GATE EC 2022 Question Paper (06-Feb-2022) (Shift 1)

Consider the two-dimensional vector field $\vec{F}(x,y)=x\vec{i}+y\vec{j}$, where $\vec{i}$ and $\vec{j}$ denote the unit vectors along the x-axis and the y-axis, respectively. A contour 𝐶 in the x - y plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by two semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral

${\oint }_C\vec{F}(x,y).(dx\vec{i}+dy\vec{j})$

is ________.

The current I in the circuit shown is ________.

Consider the circuit shown in the figure. The current I flowing through the 10 Ω resistor is _________.

The Fourier transform X(jω) of the signal

$\mathrm{x}(\mathrm{t})=\frac{\mathrm{t}}{(1+{\mathrm{t}}^2{)}^2}$

is _______.

Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is 10¹⁷ cm⁻³ and the intrinsic carrier concentration is 10¹⁰ cm⁻³ . Electron and hole diffusion lengths are 2 μm and 1 μm, respectively.

The left side of the bar (x = 0) is uniformly illuminated with a laser having photon energy greater than the bandgap of the semiconductor. Excess electron-hole pairs are generated ONLY at x = 0 because of the laser. The steady state electron density at x = 0 is 10¹⁴ cm⁻³ due to laser illumination. Under these conditions and ignoring electric field, the closest approximation (among the given options) of the steady state electron density at x = 2 μm, is ___________ .