GATE EE 2018 Question Paper (10-Feb-2018) (Shift 2)

The unit step response y(t) of a unity feedback system with open loop transfer function $G\left(s\right)H\left(s\right)=\frac{k}{{\left(s+1\right)}^2\left(s+2\right)}$ is shown in the figure. The value of K is _______ (up to 2 decimal places.)

A three-phase load is connected to a three-phase balanced supply as shown in the figure. If Vₐₙ= 100∠ 0° V, V${}_{bn}$ = 100∠ - 120° V and V${}_{cn}$ =100∠-240° V (angles are considered positive in the anti-clockwise direction), the value of R for zero current in the neutral wire is ___________Ω (up to 2 decimal places).

The voltage across the circuit in the figure, and the current through it, are given by the following expressions:

𝑣(𝑡) = 5 – 10 cos (𝜔𝑡 + 60°) V

𝑖(𝑡) = 5 + Xcos (𝜔𝑡) A

where 𝜔 = 100𝜋 radian/s. If the average power delivered to the circuit is zero, then the value of X (in Ampere) is _____ (up to 2 decimal places).

A phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given by $V_O=\frac{Vm}{2\pi }\left(3+cos\alpha \right).$ Where 𝑉${}_{\text{m}}$ = 80𝜋 volts and 𝛼 is the firing angle. If the power delivered to the lossless battery is 1600 W, 𝛼 in degree is________ (up to 2 decimal places).

The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of 100 V. The converters have inductors of identical value. The load resistance is 1 Ω. The capacitor voltage has negligible ripple. Both converters operate in the continuous conduction mode. The switching frequency is 1 kHz, and the switch control signals are as shown. The circuit operates in the steady state. Assuming that the converters share the load equally, the average value of i${}_{S1}$, the current of switch S1 (in Ampere), is _____ (up to 2 decimal places).