The open circuit impedance matrix $${Z_{OC}}$$ of a three-terminal two-port network with A as the input terminal, B as the output terminal, and C as the common terminal, is given as $$$\left[ {{Z_{OC}}} \right] = \left[ {\matrix{ 2 & 5 \cr 3 & 7 \cr } } \right]$$$

Write down the short circuit admittance matrix $${{Y_{SC}}}$$ of the network viewed as a two-port network, but now taking B as the input terminal, C as the output terminal and A as the common terminal.

The voltage V_C1, V_C2 and V_C3 across the capacitors in the circuit in Fig., under steady state, are respectively

The number of independent loops for a network with n nodes and b branches is

Refer to the circuit shown in Fig. Choosing the voltage v_C(t) across capacitor, and the current i_L(t) through the inductor as state variable,i.e., $$$\left[\mathrm x\left(\mathrm t\right)\right]\;=\;\begin{bmatrix}{\mathrm v}_\mathrm C\left(\mathrm t\right)\\{\mathrm i}_\mathrm L\left(\mathrm t\right)\end{bmatrix}$$$ Write the state equation in the form $$\frac{\operatorname d\left[x\left(t\right)\right]}{\operatorname dt}\;=\;\left[A\right]\left[x\left(t\right)\right]\;+\;\left[B\right]\left[u\left(t\right)\right]$$ and find [A], [B] and [u(t)].