Description: 3035.png
The incidence matrix is given as,
Reduced incidence matrix is,
Description: 5447.png
Branch admittance matrix is,
Description: 5453.png
∴ Description: 5464.png
∴ Description: 5470.png
Description: 5477.png
Thus, node equations are,
Description: 5483.png
Solving by Cramer’s rule, we get the voltages as,
Description: 5489.png and Description: 5495.png

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