GATE EE 2024 Question Paper (11-Feb-2024) (Shift-2)

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 $\left[\begin{array}{c}{V}_p\\ V_q\end{array}\right]=S\left[\begin{array}{c}{V}_{\alpha }\\ V_{\beta }\end{array}\right]$. The possible option(s) for matrix $S$ is/are

Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous generators?

Two passive two-port networks P and Q are connected as shown in the figure. The impedance matrix of network P is $Z_P=\left[\begin{array}{cc}40\Omega & 60\Omega \\ 80\Omega & 100\Omega \end{array}\right]$. The admittance matrix of network Q is $Y_Q=\left[\begin{array}{cc}5S& -2.5S\\ -2.5S& 1S\end{array}\right]$. Let the ABCD matrix of the two-port network R in the figure be $\left[\begin{array}{cc}\alpha & \beta \\ \gamma & \delta \end{array}\right]$. The value of $\beta$ in $\Omega$ is _______________ (rounded off to 2 decimal places).

For the circuit shown in the figure, the source frequency is 5000 rad/sec. The mutual inductance between the magnetically coupled inductors is 5 mH with their self inductances being 125 mH and 1mH. The Thevenin's impedance, $Z_{th}$, between the terminals P and Q in $\Omega$ is __________ (rounded off to 2 decimal places).

In the circuit shown, $Z_1=50\angle \text{–}90^{\circ }\Omega$ and $Z_2=200\angle \text{–}30^{\circ }\Omega$. 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).