Recent activity in Networks, Signals and Systems

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

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]$\dfrac{e^{-2 s}}{s^{2}(s-...

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} \O...

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 exc...

Two discrete time systems with impulse responses $h_t[n]=\delta[n-1]$ and $h_2[n]=\delta[n-2]$ are connected in cascade. The overall impulse response of the cascaded syst...

For a parallel $\text{RLC}$ circuit, which one of the following statements is $\text{NOT}$ correct?The bandwidth of the circuit decreases if $\mathrm{R}$ is increasedThe ...

For the two-port network shown below, the short-circuit admittance parameter matrix is$\left[\begin{array}{cc}4 & -2 \\ -2 & 4\end{array}\right] \mathrm{S}$$\left[\begin{...

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,...

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...

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...

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...

In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic(a) Continuous, aperiod...

Consider a system with input $x(t)$ and output $y(t)=x\left(e^{t}\right)$. The system isCausal and time invariant.Non-causal and time varying.Causal and time varying.Non-...

​​​​A causal and stable $\text{LTI}$ system with impulse response $h(t)$ produces an output $y(t)$ for an input signal $x(t)$. A signal $x(0.5 t)$ is applied to another c...

Consider the discrete-time system below with input $x[n]$ and output $y[n]$. In the figure, $h_{1}[n]$ and $h_{2}[n]$ denote the impulse responses of LTI Subsystems $1$ a...

In the circuit of the figure is the energy absorbed by the $4 \; \Omega$ resistor in the time interval $(0, \infty)$ is$36$ Joules$16$ Joules$256$ JoulesNone of the above

​​​​A continuous time signal $x(t)=2 \cos (8 \pi t+\pi / 3)$ is sampled at a rate of $15 \mathrm{~Hz}$. The sampled signal $x_{s}(t)$ when passed through an LTI system wi...