Question 1

If the input x(t) and output y(t) of a system are related as y(t) = max(0, x(t)), then the system is

Accepted Answer

non-linear and time-invariant. The system is non-linear because it involves the maximum function, which does not satisfy the principle of superposition, and it is time-invariant since the output does not change if the input is shifted in time.

Question 2

Two discrete-time linear time-invariant systems have impulse responses h1[n] = δ[n−1] + δ[n+1] and h2[n] = δ[n−1] + δ[n+1], where δ[n] is the Kronecker delta. The overall system is

Accepted Answer

δ[n−2] + 2δ[n] + δ[n+2]. The correct option combines the effects of both impulse responses through convolution, resulting in the sum of shifted delta functions. Each impulse response contributes to the overall system output, leading to the presence of the central term with a coefficient of 2, indicating that the system amplifies the response at n=0.

Question 3

Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is N_L. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and

Accepted Answer

N_L x (N-1). The sub-matrix M represents the relationship between the changes in voltage magnitudes at PQ buses and the changes in angles at all buses except the slack bus. Since there are N_L PQ buses and the slack bus is excluded, the dimension of M is N_L rows and (N-1) columns, corresponding to the remaining buses.

Question 4

Inductance is measured by

Accepted Answer

Maxwell bridge. The Maxwell bridge is specifically designed to measure inductance by balancing the bridge circuit, making it suitable for precise inductance measurements in electrical engineering.

Question 5

In the Nyquist plot of the open-loop transfer function G(s)H(s) = (3s + 5)/(s - 1) corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at

Accepted Answer

G(s)H(s) = 3. The infinite semicircular arc maps to the value of G(s)H(s) as s approaches infinity: lim (3s+5)/(s-1) = 3. So the arc maps to G(s)H(s)=3, which is option 2, not the stored option 1.

Question 6

Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant o

Accepted Answer

-1, 1. In a unity-gain negative feedback system with a proportional-integral controller, the controller output stabilizes to a value that compensates for the steady-state error, leading to a final output of -1 for the plant, while the output of the plant reaches 1 due to the nature of the system and the input.

Question 7

The following columns present various modes of induction machine operation and the ranges of slip

A
Mode of operation
a. Running in generator mode
b. Running in motor mode
c. Plugging in motor mode

B
Range of Slip
p) From 0.0 to 1.0
q) From 1.0 to 2.0
r) From -1.0 to 0.0

The correct mat

Accepted Answer

a-r, b-p, and c-q. The correct option matches running in generator mode (a) with a negative slip range (r), indicating the machine is supplying power back to the grid. Running in motor mode (b) corresponds to a positive slip range (p), where the machine consumes power to operate. Plugging in motor mode (c) involves a higher slip range (q) as it represents a rapid deceleration or reversal of the motor's direction.

Question 8

A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is

Accepted Answer

95 Hz. Synchronous speed Ns=120*50/10=600 rpm, so slip s=(600-540)/600=0.1. The rotor current frequency due to the backward field is (2-s)f=(1.9)(50)=95 Hz.

Question 9

A continuous-time system that is initially at rest is described by dy(t)/dt + 3y(t) = 2x(t), where x(t) is the input voltage and y(t) is the output voltage. The impulse response of the system is

Accepted Answer

2e⁻³t u(t). The correct option represents the impulse response derived from the system's differential equation, which can be solved using the Laplace transform. The term 'u(t)' indicates that the response is causal, and the exponential decay factor '2e^(-3t)' reflects the system's dynamics, confirming it matches the form of the impulse response.

Question 10

The Z-transform of a discrete signal x[n] is
X(z) = 4z / ((z − 1/5)(z − 2/3)(z − 3)) with ROC = R.
Which one of the following statements is true?

Accepted Answer

Discrete-time Fourier transform of x[n] converges if R is 2/3 < |z| < 3. The DTFT converges iff the ROC includes the unit circle. Poles are at 1/5, 2/3, and 3; the ROC 2/3<|z|<3 contains |z|=1, so the DTFT converges. A right-sided sequence would have ROC |z|>3, which excludes the unit circle, so that statement is false.

Question 11

For the three-bus power system shown in the figure, the trip signals to the circuit breakers B1 to B9 are provided by overcurrent relays R1 to R9, respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at

Accepted Answer

R3 and R4 are directional overcurrent relays blocking faults towards Line 1 and Line 2, respectively, R7 is directional overcurrent relay blocking faults towards Line 3 and R5 is directional overcurrent relay blocking faults towards bus 2. The correct option ensures that each relay effectively isolates faults in their respective lines while preventing unnecessary disconnections in other parts of the system. By using directional relays R3, R4, R7, and R5, the system can selectively trip only the affected sections, maintaining stability and minimizing disruption.

Question 12

The expressions of fuel cost of two thermal generating units as a function of the respective power generation P_G1 and P_G2 are given as
F1(P_G1) = 0.1aP_G1² + 40 P_G1 + 120 Rs/hour 0 MW ≤ P_G1 ≤ 350 MW
F2(P_G2) = 0.2P_G2² + 30 P_G2 + 100 Rs/hour 0 MW ≤ P_G2 ≤ 300 MW
where a is a constant.

Accepted Answer

P_G1 will decrease and F will increase. Increasing the value of 'a' in the fuel cost function F1(P_G1) raises the quadratic coefficient, making the cost of generating power at P_G1 more expensive. As a result, to minimize costs while maintaining the total load of 290 MW, P_G1 must decrease, leading to an overall increase in the total generation cost F.

Question 13

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

(A) If an LTI system is causal, it is stable

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

(C) If a discrete time LTI system has an impulse response h[n] of finite duration the sy

Accepted Answer

(C). A discrete time LTI system with a finite duration impulse response means that the system's output will eventually settle to a steady state, ensuring that it does not produce unbounded outputs for bounded inputs, which is the definition of stability.

Question 14

The bus admittance (Ybus) matrix of a 3-bus power system is given below.

1 2 3
1 -j15 j10 j5
2 j10 -j13.5 j4
3 j5 j4 -j8

Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?

Accepted Answer

(A) Line charging capacitor of finite value is present in all three lines. Option A cannot be true because the negative imaginary components in the Ybus matrix indicate the presence of capacitive elements, and having line charging capacitors in all three lines would lead to an overall positive imaginary part, which contradicts the given Ybus values.

Question 15

Consider a lead compensator of the form K(s) = (1 + s/a) / (1 + s/(βa)), β > 1, a > 0. The frequency at which this compensator produces maximum phase lead is 4 rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of K(s), is 6

Accepted Answer

2, 4. The correct option is right because it satisfies the conditions for maximum phase lead and gain amplification at the specified frequency. The values of a and β must be chosen such that the compensator's phase lead reaches its peak at 4 rad/s while providing a gain of 6 dB, which is achieved with a = 2 and β = 4.

Question 16

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

Accepted Answer

0.5 leading. The power factor is calculated using the formula for real power in a balanced three-phase system, which relates the total power, line current, and phase voltage. Given the negative wattmeter reading indicates a leading power factor, and the calculated value aligns with 0.5, it confirms that the load is indeed operating at a 0.5 leading power factor.

Question 17

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 infinite bus having a voltage of magnitude |V3| = 1.0 p.u. and angle of -15°. A variable current source, |I|∠φ is connected at bus 1 and controlled such th

Accepted Answer

Bus 1 P - |V| bus
Bus 2 P - Q bus
Bus 3 Slack bus. Bus 1 is a P - |V| bus because it maintains a constant voltage magnitude while allowing the active power to vary. Bus 2 is a P - Q bus as it can absorb or supply both active and reactive power, and Bus 3 is the slack bus, which balances the system by providing the necessary power to maintain the overall power flow.

Question 18

In the figure, the electric field E and the magnetic field B point to x and z directions, respectively, and have constant magnitudes. A positive charge 'q' is released from rest at the origin. Which of the following statement(s) is/are true.

Accepted Answer

The charge will progress in the direction of y.. The charge will progress in the direction of y because the electric field exerts a force on the positive charge, causing it to accelerate in that direction, while the magnetic field does not exert a force in the y direction when the charge is initially at rest.

Question 19

In a given 8-bit general purpose micro-controller there are following flags. C - Carry, A - Auxiliary Carry, O - Overflow flag, P - Parity (0 for even, 1 for odd) R0 and R1 are the two general purpose registers of the micro-controller. After execution of the following instructions, the dec

Accepted Answer

2. The correct option is 2 because the addition of R0 (0x60) and R1 (0x46) results in a sum that sets the Auxiliary Carry (A) and Overflow (O) flags, while the Carry (C) and Parity (P) flags remain clear. This corresponds to the binary pattern 0010, which is 2 in decimal.

Question 20

A surveyor has to measure the horizontal distance from her position to a distant reference point C. Using her position as the center, a 200 m horizontal line segment is drawn with the two endpoints A and B. Points A, B, and C are not collinear. Each of the angles ∠CAB and ∠CBA are measured

Accepted Answer

2603. With AB=200 and base angles 87.8 degrees, the apex C lies above the midpoint; its distance is 100*tan(87.8)=100*26.03=2603 m. The stored 2063 is wrong; the answer is 2603.

Question 21

A three phase, 50 Hz, 6 pole induction motor runs at 960 rpm. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is

Accepted Answer

96. Ns=120*50/6=1000 rpm, so slip s=(1000-960)/1000=0.04. With stator copper, core, and rotational losses neglected, efficiency equals (1-s)=0.96, i.e. 96%.

Question 22

Consider the standard second-order system of the form (ωₙ²)/(s²+2ζωₙ s+ωₙ²) with the poles p and p^* having negative real parts. The pole locations are also shown in the figure. Now consider two second-order systems as defined below:
System 1: ωₙ = 3 rad/sec and θ = 60°
System 2: ωₙ = 1 ra

Accepted Answer

Settling time of System 2 is more than that of System 1.. The settling time of a second-order system is influenced by the natural frequency ( ext{n}) and damping ratio ( ext{z}). System 1, with a higher natural frequency of 3 rad/sec, will settle faster than System 2, which has a lower natural frequency of 1 rad/sec, despite the difference in damping angles.

Question 23

The table lists two instrument transformers and their features:

Instrument Transformers | Features
X) Current Transformer (CT)
Y) Potential Transformer (PT)

P) Primary is connected in parallel to the grid
Q) Open circuited secondary is not desirable
R) Primary current is the line current

Accepted Answer

X matches with Q and R; Y matches with P and S.. Current Transformers (CT) are designed to measure line current, hence their primary is connected in series (not parallel), and an open-circuited secondary is undesirable as it can lead to high voltage. Potential Transformers (PT), on the other hand, are connected in parallel to the grid, and the secondary burden does affect the primary current, making the correct matches Q and R for CT, and P and S for PT.

Question 24

If the following switching devices have similar power ratings, which one of them is the fastest?

Accepted Answer

Power MOSFET. Power MOSFETs are known for their high switching speeds due to their voltage-controlled operation, which allows for rapid turn-on and turn-off times compared to other devices like SCRs and GTOs that rely on current control.

Question 25

A single-phase triac based A C voltage controller feeds a series R L load. The input A C supply is 230 V, 50 Hz. The values of R and L are 10 Ω and 18.37 mH, respectively. The minimum triggering angle of the triac to obtain controllable output voltage is

Accepted Answer

30°. The minimum triggering angle of 30° is required to ensure that the triac can effectively control the output voltage across the RL load, allowing for sufficient time for the inductor to build up its magnetic field and avoid excessive current spikes.

Question 26

Consider the discrete-time systems T1 and T2 defined as follows:

{T1 x}[n] = x[0] + x[1] +... + x[n]

{T2 x}[n] = x[0] + 1/2 x[1] +... + 1/n x[n]

Which one of the following statements is true?

Accepted Answer

T1 and T2 are not BIBO stable.. Both T1 and T2 fail to be BIBO stable because their output can become unbounded for bounded input signals. T1 accumulates all previous inputs, leading to an ever-increasing output, while T2's weighted sum diverges as n increases, indicating instability.

Question 27

A 3-phase, 11 kV, 10 MVA synchronous generator is connected to an inductive load of power factor (√3/2) via a lossless line with a per-phase inductive reactance of 5 Ω. The per-phase synchronous reactance of the generator is 30 Ω with negligible armature resistance. If the generator is pro

Accepted Answer

0.87 lagging.. The correct option is right because the power factor at the terminal of the generator is determined by the relationship between the voltage, current, and the reactances involved. Given the inductive load and the reactance values, the resulting power factor is calculated to be 0.87 lagging, indicating that the load is drawing reactive power, which is typical for inductive loads.

Question 28

For a two-phase network, the phase voltages Vp and Vq are to be expressed in terms of sequence voltages Vα and Vβ as [Vp Vq]^T = S [Vα Vβ]^T. The possible option(s) for matrix S is/are

Accepted Answer

[1 1; 1 -1]. The correct matrix S, [1 1; 1 -1], effectively transforms the sequence voltages Vα and Vβ into the phase voltages Vp and Vq by combining them in a way that reflects the characteristics of a two-phase system, where Vp is the sum of both sequence voltages and Vq is their difference.

Question 29

Which one of the following statements is true about the small signal voltage gain of a MOSFET based single stage amplifier?

Accepted Answer

Common source amplifier is inverting and common gate amplifier is non-inverting amplifier. The common source amplifier inverts the input signal, producing a 180-degree phase shift, while the common gate amplifier does not invert the signal, maintaining the same phase as the input. This distinction is fundamental to understanding the behavior of these amplifier configurations.

Question 30

A nullator is defined as a circuit element where the voltage across the device and the current through the device are both zero. A series combination of a nullator and a resistor of value, R, will behave as a

Accepted Answer

nullator.. A nullator inherently has both zero voltage and zero current, so when combined in series with a resistor, the entire circuit will still exhibit these nullator characteristics, effectively behaving as a nullator.

Question 31

Consider a discrete-time linear time-invariant (LTI) system S, where y[n] = S{x[n]}

Let

S{δ[n]} = { 1, n ∈ {0,1,2}
 { 0, otherwise

where δ[n] is the discrete-time unit impulse function. For an input signal x[n], the output y[n] is

Accepted Answer

x[n] + x[n - 1] + x[n - 2]. The correct option is right because the output of the LTI system for the input signal x[n] is determined by the system's response to the impulse function, which indicates that the output is a weighted sum of the current and previous input values, specifically x[n], x[n-1], and x[n-2]. This aligns with the system's impulse response.

Question 32

During a power failure, a domestic household uninterruptible power supply (UPS) supplies AC power to a limited number of lights and fans in various rooms. As per a Newton-Raphson load-flow formulation, the UPS would be represented as a

Accepted Answer

Slack bus. The UPS acts as a slack bus because it provides a constant voltage and can adjust its output to balance the power supply and demand during a power failure, ensuring stability in the system.

Question 33

The operating region of the developed torque (T_em) and speed (ω) of an induction motor drive is given by the shaded region OQRF in the figure. The load torque (T_L) characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which

Accepted Answer

O – P – S. The trajectory O – P – S is the most direct path from the initial to the final operating point, minimizing the time taken by avoiding unnecessary intermediate points and maintaining a more efficient transition through the operating region.

Question 34

The input voltage v(t) and current i(t) of a converter are given by,

v(t) = 300 sin(ωt) V

i(t) = 10 sin(ωt − π/6) + 2 sin(3ωt + π/6) + sin(5ωt + π/2) A

where, ω = 2π × 50 rad/s. The input power factor of the converter is closest to

Accepted Answer

0.845. Voltage is purely fundamental, so only the fundamental current (10 A peak, lagging 30 deg) delivers real power. Power factor = (I1_rms/I_total_rms) x cos(30) = (10/sqrt(105)) x 0.866 = 0.845. The stored 0.867 is wrong.

Question 35

Instrument(s) required to synchronize an alternator to the grid is/are

Accepted Answer

Synchroscope. A synchroscope is specifically designed to indicate the phase difference between the voltage of the alternator and the grid, allowing operators to synchronize the two systems effectively.

Question 36

Let continuous-time signals x1(t) and x2(t) be

x1(t) = { 1, t ∈ [0,1]
 { 2 − t, t ∈ [1,2]
 { 0, otherwise

and

x2(t) = { t, t ∈ [0,1]
 { 2 − t, t ∈ [1,2]
 { 0, otherwise

Consider the convolution y(t) = x1(t) * x2(t). Then ∫_(−∞)^(∞) y(t) dt is

Accepted Answer

1.5. Integral of y = (integral of x1)(integral of x2). Integral x1 = 1 (on [0,1]) + 0.5 (triangle) = 1.5; integral x2 = 0.5+0.5 = 1. Product = 1.5.

Question 37

Let G(s) = 1/((s+1)(s+2)). Then the closed-loop system shown in the figure below is

Accepted Answer

stable for all K > 1.. The closed-loop system is stable for all K > 1 because the poles of the characteristic equation move to the left half of the s-plane as K increases, ensuring that the system remains stable.

Question 38

A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. A linear magnetic circuit. The external resistance, in Ω, that must

Accepted Answer

23.28. To reduce the speed of a DC series motor by half, the armature voltage must also be halved, which requires adding external resistance to drop the voltage across the armature. The calculated resistance of approximately 23.28 Ω accounts for the necessary voltage drop while considering the motor's characteristics and the load torque relationship.

Question 39

A 3-phase, 400 V, 4 pole, 50 Hz star connected induction motor has the following parameters referred to the stator:
R'2 = 1Ω, Xs = X'r = 2Ω
Stator resistance, magnetizing reactance and core loss of the motor are neglected.
The motor is run with constant V/f control from a drive. For maximu

Accepted Answer

100 V and 12.5 Hz. At standstill (s=1) maximum torque occurs when total leakage reactance equals R2'=1 ohm. Since Xs+Xr'=4 ohm at 50 Hz, the frequency must drop to 50*(1/4)=12.5 Hz; keeping V/f=400/50=8 gives V=8*12.5=100 V. So 100 V and 12.5 Hz.

Question 40

The 3-phase modulating waveforms (vₐ(t), v_b(t) and v_c(t)), used in sinusoidal PWM in a V Voltage Source Inverter (V SI) are

vₐ(t) = 0.8 sin(ωt) V

v_b(t) = 0.8 sin(ωt − 2π/3) V

v_c(t) = 0.8 sin(ωt + 2π/3) V

where ω = 2π × 40 rad/s is the fundamental frequency. The modulating waveforms

Accepted Answer

169.71. In linear sinusoidal PWM the per-phase fundamental peak = ma x Vdc/2 = 0.8 x 300 = 240 V. RMS = 240/sqrt(2) = 169.71 V. Stored 212.13 V is incorrect.

Question 41

An ideal sinusoidal voltage source v(t) = 230√2 sin(2π × 50t) V feeds an ideal inductor L through an ideal SCR with firing angle α = 0°. If L = 100 mH, then the peak of the inductor current, in ampere, is closest to.

Accepted Answer

20.71. The peak current through the inductor can be calculated using the relationship between the peak voltage and the inductance, considering the firing angle of the SCR. With a firing angle of 0°, the full peak voltage is applied across the inductor, leading to a peak current of approximately 20.71 A.

GATE Technical: Electrical Engineering (EE) questions with solutions

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