A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltmeters $${V_1}$$, $${V_2}$$ and ammeter $${A_1}$$, $${A_2}$$ (all assumed to be ideal), as indicated. Under following switch conditions, the readings obtained are:

(i) $${S_1} - open,\,\,\,\,{S_2} - closed$$
$${A_1} = 0\,A,\,\,\,\,\,\,{V_1} = \,4.5\,\,V,$$
$${V_2}\, = \,1.5\,V,\,\,\,\,{A_2}\, = \,1\,A$$

(ii) $${S_1} - Closed,\,\,\,\,{S_2} - Open$$
$${A_1} = 4\,A,\,\,\,\,\,\,{V_1} = \,6\,\,V,$$
$${V_2}\, = \,6\,V,\,\,\,\,{A_2}\, = \,0\,A$$

The z-parameter matrix for this network is

In the following graph, the number of trees (P) and the number of cut-sets (Q) are

The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The switches S1 and S2 are mechanically coupled and connected as follows

Assume that the capacitor has zero initial charge. Given that u(t) is a unit step function, the voltage V_c(t) across the capacitor is given by

The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For t > 0, the voltage across the resistor is