GATE EC Circuit Analysis questions

The current $I$ in the given network is

For the given circuit, which one of the following is correct state equation?

Using the incremental low frequency small-signal model of the $\text{MOS}$ device, the Norton equivalent resistance of the following circuit is

Consider the two-port resistive network shown in the figure. When an excitation of $5\: V$ is applied across Port $1$, and Port $2$ is shorted, the current through the short circuit at Port $2$ is measured to be $1\: A$ (see (a) in the figure). Now, if an excitation of $5\: V$ is applied across Port $2$, and Port $1$ is shorted (see (b) in …

In the circuit shown, if $v(t)=2 \sin(1000\: t)$ volts, $R=1\:k \Omega$ and $C=1\:\mu F,$ then the steady-state current $i(t)$, milliamperes (mA), is

The block diagram of a system is illustrated in the figure shown, where $X(s)$ is the input and $Y(s)$ is the output. The transfer function $H(s)=\dfrac{Y(s)}{X(s)}$ is

Let the state-space representation of an LTI system be $x(t)=A x(t)+B u(t), y(t)=Cx(t)+du(t)$ where $A,B,C$ are matrices, $d$ is a scalar, $u(t)$ is the input to the system, and $y(t)$ is its output. Let $B=[0\quad0\quad1]^{T}$ and $d=0$ .Which one of the following options for $A$ and $C$ will ensure that the transfer function of this LTI …

Consider a unity feedback system, as in the figure shown, with an integral compensator $\dfrac{K}{s}$ and open-loop transfer function $$G(s)=\dfrac{1}{s^{2}+3s+2}$$ where $K>0.$ The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j\omega$ axis is equal to ________ (rounded off to two decimal …

The $\text{ABCD}$ matrix for a two-port network is defined by: $$\begin{bmatrix} V_{1}\\ I_{1} \end{bmatrix}=\begin{bmatrix} A &B \\ C& D \end{bmatrix}\begin{bmatrix} V_{2}\\ -I_{2} \end{bmatrix}$$ The parameter $\text{B}$ for the given two-port network (in ohms, correct to two decimal places) is _________.

The state equation and the output equation of a control system are given below: $\dot{x}=\begin{bmatrix} -4 & -1.5\\ 4& 0 \end{bmatrix}x+\begin{bmatrix} 2\\ 0 \end{bmatrix}u,$ $y=\begin{bmatrix} 1.5 & 0.625 \end{bmatrix}x.$ The transfer function representation of the system is

Consider the network shown below with $R_{1}=1\:\Omega,R_{2}=2\:\Omega$ and $R_{3}=3\:\Omega.$ The network is connected to a constant voltage source of $11\:V$. The magnitude of the current (in amperes, accurate to two decimal places ) through the source is _________.

The figure shows an RLC circuit excited by the sinusoidal voltage $100 \cos(3t)$ Volts, where $t$ is in seconds. The ratio $\frac{\text{amplitude of }V_{2}}{\text{amplitude of }V{1}}$ is______.

In the circuit shown, V is a sinusoidal voltage source. The current $I$ is in phase with voltage V. The ratio$\frac{\text{amplitude of voltage across the capacitor}}{\text{amplitude of voltage across the resistor}}$ is ___________.

A connection is made consisting of resistance A in series with a parallel combination of resistances $B$ and $C$. Three resistors of value $10 Ω, 5 Ω, 2 Ω$ are provided. Consider all possible permutations of the given resistors into the positions $A, B, C$, and identify the configurations with maximum possible overall resistance, and also the ones …

Consider the state space realization $\begin{bmatrix} \dot{x_1}(t)\\ \dot{x_2}(t) \end{bmatrix}=\begin{bmatrix} 0 &0 \\ 0&-9 \end{bmatrix}\begin{bmatrix} x_1(t)\\ x_2(t) \end{bmatrix}+\begin{bmatrix} 0\\ 45 \end{bmatrix} u(t)$ , with the initial condition $\begin{bmatrix} x_1(0)\\ x_2(0) \end{bmatrix}=\begin{bmatrix} 0\\ 0 \end{bmatrix}$ , where …

Consider the circuit shown in the figure. The Thevenin equivalent resistance (in Ω) across P-Q is _____________

Which one of the following is a property of the solutions to the Laplace equation: $\nabla^2f = 0$?

Consider a two-port network with the transmission matrix: $T = \begin{pmatrix}A & B \\C & D\end{pmatrix}$. If the network is reciprocal, then

The Laplace transform of the casual periodic square wave of period $T$ shown in the figure below is

A first-order low-pass filter of time constant $T$ is excited with different input signals (with zero initial conditions up to $t = 0$). Match the excitation signals $X, Y, Z$ with the corresponding time responses for $t \geq 0$: …