GATE EC Circuit Analysis questions

A unity negative feedback system has an open-loop transfer function $G(S) = \dfrac{K}{s(s+10)}$. The gain $K$ for the system to have a damping ratio of $0.25$ is ________.

In the circuit shown, the Norton equivalent resistance $(\text{in}\: \Omega)$ across terminals $a-b$ is _______.

In the circuit shown, the initial voltages across the capacitors $C_{1}$ and $C_{2}$ are $1\: V$ and $3\: V,$ respectively. The switch is closed at time $t = 0$. The total energy dissipated (in Joules) in the resistor $R$ until steady state is reached, is __________.

Let $x(t) = \alpha s(t) + s(-t)$ with $s(t) = \beta e^{-4t}u(t),$ where $u(t)$ is unit step function. If the bilateral Laplace transform of $x(t)$ is $$X(s) = \dfrac{16}{s^{2} – 16}\:\: -4 < Re\{s\}<4;$$ then the value of $\beta$ is ______.

The output of a standard second-order system for a unit step input is given as $y(t) = 1-\dfrac{2}{\sqrt{3}}e^{-t}\cos \left(\sqrt{3t}-\dfrac{\pi}{6}\right)$. The transfer function of the system is

Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency $3\: MHz$ and phase shift of $\frac{\pi}{2}$ between them (the element at the origin leads in phase). If the maximum radiated $E$-field at the point $P$ in the $x-y$ plane occurs at an azimuthal angle of $60^{\circ},$ the …

For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals $a-b$ is _______.

The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit is

The $ABCD$ parameters of the following $2$-port network are

A network is described by the state model as $$\dot{x_{1}}=2x_{1}-x_{2}+3u \\ \dot{x_{2}}=-4x_{2}-u \\ y=3x_{1}-2x_{2}$$ The transfer function $H(s)\left(=\dfrac{Y(s)}{U(s)}\right)$ is

The position control of a DC servo-motor is given in the figure. The values of the parameters are $K_{T}=1 \: N-m/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kg-m^{2},B=1N-m/(rad/sec)$ and $K_{b} = 1V/(rad/sec) .$ The steady-state position response (in radians) due to unit impulse disturbance torque $T_{d}$ is _______.

Consider the configuration shown in the figure which is a portion of a larger electrical network For $R = 1\: \Omega$ and currents $i_{1} = 2A,i_{4} = -1A,i_{5} = -4A,$ which one of the following is $\textbf{TRUE}?$

A two-port network has scattering parameters given by $[S] = \begin{bmatrix}s_{11} &s_{12} \\s_{21} &s_{22} \end{bmatrix}.$ If the port-2 of the two-port is short circuited, the $s_{11}$ parameter for the resultant one-port network is

A $Y$-network has resistances of $10\Omega$ each in two of its arms, while the third arm has a resistance of $11\Omega.$ In the equivalent $\Delta$ – network, the lowest value (in $\Omega)$ among the three resistances is ______.

A $230\: V$ rms source supplies power to two loads connected in parallel. The first load draws $10 \: kW$ at $0.8$ leading power factor and the second one draws $10\: kVA$ at $0.8$ lagging power factor. The complex power delivered by the source is

Norton’s theorem states that a complex network connected to a load can be replaced with an equivalent impedance

In the h-parameter model of the $2$-port network given in the figure shown, the value of $h_{22}$ (in S) is ______ .

In the magnetically coupled circuit shown in the figure, $56 \%$ of the total flux emanating from one coil links the other coil. The value of the mutual inductance (in H) is ____ .

The input $-3e^{2t}u(t),$ where $u(t)$ is the unit step function, is applied to a system with transfer function $\frac{s-2}{s+3}.$ If the initial value of the output is $-2$, then the value of the output at steady state is _______.

Consider the building block called ‘Network N’ shown in the figure. Let $C= 100\mu F$ and $R= 10 k \Omega.$ Two such blocks are connected in cascade, as shown in the figure. The transfer function $\frac{V_{3}(s)}{V_{1}(s)}$ of the cascaded network is