GATE Technical: ELECTRICAL ENGINEERING questions with solutions

Q1. In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is

1. 0
2. 45
3. 60
4. 90

Answer: 45

The developed reluctance torque in a salient pole synchronous motor reaches its maximum at a load angle of 45 degrees because this angle optimally balances the magnetic forces, maximizing the torque produced by the difference in reluctance between the rotor and stator.

Q2. A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. With which one of the following is true for instantaneous load voltage and current?

1. vₒ ≥ 0 & iₒ < 0
2. vₒ < 0 & iₒ < 0
3. vₒ ≥ 0 & iₒ ≥ 0
4. vₒ < 0 & iₒ ≥ 0

Answer: vₒ ≥ 0 & iₒ ≥ 0

In a fully controlled rectifier with an anti-parallel diode, the load voltage can be controlled to be positive (vₒ ≥ 0) when the thyristors are conducting, and the load current will also be positive (iₒ ≥ 0) as it flows in the same direction as the voltage, indicating that both voltage and current are in the forward direction.

Q3. Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is

1. 0.532
2. 0.632
3. 0.707
4. 0.866

Answer: 0.866

In a balanced three-phase system, when one wattmeter reads half of the other, it indicates a specific relationship between the active power and the reactive power, leading to a power factor of 0.866, which corresponds to a cosine of 30 degrees.

Q4. A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x-y plane to be a conducting ground plane. Take ε0 = 8.85×10⁻¹² F/m. The z component of the E field at (0, 0, 0.1) is closest to

1. 899.18 V/m
2. -899.18 V/m
3. 999.09 V/m
4. -999.09 V/m

Answer: -999.09 V/m

By image theory, place -1 nC at z=-0.2. At (0,0,0.1) the real charge (0.1 m away) gives E_z=-899.18 V/m and the image charge (0.3 m away) gives E_z=-99.91 V/m, both in the -z direction. The total is about -999.09 V/m.

Q5. A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

1. k x(t), where k is an eigenvalue
2. k e^(jωt) x(t), where k is an eigenvalue and e^(jωt) is a complex exponential signal
3. x(t) e^(jωt), where e^(jωt) is a complex exponential signal
4. k H(ω), where k is an eigenvalue and H(ω) is a frequency response of the system

Answer: k x(t), where k is an eigenvalue

An eigenfunction of an LTI system is defined as a signal that, when passed through the system, results in a scaled version of itself, represented by k x(t), where k is a constant (eigenvalue). This property indicates that the system's response to the eigenfunction is proportional to the input, maintaining its form.

Q6. Consider a system governed by the following equations dx1(t)/dt = x2(t) - x1(t) dx2(t)/dt = x1(t) - x2(t) The initial conditions are such that x1(0) < x2(0) < ∞. Let x1f = lim(t→∞) x1(t) and x2f = lim(t→∞) x2(t). Which one of the following is true?

1. x1f < x2f < ∞
2. x2f < x1f < ∞
3. x1f = x2f < ∞
4. x1f = x2f = ∞

Answer: x1f = x2f < ∞

The system of equations describes a coupled linear system where both variables approach the same limit over time due to their symmetric behavior. Given the initial condition that x1(0) is less than x2(0), both variables converge to the same finite value as time approaches infinity.