GATE EE 2021 Question Paper (07-Feb-2021) (Shift 1)

A 100 Hz square wave, switching between 0 V and 5 V, is applied to a CR high-pass filter circuit as shown. The output voltage waveform across the resistor is 6.2 V peak-to-peak. If the resistance R is 820 Ω, then the value C is ______ μF.

(Round off to 2 decimal places)

An alternator with internal voltage of 1∠δ₁ p.u. and synchronous reactance of 0.4 p.u. is connected by a transmission line of reactance 0.1 p.u. to a synchronous motor having synchronous reactance 0.35 p.u. and internal voltage of 0.85 ∠δ₂ p.u. If the real power supplied by the alternator is 0.866 p.u., then (δ₁ - δ₂) is _____ degrees. (Round off to 2 decimal places.)

(Machines are of non-salient type. Neglect resistances)

Let A be a 10 × 10 matrix such that A⁵ is a null matrix, and let I be the 10 × 10 identity matrix. The determinant of A + I is ______.

The power input to a 500 V, 50 Hz, 6-pole, 3-phase induction motor running at 975 RPM is 40 kW. The total stator losses are 1 kW. If the total friction and windage losses are 2.025 kW, then the efficiency is _____%

The causal signal with z-transform z ²(z - a) ⁻²is

(u[n] is the unit step signal)