GATE EC question library

The current, $\text{i(t)}$, through a $10 \; \Omega$ resistor in series with an inductance, is given by $i(t)=3+4 \sin \left(100 t+45^{\circ}\right)+4 \sin \left(300 t+60^{\circ}\right)$ Amperes The $\text{RMS}$ value of the current and the power dissipated in the circuit are :

The value of the resistance, $R$, connected across the terminals, $A$ and $B$, which will absorb the maximum power, is

If $L[f(t)]=\frac{2(s+1)}{s^{2}+2 s+5}$ then $f(0+)$ and $f(\infty)$ are given by [Note : 'L' stands for 'Laplace Transform of']

The $\text{RMS}$ value of a rectangular wave of period $T$, having a value of $+V$ for a duration, $T_1(<T)$ and $-V$ for the duration, $T-T_1=T_2$, equals

Two $2 \; \mathrm{H}$ inductance coils are connected in series and are also magnetically coupled to each other the coefficient of coupling being $0.1$. The total inductance of the combination can be

Consider a $\text{DC}$ voltage source connected to a series $\mathrm{R}-\mathrm{C}$ circuit. When the steady-state reaches, the ratio of the energy stored in the capacitor to the total energy supplied by the voltage source, is equal to

A $\text{DC}$ voltage source is connected across a series $\text{R-L-C}$ circuit. Under steady-state conditions, the applied $\text{DC}$ voltage drops entirely across the

For a dipole antenna

A plane eelctromagnetic wave travelling along $+z$ – direction, has its electric field given by $\mathrm{E}_{x}=2 \cos \left({ }^{*} t\right)$ and $\mathrm{E}_{y}=2 \cos \left({ }^{*} t+90^{\circ}\right)$. The wave is

For a short wave radio link between two stations via the ionosphere, the ratio of the maximum usable frequency to the critical frequency

Medium wave radio signals may be received at far off distances at night because

Increased pulse-width in the flat-top sampling, leads to

$v(t)=5[\cos (106 \; \pi t)-\sin (103 \; \pi t) \times \sin (106 \; \pi t)$ represents

A dynamic $\text{RAM}$ consists of

A $\text{PLA}$ can be used

The output of a logic gate is ‘$1$’ when all its inputs are at logic ‘$0$’. Then gate is either

Data can be changed from spatial code to temporal code and vice-versa by using

A class - A transformer coupled, transistor power amplifier is required to deliver a power output of $10$ watts. The maximum power rating of the transistor should not be less than

The threshold voltage of an $n$ channel $\text{MOSFET}$ can be increased by

A small concentration of minority carries is injected into a homogeneous semiconductor crystal at one point. An electric field of $10 \mathrm{~V} . \mathrm{cm}$ is applied across the crystal and this moves the minority carriers a distance of $1 \mathrm{~cm}$ is $20 \; \mu \; \mathrm{sec}$. The mobility (in $\mathrm{cm}^{2} /$ volt. sec) will be