Electrical Engineering GATE 2023 Questions with Answer

Ques 53 Power Systems

A 50 Hz, 275 kV line of length 400 km has the following parameters:
Resistance, R=0.035 Ω/km;
Inductance, L=1 mH/km;
Capacitance, C=0.01 μF/km.
The line is represented by the nominal-π model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by V_S and V_R, respectively) maintained at 275 kV, the phase angle difference (δ) between V_S and V_R required for maximum possible active power to be delivered to the receiving end, in degrees, is _______. (Round off to 2 decimal places).

31.44 is the correct answer.

Ques 54 Power Systems

A 3-phase, star-connected, balanced load is supplied from a 3-phase, 400 V (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is -400 W and the line current is I_R=2 A (rms), then the power factor of the load per phase is _______.

Unity

0.5 leading

0.866 leading

0.707 lagging

Ques 55 Power Systems

The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is an infinite bus having a voltage of magnitude |V₃|=1.0 p.u. and an angle of -15°. A variable current source, |I|∠φ, is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u. and the phase angle of the source current, φ=θ₁±π/2, where θ₁ is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as _______.

Bus 1: Slack bus,
Bus 2: PV bus,
Bus 3: PQ bus

Bus 1: PV bus,
Bus 2: PV bus,
Bus 3: Slack bus

Bus 1: PQ bus,
Bus 2: Slack bus,
Bus 3: PQ bus

Bus 1: PV bus,
Bus 2: PQ bus,
Bus 3: Slack bus

Ques 56 Power Systems

The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a Y-Δ transformer. The positive, negative, and zero-sequence diagrams of the system are shown in figures (ii), (iii), and (iv), respectively. All reactances in the sequence diagrams are in p.u. For a bolted line-to-line fault (fault impedance = zero) between phases 'b' and 'c' at bus 1, neglecting all pre-fault currents, the magnitude of the fault current (from phase 'b' to 'c') in p.u. is _______. (Round off to 2 decimal places).

3.09 is the correct answer.

Ques 57 Power Systems

A balanced delta connected load consisting of the series connection of one resistor (R=15 Ω) and a capacitor (C=212.21 μF) in each phase is connected to three-phase, 50 Hz, 415 V supply terminals through a line having an inductance of L=31.83 mH per phase, as shown in the figure. Considering the change in the supply terminal voltage with loading to be negligible, the magnitude of the voltage across the terminals V_AB in Volts is _______. (Round off to the nearest integer).

390 is the correct answer.

Ques 58 Signals and Systems

A continuous-time system that is initially at rest is described by

where x(t) is the input voltage and y(t) is the output voltage. The impulse response of the system is _______.

3e^-2t

(1/3)e^-2tu(t)

2e^-3tu(t)

2e^-3t

Ques 59 Signals and Systems

The Fourier transform X(ω) of the signal x(t) is given by X(ω)=1, for

Which one of the following statements is true?

x(t) tends to be an impulse as W₀→∞.

x(0) decreases as W₀ increases.

At t=π/(2W₀), x(t)=-1/π.

At t=π/(2W₀), x(t)=1/π.

Ques 60 Signals and Systems

The Z-transform of a discrete signal x[n] is

with ROC=R. Which one of the following statements is true?

Discrete-time Fourier transform of x[n] converges if R is |z|>3.

Discrete-time Fourier transform of x[n] converges if R is 2/3<|z|<3.

Discrete-time Fourier transform of x[n] converges if R is such that x[n] is a left-sided sequence.

Discrete-time Fourier transform of x[n] converges if R is such that x[n] is a right-sided sequence.

Ques 61 Signals and Systems

Which of the following statement(s) is/are true?

If an LTI system is causal, it is stable.

A discrete time LTI system is causal if and only if its response to a step input u[n] is 0 for n<0.

If a discrete time LTI system has an impulse response h[n] of finite duration, the system is stable.

If the impulse response 0<|h[n]|<1 for all n, then the LTI system is stable.

Ques 62 Signals and Systems

For the signals x(t) and y(t) shown in the figure, z(t)=x(t)y(t) is maximum at t=T₁. Then T₁ in seconds is _______. (Round off to the nearest integer).

1 is the correct answer.

Ques 63 Signals and Systems

The period of the discrete-time signal x[n] described by the equation

is N=___________. (Round off to the nearest integer).

48 is the correct answer.

Ques 64 Signals and Systems

The discrete-time Fourier transform of a signal x[n] is X(Ω)=(1+cos Ω)e^-jΩ. Consider that x_p[n] is a periodic signal of period N=5 such that

Note that x_p[n]=Σ^N-1_k=0a_ke^j2πkn/N. The magnitude of the Fourier series coefficient a₃ is _______. (Round off to 3 decimal places).

0.363 is the correct answer.

Ques 65 Signals and Systems

A signal x(t)=2cos(180πt)cos(60πt) is sampled at 200 Hz and then passed through an ideal low pass filter having a cut-off frequency of 100 Hz. The maximum frequency present in the filtered signal in Hz is _______. (Round off to the nearest integer).

90 is the correct answer.

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Electrical Engineering GATE 2023 Questions with Answer