List of top Analog Electronics Questions on Miscellaneous asked in GATE EE

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 wattmeters \( W_1 \) 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).

 

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

 

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

 

Consider the complex function \( f(z) = \cos z + e^{z^2} \). The coefficient of \( z^5 \) in the Taylor series expansion of \( f(z) \) about the origin is _____________ (rounded off to 1 decimal place).