GATE EC Circuit Analysis questions

For the $Y$-network shown in the figure, the value of $R_{1}$ (in $\Omega$) in the equivalent $\Delta$-network is __________.

The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. Which one of the following is the unilateral Laplace transform of $g(t) = t \cdot f(t)$?

The steady state output of the circuit shown in the figure is given by $y(t)=A(\omega) \sin (\omega t + \phi ( \omega))$. If the amplitude $\mid A (\omega ) \mid =0.25$, then the frequency $\omega$ is

In the circuit shown in the figure, the value of $v_0(t)$ (in Volts) for $t \to \infty$ is ___________

The equivalent resistance in the infinite ladder network shown in the figure, is $R_e$. The value of $R_e/R$ is __________

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor $k, \: k> 0,$ the elements of the corresponding star equivalent will be scaled by a factor of

The transfer function $\dfrac{V_{2}(s)}{V_{1}(s)}$ of the circuit shown below is

In the circuit shown below, if the source voltage $V_S = 100\angle 53.13^{\circ}\: V$ then the Thevenin’s equivalent voltage in Volts as seen by the load resistance $R_{L}$ is

The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of $tf(t)$ is

In the circuit shown below, the current through the inductor is

The circuit shown is a

If $V_A-V_B=6\:V$, then $V_C-V_D$ is

With $10\:V$ dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1\: \Omega$ connected at port B draws a current of $3\:A$ $2.5\: \Omega$ connected at port B draws a current of $2\:A$ With $10\: V$ dc connected at port A, the current drawn by $7\:\Omega$ connected at port B is

With $10\:V$ dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1\: \Omega$ connected at port B draws a current of $3\:A$ $2.5\: \Omega$ connected at port B draws a current of $2\:A$ For the same network, with $6\: V$ dc connected at port A, $1\:\Omega$ connected at port B draws …

A two-port network is represented by $\text{ABCD}$ parameters given by $$\left[\begin{array}{c} \mathrm{V}_1 \\ \mathrm{I}_1 \end{array}\right]=\left[\begin{array}{ll} \mathrm{A} & \mathrm{B} \\ \mathrm{C} & \mathrm{D} \end{array}\right]\left[\begin{array}{c} \mathrm{V}_2 \\ -\mathrm{I}_2 \end{array}\right]$$ if port-$2$ is terminated by …

In the two port network shown in the figure below, $z_{12}$ and $z_{21}$ are, respectively

The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by

A $2 \; \mathrm{mH}$ inductor with some initial current can be represented as shown below, where $s$ is the Laplace Transform variable. The value of initial current is

In the figure shown, assume that all the capacitors are initially uncharged. If $\text{V}_i(t)=10 u(t)$ Volts, then $\text{V}_0(t)$ is given by

The condition on $\mathrm{R}, \mathrm{L}$ and $\mathrm{C}$ such that the step response $y(t)$ in the figure has no oscillations, is