GATE EC Circuit Analysis questions

The Laplace Transform of the signal $x(t)=u(t-2) *(t u(t))$ is given by which of the following expressions? ["*" represents convolution operator]

The relation between the input current ( $I$ ) and the output voltage ( $V$ ) of a circuit is governed by the equation: $C \dfrac{d V}{d t}=I(t)-m(t)$. The circuit is excited by $I(t)=q \delta(t)$, where $q$ is a real valued constant. $V$ at $t=0^{-}$is $V_{0}$. Which of the following is an equivalent representation of the above case?

The output voltage $V_{o}$ (in Volt) for the network given in the Figure is $\_\_\_\_$ . (rounded off to two decimal places)

Consider the circuit shown in the Figure, where the input $v_{i}(t)$ is in Volt. The average power (in $\text{mW}$ ) dissipated in the load resistance of $1 ~\mathrm{k} \Omega$ at the resonant frequency is $\_\_\_\_$ . (rounded off to two decimal places)

For a lossless passive two-port network, $\left|S_{11}\right|$ and $\left|S_{21}\right|$ intersect at $-3$ dB . For a lossy passive two-port network, $\left|S_{11}\right|$ and $\left|S_{21}\right|$ intersect at $-4$ dB . The percentage of power dissipated in the lossy network at the intersection frequency is $\_\_\_\_$. (rounded off to two …

In the given circuit, $L=1 \mu \mathrm{H}$ and $C=1 \mu \mathrm{~F}$. The phasor diagram for $I_{C}$ and $I_{L}$ is also shown. Assume that the phase $\left(\theta_{1}+\theta_{2}\right)$ is $90^{\circ}$ at a frequency of $159.15 ~\text{kHz}.$ Among the following options, what is the nearest integer value of $R_{C} \times R_{L}?$

Consider the two-port network as shown in the Figure. Which of the following options provides the correct set of values of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\text{D}$ parameters?

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $3 \Omega$ resistor are as indicated. The voltage (in Volts) at node $X$ is $\_\_\_\_\_\_$

Let $i_{C}, i_{L}$, and $i_{R}$ be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens (S). Which one of the following is TRUE?

All the components in the bandpass filter given below are ideal. The lower $-3$ dB frequency of the filter is $1$ MHz. The upper $-3$ dB frequency (in MHz , rounded off to the nearest integer) is $\_\_\_\_\_\_\_$

In the circuit below, $M_{1}$ is an ideal AC voltmeter and $M_{2}$ is an ideal AC ammeter. The source voltage (in Volts) is $v_{s}(t)=100 \cos (200 t)$. What should be the value of the variable capacitor $C$ such that the RMS readings on $M_{1}$ and $M_{2}$ are $25 \: \mathrm{V}$ and $5 \: \mathrm{A}$, respectively?

The $Z$-parameter matrix of a two port network relates the port voltages and port currents as follows: $$\left[\begin{array}{l} V_{1} \\ V_{2} \end{array}\right]=Z\left[\begin{array}{l} I_{1} \\ I_{2} \end{array}\right]$$ The $Z$-parameter matrix (with each entry in Ohms) of the network shown below is $\_\_\_\_\_\_\_$

Two resistors are connected in a circuit loop of area $5 \mathrm{~m}^{2}$, as shown in the figure below. The circuit loop is placed on the $x-y$ plane. When a time-varying magnetic flux, with flux-density $B(t)=0.5 t$ (in Tesla), is applied along the positive $z$-axis, the magnitude of current $I$ (in Amperes, rounded off to two decimal places) in …

In the circuit given below, the switch $\text{S}$ was kept open for a sufficiently long time and is closed at time $t=0$. The time constant (in seconds) of the circuit for $t>0$ is $\_\_\_\_\_\_$.

For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is $\_\_\_\_\_\_$.

In the network shown below, maximum power is to be transferred to the load $R_{L}$. The value of $R_{L}$ (in $\Omega$ ) is $\_\_\_\_\_\_\_$.

A series $\text{RLC}$ circuit has a quality factor $\text{Q}$ of $1000$ at a center frequency of $10^{6} \; \mathrm{rad} / \mathrm{s}$. The possible values of $\text{R, L}$ and $\text{C}$ are

In the circuit shown below, the current $i$ flowing through $200 \; \Omega$ resistor is___________ $\mathrm{mA}$ (rounded off to two decimal places).

For the two port network shown below, the $[\mathrm{Y}] –$parameters is given as $$[Y]=\frac{1}{100}\left[\begin{array}{cc}2 & -1 \\ -1 & 4 / 3\end{array}\right] S$$ The value of load impedance $\mathrm{Z}_{\mathrm{L},}$ in $\Omega$, for maximum power transfer will be ____________ (rounded off to the nearest integer).

In the circuit shown below, switch $\mathrm{S}$ was closed for a long time. If the switch is opened at $t=0$, the maximum magnitude of the voltage $\mathrm{V}_{\mathrm{R}}, \text{in volts,}$ is_____________ (rounded off to the nearest integer).