GATE EE 2024 Question Paper (11-Feb-2024) (Shift-2)

The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being $P_{max}\sin \delta$, where $\delta$ is the load angle and the mechanical power input is $0.5P_{max}$. A fault occurs on line 2 such that the power output of the generator is less than $0.5P_{max}$ during the fault. After the fault is cleared by opening line 2, the power output of the generator is $\{P_{max}/\sqrt{2}\}\sin \delta$. If the critical fault clearing angle is $\pi /2$ radians, the accelerating area on the power angle curve is______________ times $P_{max}$ (rounded off to 2 decimal places).

Consider the closed-loop system shown in the figure with
$G(s)=\frac{K(s^2-2s+2)}{(s^2+2s+5)}$
The root locus for the closed-loop system is to be drawn for $0\le K<\infty$. The angle of departure (between $0^{\circ }$ and $360^{\circ }$) of the root locus branch drawn from the pole $(-1+j2)$, in degrees, is ______________(rounded off to the nearest integer).

Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of -20 dB/decade at least till 100 rad/sec with the gain crossover frequency being 10 rad/sec. The asymptotic Bode phase plot remains constant at -90° at least till $\omega =10$ rad/sec. The steady-state error of the closed-loop system for a unit ramp input is ______________(rounded off to 2 decimal places).

Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $G(s)$ are given in the table. The value of the gain $K_1(>0)$ for a $50^{\circ }$ phase margin is ______________(rounded off to 2 decimal places).

In the given circuit, the diodes are ideal. The current $I$ through the diode D1 in milliamperes is ______________ (rounded off to two decimal places).