GATE EE 2015 Question Paper (07-Feb-2015) (Shift 2)

Two three-phase transformers are realized using single-phase transformers as shown in the figure.



The phase different (in degree) between voltage $V_{1}and{V}_2$ is _____________.

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables x and y. the integration time step is h.

$\begin{array}{l}\frac{x_{k+1}-x_k}{h}=y_k\\ \frac{y_{k+1}-y_k}{h}=-x_k\end{array}$

For this discrete-time system, which one of the following statements is TRUE?

The unit step response of a system with the transfer function $G\left(s\right)=\frac{1-2s}{1+s}$ is given by which one of the following waveforms?

An open loop transfer function G(s) of a system is

$G\left(s\right)=\frac{K}{s\left(s+1\right)\left(s+2\right)}$

for a unity feedback system, the breakaway point of the root loci on the real axis occurs at.

For the system governed by the set of equations:

$\begin{array}{l}\frac{d{x}_1}{dt}=2x_1+x_2+u\\ \frac{d{x}_2}{dt}=-2x_1+u\\ y=3x_1\end{array}$

the transfer function $Y\left(s\right)/U\left(s\right)$ is given by