Electrical Engineering GATE 2016 Set-2 Questions with Answer

Ques 53 Power Systems

A power system with two generators is shown in the figure below. The system (generators, buses and transmission lines) is protected by six overcurrent relays R₁ to R₆. Assuming a mix of directional and non-directional relays at appropriate locations, the remote backup relays for R₄ are

Ques 54 Power Systems

A power system has 100 buses including 10 generator buses. For the load flow analysis using Newton-Raphson method in polar coordinates, the size of the Jacobian is

Ques 55 Power Systems

The inductance and capacitance of a 400 kV, three-phase, 50 Hz lossless transmission line are 1.6 mH/km/phase and 10 nF/km/phase respectively. The sending end voltage is maintained at 400 kV. To maintain a voltage of 400 kV at the receiving end, when the line is delivering 300 MW load, the shunt compensation required is

Ques 56 Power Systems

A 50 MVA, 10 kV, 50 Hz, star-connected, unloaded three-phase alternator has a synchronous reactance of 1 p.u. and a sub-transient reactance of 0.2 p.u. If a 3-phase short circuit occurs close to the generator terminals, the ratio of initial and final values of the sinusoidal component of the short circuit current is ________.

Ques 57 Power Systems

The single line diagram of a balanced power system is shown in the figure. The voltage magnitude at the generator internal bus is constant and 1.0 p.u. The p.u. reactances of different components in the system are also shown in the figure. The infinite bus voltage magnitude is 1.0 p.u. A three phase fault occurs at the middle of line 2. The ratio of the maximum real power that can be transferred during the pre-fault condition to the maximum real power that can be transferred under the faulted condition is ________.

Ques 58 Power Systems

At no load condition, a 3-phase, 50 Hz, lossless power transmission line has sending-end and receiving-end voltages of 400 kV and 420 kV respectively. Assuming the velocity of traveling wave to be the velocity of light, the length of the line, in km, is ________.

Ques 59 Power Systems

The power consumption of an industry is 500 kVA, at 0.8 p.f. lagging. A synchronous motor is added to raise the power factor of the industry to unity. If the power intake of the motor is 100 kW, the p.f. of the motor is ________.

Ques 60 Power Systems

Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedances of j0.4 p.u., j0.3 p.u. and j0.15 p.u., respectively. If the pre-fault voltage is 1 p.u., for a line-to-ground (L-G) fault at the terminals of the generators, the fault current, in p.u., is ________.

Ques 61 Signals and Systems

Consider a causal LTI system characterized by differential equation dy(t)/dt + (1/6)y(t) = 3x(t). The response of the system to the input, x(t) = 3e^-t/3u(t), where u(t) denotes the unit step function, is

Ques 62 Signals and Systems

Suppose the maximum frequency in a band-limited signal x(t) is 5 kHz. Then, the maximum frequency in x(t)cos(2000πt), in kHz, is ________.

Ques 63 Signals and Systems

Let f(x) be a real, periodic function satisfying f(-x) = -f(x). The general form of its Fourier series representation would be

Ques 64 Signals and Systems

Let x₁(t) ↔ X₁(ω) and x₂(t) ↔ X₂(ω) be two signals whose Fourier Transforms are as shown in the figure below. In the figure, h(t) = e^-2|t| denotes the impulse response. For the system shown above, the minimum sampling rate required to sample y(t), so that y(t) can be uniquely reconstructed from its samples, is

Ques 65 Signals and Systems

The value of the integral 2 ∫_-∞^∞ (sin(2πt)/πt) dt is equal to