For the circuit shown, if $$i = \sin 1000t$$, the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals a-b at time t = 5 ms is __________ (Round off to 2 decimal places).

The admittance parameters of the passive resistive two-port network shown in the figure are

$${y_{11}} = 5\,S,{y_{22}} = 1\,S,{y_{12}} = {y_{21}} = - 2.5\,S$$

The power delivered to the load resistor $$R_L$$ in Watt is __________ (Round off to 2 decimal places).

The circuit shown in the figure is initially in the steady state with the switch K in open condition and $$\overline K $$ in closed condition. The switch K is closed and $$\overline K $$ is opened simultaneously at the instant $$t=t_1$$, where $$t_1 > 0$$. The minimum value of $$t_1$$ in milliseconds, such that there is no transient in the voltage across the 100 $$\mu$$F capacitor, is ___________ (Round off to 2 decimal places).

A balanced delta connected load consisting of the series connection of one resistor (R = 15 $$\Omega$$) and a capacitor (C = 212.21 $$\mu$$F) in each phase is connected to three-phase, 50 Hz, 415 V supply terminals through a line having an inductance of L = 31.83 mH per phase, as shown in the figure. Considering the change in the supply terminal voltage with loading to be negligible, the magnitude of the voltage across the terminals $$V_{AB}$$ in Volts is ___________ (Round off to the nearest integer).