GATE

Q. A separately excited dc motor has an armature resistance 𝑅𝑎 = 0.05 Ω. The field excitation is kept constant. At an armature voltage of 100 V, the motor produces a torque of 500 Nm at zero speed. Neglecting all mechanical losses, the no-load speed of the motor (in radian/s) for an armature voltage of […]

Q. A 1000 × 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are (up to 2 decimal places). Ans: 3500 Sol:

Q. The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are 𝑗0.1 pu, 𝑗0.05 pu and 𝑗0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. If the grounding impedance of the generator is 𝑗0.01 pu, then

Q. Consider a non-singular 2×2 square matrix A . If trace(A) = 4 and trace(A2 ) = 5 , the determinant of the matrix A is__________(up to 1 decimal place). Ans: 5.5 Sol:

Q. In the logic circuit shown in the figure, Y is given by (A) Y = ABCD                                              (B) Y = (A + B)(C + D) (C) Y = A + B + C + D                                  (D) Y = AB + CD Ans: Y = AB + CD

Q. The value of the directional derivative of the function 𝛷(𝑥, 𝑦, 𝑧) = 𝑥𝑦2 + 𝑦𝑧2 + 𝑧𝑥2 at the point (2, -1, 1) in the direction of the vector 𝐩 = 𝐢 + 2𝐣 + 2𝐤 is (A) 1                           (B) 0.95                      (C) 0.93                      (D) 0.9 Ans: 1 Sol:

Q. In the figure, the voltages are 𝑣1(𝑡) = 100cos(𝜔𝑡), 𝑣2(𝑡) = 100cos(𝜔𝑡 + 𝜋/18) and 𝑣3(𝑡) = 100cos(𝜔𝑡 + 𝜋/36). The circuit is in sinusoidal steady state, and 𝑅 << 𝜔𝐿. 𝑃1, 𝑃2 and 𝑃3 are the average power outputs. Which one of the following statements is true? (A) 𝑃1 = 𝑃2 = 𝑃3

Q. The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is (A) 11                         (B) 12                         (C) 13                        (D) 14 Ans: 12

Q. 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 (A) 0.532                    (B) 0.632                    (C) 0.707                   (D) 0.866 Ans: 0.866 Sol: In two Wattmeter

Q. Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated appropriately is (are) A. Triac only B. Triac and MOSFET C. Triac and GTO D. Thyristor and Triac Ans: Triac and MOSFET