GATE EC Circuit Analysis questions

The $\text{ABCD}$ parameters of an ideal $n: 1$ transformer shown in the figure are $\left[\begin{array}{ll}n & 0 \\ 0 & \mathrm{X}\end{array}\right]$. The value of $X$ will be

In a series $\mathrm{RLC}$ circuit, $\mathrm{R}=2 \; \mathrm{k} \Omega, \mathrm{L}=1 \; \mathrm{H}$, and $\mathrm{C} \frac{1}{400}=\mu \mathrm{F}$. The resonant frequency is

The maximum power that can be transferred to the load resistor $R_{L}$ from the voltage source in the figure is

The first and the last critical frequency of an $\text{RC}$-driving point impedance function must respectively be

In what range should $\operatorname{Re}(s)$ remain so that the Laplace transform of the function $e^{(n+2)t+5}$ exits?

For the circuit show in the figure, the instantaneous current $i_{i}(t)$ is

Impedance $\mathrm{Z}$ as shown in the given figure is

For the circuit shown in the figure, Thevenin's voltage and Thevenin's equivalent resistance atterminals $a-b$ is

If $R_{1}=R_{2}=R_{4}=R$ and $R_{3}=1.1 R$ in the bridge circuit shown in the figure, then the reading in the ideal voltmeter connected between $a$ and $b$ is

The $h$ parameters of the circuit shown in the figure are

A square pulse of $3$ volts amplitude is applied to $C-R$ circuit shown in the figure. The capacitor is initially uncharged. The output voltage $\mathrm{V}_{0}$ at time $t=2 \mathrm{sec}$ is

The equivalent inductance measured between the terminals $1$ and $2$ for the circuit shown in the figure is

The circuit shown in in the figure, with $R=\frac{1}{3} \Omega$, $\mathrm{L}=\frac{1}{4} \mathrm{H}, \mathrm{C}=3 \mathrm{~F}$ has input voltage $v(t)=\sin 2 t$. The resulting current $i(t)$ is

For the circuit shown in in the figure, the time constant $\text{RC}=1 \mathrm{~ms}$. The input voltage is $v_{i}(t)=\sqrt{2}$ $\sin 10^{3} t$. The output voltage $v_{0}(t)$ is equal to

For the lattice circuit shown in the figure, $Z_{a}=j 2 \Omega$ and $Z_{b}=2 \Omega$. The values of the open circuit impedance parameters $Z=\left[\begin{array}{ll}z_{11} & z_{12} \\ z_{21} & z_{22}\end{array}\right]$ are

The circuit shown in the figure has initial current $i_{t}\left(0^{-}\right)=1 \mathrm{~A}$ through the inductor and an initial voltage $v_{c}\left(0^{-}\right)=-1 \mathrm{~V}$ across the capacitor. For input $v(t)=u(t)$, the Laplace transform of the current $i(t)$ for $t \geq 0$ is

For the circuit shown in the figure, the initial conditions are zero. Its transfer function $$H(s) = \frac{V_{c}(s)}{V_{i}(s)}$$

Consider the following statements $\text{S1}$ and $\text{S2}$ $\text{S1} :$ At the resonant frequency the impedance of a series $\mathrm{R}-\mathrm{L}-\mathrm{C}$ circuit is zero. $\text{S2} :$ In a parallel $\mathrm{G}-\mathrm{L}-\mathrm{C}$ circuit, increasing the conductance $\mathrm{G}$ results in increase in its $\mathrm{Q}$ factor. …

Consider an impedance $\mathrm{Z = R + j X }$ marked with point $\mathrm{P}$ in an impedance Smith chart as shown in the figure. The movement from point $\mathrm{P}$ along a constant resistance circle in the clockwise direction by an angle $45^{\circ}$ is equivalent to

The minimum number of equations required to analyze the circuit shown in the figure is