For a two-phase network, the phase voltages $V_p$ and $V_q$ are to be expressed in terms of sequence voltages $V_\alpha$ and $V_\beta$ as $\begin{bmatrix} V_p \\ V_q \end{bmatrix} = S \begin{bmatrix} V_\alpha \\ V_\beta \end{bmatrix}$. The possible option(s) for matrix $S$ is/are

In the circuit shown, $Z_1 = 50\angle -90^{\circ} \Omega$ and $Z_2 = 200\angle -30^{\circ} \Omega$. It is supplied by a three phase 400 V source with the phase sequence being R-Y-B. Assume the watt meters $W_1$ and $W_2$ to be ideal. The magnitude of the difference between the readings of $W_1$ and $W_2$ in watts is _________________ (rounded off to 2 decimal places).

A 3-phase, star-connected, balanced load is supplied from a 3-phase, 400 V (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is $$-$$400 W and the line current is $$I_R=2$$ A (rms), then the power factor of the load per phase is

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).