GATE EC question library

The circuit shown in the figure has initial current $i_{t}\left(0^{-}\right)=1 \mathrm{~A}$ through the inductor and an initial voltage $v_{c}\left(0^{-}\right)=-1 \mathrm{~V}$ across the capacitor. For input $v(t)=u(t)$, the Laplace transform of the current $i(t)$ for $t \geq 0$ is

Consider the Bode magnitude plot shown in the given figure. The transfer function $\mathrm{H}(s)$ is

The transfer function $H(s)=\frac{V_{0}(s)}{V_{i}(s)}$ of an R-L-C circuit is given by $$H(s)=\frac{10^{6}}{s^{2}+20 s+10^{6}}$$ The Quality factor (Q-factor) of this circuit is

For the circuit shown in the figure, the initial conditions are zero. Its transfer function $$H(s) = \frac{V_{c}(s)}{V_{i}(s)}$$

A system described by the following differential equation $\frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y=x(t)$ is initially at rest. For input $x(t)=2 u(t)$, the output $y(t)$ is

Consider the following statements $\text{S1}$ and $\text{S2}$ $\text{S1} :$ At the resonant frequency the impedance of a series $\mathrm{R}-\mathrm{L}-\mathrm{C}$ circuit is zero. $\text{S2} :$ In a parallel $\mathrm{G}-\mathrm{L}-\mathrm{C}$ circuit, increasing the conductance $\mathrm{G}$ results in increase in its $\mathrm{Q}$ factor. …

In an abrupt $p-n$ junction, doping concentrations on $p$-side and $n$-side are $\mathrm{N}_{\mathrm{A}}=9 \times 10^{16} / \mathrm{cm}^{3}$ and $N_{0}=1 \times 10^{16} / \mathrm{cm}^{3}$ respectively. The $p-n$ junction is reverse biased and the total depletion width is $3 \; \mu \mathrm{m}$. The depletion width on the $p$-side is

The resistivity of a uniformloy doped $n$-type silicon sample is $0.5 \; \Omega-\mathrm{cm}$. If the electron mobility $\left(\mu_{n}\right)$ is $1250 \mathrm{~cm}^{2} / \mathrm{V}$-sec and the charge of an electron is $1.6 \times 10^{-19}$ Coulomb, the donor impurity concentration $\left(\mathrm{N}_{\text{n}}\right)$ in the sample is

Consider an abrupt $p$-junction. Let $V_{\text{in }}$ be the built-in potential of this junction and $\mathrm{V}_{\mathrm{R}}$ be the applied reverse bias. If the junction capacitance $\left(\mathrm{C}_{t}\right)$ is $1 \; \mathrm{pF}$ for $V_{\text{in}}+V_{\mathrm{R}}=1 \mathrm{~V}$, then for …

Consider the following statements $\mathrm{S} 1$ and $\mathrm{S} 2$. $\mathrm{S} 1 :$ The threshold voltage $\left(V_{T}\right)$ of a MOS capacitor decreases with increase in gate oxide thickness $\mathrm{S} 2 :$ The threshold voltage $\left(V_{t}\right)$ of a MOS capacitor decreases with increase in substrate doping concentration Which one of …

The drain of an $n$-channel MOSFET is shorted to the gate so that $V_{G S}=V_{D s}$. The threshold voltage $\left(V_{T}\right)$ of MOSFET is $1 \mathrm{~V}$. If the drain current $\left(\mathrm{I}_{\mathrm{D}}\right)$ is $1 \mathrm{~mA}$ for $\mathrm{V}_{G S}=2 \mathrm{~V}$, then for …

The longest wavelength that can be absorbed by silicon, which has the bandgap of $1.12 \; \mathrm{eV}$, is $1$. If the longest wavelength that can be absorbed by another material is $0.87 \; \mu \mathrm{m}$, then the bandgap of this material is

The neutral base width of a bipolar transistor, biased in the active region, is $0.5 \; \mu \mathrm{m}$. The maximum electron concentration and the diffusion constant in the base are $10^{14} / \mathrm{cm}^{3}$ and $\mathrm{D}_{n}$ $=25 \mathrm{~cm}^{2} / \mathrm{sec}$ respectively. Assuming negligible recombination in the base, the collector current …

Assuming that the $\beta$ of the transistor is extremely large and $\text{V}_{\text{B E}}=0.7 \mathrm{~V}, \text{I}_{\text{C}}$ and $\text{V}_{\text{CE}}$ in the circuit shown in the figure are

A bipolar transistor is operating in the active region with a collector current of $1 \mathrm{~mA}$. Assuming that the $\beta$ of the transistor is $100$ and the thermal voltage $\left(\mathrm{V}_{\mathrm{T}}\right)$ is $25 \; \mathrm{mV}$, the transconductance $\left(g_{m}\right)$ and the input resistance $\left(r_{n}\right)$ of the transistor …

The value of $\mathrm{C}$ required for sinusoidal oscillations of frequency $1 \; \mathrm{kHz}$ in the circuit of given figure is

In the $\text{op-amp}$ circuit given in the figure, the load current $i_{\text{L}}$ is

In the voltage regulator shown in the given figure, the load current can vary from $100 \mathrm{~mA}$ to $500 \mathrm{~mA}$. Assuming that the Zener diode is ideal (i.e., the Zener knee current is negligibly small and Zener resistance is zero in the breakdown region), the value of $R$ is

In a full-wave rectifier using two ideal diodes, $V_{d i}$ and $V_{i d}$ are the $d c$ and peak values of the voltage respectively across a resistive load. If PIV is the peak inverse voltage of the diode, then the appropriate relationships for this rectifier are

The minimum number of $2$-to-$1$ multiplexers required to realize a $4$-to $1$ mulitiplexer is