GATE EE 2025 Question Paper (02-Feb-2025) (Shift-2)

The 3-phase modulating waveforms ($v_a(t)$, $v_b(t)$, $v_c(t)$), used in sinusoidal PWM in a voltage source inverter (VSI) are
$v_a(t)=0.8\sin (\omega t)\text{ V}$
$v_b(t)=0.8\sin \left(\omega t-\frac{2\pi }{3}\right)\text{ V}$
$v_c(t)=0.8\sin \left(\omega t+\frac{2\pi }{3}\right)\text{ V}$
where $\omega =2\pi \times 40\text{ rad/s}$ is the fundamental frequency. The modulating waveforms are compared with a $10\text{ kHz}$ triangular carrier whose magnitude varies between $+1$ and $-1$. The VSI has a DC link voltage of $600\text{ V}$ and feeds a star connected motor. The per phase fundamental RMS motor voltage in volts is closest to

An ideal sinusoidal voltage source $v(t)=230\sqrt{2}\sin (2\pi \times 50t)\text{ V}$ feeds an ideal inductor $L$ through an ideal SCR with firing angle $\alpha =0^{\circ }$. If $L=100\text{ mH}$, then the peak of the inductor current, in ampere, is closest to

In the following circuit, the average voltage
$V_0=400\left(1+\frac{\cos \alpha }{3}\right)\text{ V}$
where $\alpha$ is the firing angle. If the power dissipated in the resistor is $64\text{ W}$, then the closest value of $\alpha$ in degrees is

In the system shown below, the generator was initially supplying power to the grid. A temporary LLLG bolted fault occurs at F very close to circuit breaker-1. The circuit breakers open to isolate the line. The fault self-clears. The circuit breakers reclose and restore the line. Which one of the following diagrams best indicates the rotor accelerating and decelerating areas?

An air filled cylindrical capacitor (capacitance $C_0$) of length $L$, with $a$ and $b$ as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Figure (i). In order to increase the capacitance, a dielectric material of relative permittivity ${ϵ}_r$ is inserted inside $50\%$ of the annular region as shown in figure (ii). The value of ${ϵ}_r$ for which the capacitance of the capacitor in figure (ii), becomes $5C_0$ is