# GATE EE 2013

 Question 1
In the circuit shown below what is the output voltage $(V_{out})$ if a silicon transistor Q and an ideal op-amp are used?
 A $-15 V$ B $-0.7 V$ C $+0.7 V$ D $+15 V$
Analog Electronics   Operational Amplifiers
Question 1 Explanation:

Using the concept of vitual ground, V=0

$V_{out}=-0.7V$
 Question 2
The transfer function $\frac{V_{2}(s)}{V_{1}(s)}$ of the circuit shown below is
 A $\frac{0.5s+1}{s+1}$ B $\frac{3s+6}{s+2}$ C $\frac{s+2}{s+1}$ D $\frac{s+1}{s+2}$
Control Systems   Mathematical Models of Physical Systems
Question 2 Explanation:

$\frac{V_2(s)}{V_1(s)}=\frac{R+\frac{1}{Cs}}{\frac{1}{Cs}+R+\frac{1}{Cs}}$
$=\frac{1+RCs}{2+RCs}$
$=\frac{1+10 \times 10^3 \times 100 \times 10^{-6}s}{2+10 \times 10^3 \times 100 \times 10^{-6}s}$
$=\frac{s+1}{s+2}$
 Question 3
Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is
 A u(t) B tu(t) C $\frac{t^{2}}{2}u(t)$ D $e^{-t}u(t)$
Signals and Systems   Laplace Transform
Question 3 Explanation:
\begin{aligned} Y(s)&=\frac{1}{s}U(s)=\frac{1}{s^2}\\ y(t)&=tu(t) \end{aligned}
 Question 4
The impulse response of a system is h(t)=tu(t). For an input u(t-1), the output is
 A $\frac{t^{2}}{2}u(t)$ B $\frac{t(t-1)}{2}u(t-1)$ C $\frac{(t-1)^{2}}{2}u(t-1)$ D $\frac{t^{2}-1}{2}u(t-1)$
Signals and Systems   Linear Time Invariant Systems
Question 4 Explanation:
\begin{aligned} h(t) &=tu(t) \\ H(s) &=\frac{1}{s^2} \\ \Rightarrow \; \frac{Y(s)}{U(s)} &=\frac{1}{s^2} \\ Y(s) &=\frac{1}{s^2} \frac{e^{-s}}{s}\\ \Rightarrow \; y(t) &=\frac{(t-1)^2}{2}u(t-1) \end{aligned}
 Question 5
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
 A All the poles of the system must lie on the left side of the $j \omega$ axis B Zeros of the system can lie anywhere in the s-plane C All the poles must lie within |s| = 1 D All the roots of the characteristic equation must be located on the left side of the $j \omega$ axis.
Signals and Systems   Laplace Transform
Question 5 Explanation:
All poles must lie within |Z|=1
 Question 6
Two systems with impulse responses $h_{1}(t) \; and \; h_{2}(t)$ are connected in cascade. Then the overall impulse response of the cascaded system is given by
 A product of $h_{1}(t) \; and \; h_{2}(t)$ B sum of $h_{1}(t) \; and \; h_{2}(t)$ C convolution of $h_{1}(t) \; and \; h_{2}(t)$ D subtraction of $h_{1}(t) \; and \; h_{2}(t)$
Signals and Systems   Linear Time Invariant Systems
Question 6 Explanation:

\begin{aligned} H(s) &=H_1(s)\cdot H_2(s)\\ \Rightarrow \; h(t)&=h_1(t) * h_2(t) \end{aligned}
 Question 7
A source $v_{s}(t)=V \cos 100\pi t$ has an internal impedance of $(4+j3)\Omega$. If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\Omega$ should be
 A 3 B 4 C 5 D 7
Electric Circuits   Network Theorems
Question 7 Explanation:
Using maximum power transfer theorem,
$R_L=|Z|=|4-j3|$
$\;\;=\sqrt{4^2+3^2}=5\Omega$
 Question 8
A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is $10\angle -150^{\circ}$A and if the voltage at the load terminal is $100\angle 60^{\circ}$V, then the
 A load absorbs real power and delivers reactive power B load absorbs real power and absorbs reactive power C load delivers real power and delivers reactive power D load delivers real power and absorbs reactive power
Question 8 Explanation:

Complex power supplied by load $=(100\angle 60^{\circ})(10\angle -150^{\circ})=-866.022-j500 VA$
As supplied active and reactive power are negative.
Load absorbs active and reactive power both.
 Question 9
A single-phase transformer has no-load loss of 64W, as obtained from an open circuit test. When a short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV windings, he measured loss is 81 W. The transformer has maximum efficiency when operated at
 A 50.0% of the rated current B 64.0% of the rated current C 80.0% of the rated current D 88.8% of the rated current
Electrical Machines   Transformers
Question 9 Explanation:
For 90% current,
\begin{aligned} P_{cu} &=(0.9)^2 P_{fl\;cu} \\ P_{fl\;cu} &= \frac{81}{0.81}=100W\\ x&=\sqrt{\frac{P_{core}}{P_{fl\;cu}}}=\sqrt{\frac{64}{100}}=0.8=80\% \end{aligned}
 Question 10
The flux density at a point in space is given by $B=4xa_{x}+2kya_{y}+8a_{z} Wb/m^{2}$. The value of constant k must be equal to
 A -2 B -0.5 C 0.5 D 2
Electromagnetic Fields   Magnetostatic Fields
Question 10 Explanation:
\begin{aligned} \bigtriangledown \cdot B &=0 \\ \left ( \frac{\partial }{\partial x}a_x +\frac{\partial }{\partial y}a_y + \frac{\partial }{\partial z}a_z\right )&(4xa_x+2kya_y+8a_z)=0 \\ 4+2k&=0\\ k&=-2 \end{aligned}
There are 10 questions to complete.