List of top Network Theory Questions asked in GATE EE

A circuit with ideal elements is shown.

The circuit has a DC source \(V_{DC}\) in series with an ideal diode \(D\), a resistor \(R\), an inductor \(L\), and a capacitor \(C\) (the capacitor is connected across the series combination of \(L\) at the far end of the loop).

Which one of the following options correctly identifies all the linear elements in the circuit?

For the circuit shown, which one of the following options correctly identifies the Thevenin's equivalent parameters between nodes Y and Z?

The circuit has nodes X, Y, Z, and W. Between X and Y there is a 20 V ideal source (in parallel with a 10 k\(\Omega\) resistor directly connecting X and Y). Between Y and Z there is a 10 k\(\Omega\) resistor. Between Y and W there is a 2 k\(\Omega\) resistor. Between X and W there is an ideal 100 V source (no series resistor in this branch). Between Z and W there is an ideal 20 V source (no series resistor in this branch) and, separately, a 1 k\(\Omega\) resistor.

The circuit shown in the figure is initially in 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 μF capacitor, is .............. (Round off to 2 decimal places). \begin{center} \includegraphics[width=0.5\textwidth]{25.jpeg} \end{center}

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 \(t=5 \, \text{ms}\) is ..................... (Round off to 2 decimal places). \begin{center} \includegraphics[width=0.55\textwidth]{22.jpeg} \end{center}

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). \begin{center} \includegraphics[width=0.55\textwidth]{23.jpeg} \end{center}

For the circuit shown in the figure, $V_{1 = 8$ V, DC and $I_{1} = 8$ A, DC. The voltage $V_{ab}$ in Volts is \underline{\hspace{1cm}} (Round off to 1 decimal place).} \begin{center} \includegraphics[width=0.5\textwidth]{14.jpeg} \end{center}

The value of parameters of the circuit shown in the figure are $R_{1 = 2\Omega, R_{2} = 2\Omega, R_{3} = 3\Omega, L = 10 \,\text{mH}, C = 100 \,\mu\text{F}$. For time $t < 0$, the circuit is at steady state with the switch $K$ in closed condition. If the switch is opened at $t = 0$, the value of the voltage across the inductor ($V_{L}$) at $t = 0^{+}$ in Volts is \underline{\hspace{3cm}} (Round off to 1 decimal place).} \begin{center} \includegraphics[width=0.5\textwidth]{12.jpeg} \end{center}