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⚑ Graduate Aptitude Test in Engineering

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🎯 Today's GATE EE Practice Target

Q1. A 3-phase, 4-pole, 50 Hz induction motor runs at a rotor speed of 1440 rpm. What is the fractional rotor slip (s) and rotor electrical frequency? GATE EE β€’ Electrical Machines
πŸ’‘ Solution (Option A): Synchronous speed N_s = 120 * f / P = 120 * 50 / 4 = 1500 rpm. Slip s = (N_s - N_r) / N_s = (1500 - 1440) / 1500 = 60 / 1500 = 0.04 (4%). Rotor induced frequency f_r = s * f = 0.04 * 50 = 2.0 Hz.
Q2. An open-loop transfer function is given by G(s)H(s) = K / [s(s+1)(s+2)]. What are the angles of the root locus asymptotes as s approaches infinity? GATE EE β€’ Control Systems
πŸ’‘ Solution (Option B): Number of poles P = 3 (at s = 0, -1, -2) and zeros Z = 0. Number of asymptotes = P - Z = 3. Asymptote angles ΞΈ_k = (2k + 1) * 180Β° / (P - Z) for k = 0, 1, 2. For k = 0: ΞΈβ‚€ = 180Β° / 3 = 60Β°. For k = 1: θ₁ = 3 * 180Β° / 3 = 180Β°. For k = 2: ΞΈβ‚‚ = 5 * 180Β° / 3 = 300Β°.
Q3. In an ideal DC-DC Buck converter operating in continuous conduction mode (CCM), the DC input voltage is 100 V and the switching duty cycle D is 0.40. What is the average output DC voltage? GATE EE β€’ Power Electronics
πŸ’‘ Solution (Option B): In a Buck (step-down) DC-DC converter, the output voltage V_o is related to the input voltage V_in by V_o = D * V_in. With D = 0.40 and V_in = 100 V: V_o = 0.40 * 100 = 40 V.

πŸ“š GATE 30-Year PYQ Khazana & Topper Registers

Power Systems & Switchgear

Transmission line parameters (A, B, C, D), surge impedance loading (SIL), symmetrical & unsymmetrical faults (LG, LL, LLG), equal area criterion, and differential protection.

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Electrical Machines & Transformers

Transformer equivalent circuits, voltage regulation, open/short circuit tests, autotransformers, DC machine speed control (Ward-Leonard), and synchronous alternator V-curves.

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Power Electronics & Control Systems

SCR firing circuits, 1-phase & 3-phase converter average voltages, inverter harmonics (THD), State space representation, Nyquist stability contour, and lead-lag compensators.

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