GATE Electrical Engineering 2022

Question 1
The transfer function of a real system, H(s), is given as:
H(s)=\frac{As+B}{s^2+Cs+D}
where A, B, C and D are positive constants. This system cannot operate as
A
low pass filter.
B
high pass filter
C
band pass filter.
D
an integrator.
Electric Circuits   Magnetically Coupled Circuits, Network Topology and Filters
Question 1 Explanation: 
Put s=0, H(0)=\frac{A \times 0+B}{0+C \times 0+D}=\frac{B}{D}
So, the system pass low frequency component. Put s=\infty , H(\infty )=0
For high pass filter, high frequency component should be non zero. Hence this system cannot be operated as high pass filter.
Question 2
For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is
A
0
B
1
C
100
D
infinite
Analog Electronics   Small Signal Analysis
Question 2 Explanation: 
For ideal MOSFET, i_G=0
Therefore, Current gain, A_I=\frac{i_s}{i_G}=\infty
Question 3
The most commonly used relay, for the protection of an alternator against loss of excitation, is
A
offset Mho relay.
B
over current relay.
C
differential relay
D
Buchholz relay.
Power Systems   Switch Gear and Protection
Question 4
The geometric mean radius of a conductor, having four equal strands with each strand of radius 'r', as shown in the figure below, is

A
4r
B
1.414r
C
2r
D
1.723r
Power Systems   Performance of Transmission Lines, Line Parameters and Corona
Question 4 Explanation: 
Redraw the configuration:

\therefore \; GMR=(r' \times 2r\times 2r\times 2\sqrt{2}r)^{1/4}
Where, r'=0.7788r
Hence, GMR=1.723r
Question 5
The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices are
A
1.1, 0.15 and 0.08
B
0.15, 0.15 and 0.35
C
0.2, 0.2 and 0.2
D
0.1, 0.3 and 0.1
Power Systems   Fault Analysis
Question 5 Explanation: 
We have,
X_0 \gt X_1=X_2
(for 3-\phi transposed transmission line)
Question 6
The steady state output (V_{out}), of the circuit shown below, will

A
saturate to +V_{DD}
B
saturate to -V_{EE}
C
become equal to 0.1 V
D
become equal to -0.1 V
Analog Electronics   Operational Amplifiers
Question 6 Explanation: 
Redraw the circuit:

From circuit,
\begin{aligned} V_{out} &=-\frac{1}{C_1}\int I\cdot dt \\ &= -\frac{1}{R_1C_1}\int 0 \cdot 1dt \\ \\ &=-\frac{0.1}{R_1C_1}\int dt \\ \\ &= -\frac{0.1}{R_1C_1}t \end{aligned}


Hence, V_{out}=-V_{EE}
Question 7
The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is -180^{\circ}. This system has

A
one LHP pole and one RHP zero at the same frequency
B
one LHP pole and one LHP zero at the same frequency
C
two LHP poles and one RHP zero
D
two RHP poles and one LHP zero.
Control Systems   Frequency Response Analysis
Question 7 Explanation: 
The given system is non-minimum phase system Therefore, transfer function, T.F=\frac{s-1}{s+1}
Hence, one LHP pole and one RHP zero at the same frequency.
Question 8
A balanced Wheatstone bridge ABCD has the following arm resistances:
R_{AB}=1k\Omega \pm 2.1%; R_{BC}=100\Omega \pm 0.5%, R_{CD} is an unknown resistance; R_{DA}=300\Omega \pm 0.4%; . The value of R_{CD} and its accuracy is
A
30\Omega \pm 3\Omega
B
30\Omega \pm 0.9\Omega
C
3000\Omega \pm 90\Omega
D
3000\Omega \pm 3\Omega
Electrical and Electronic Measurements   A.C. Bridges
Question 8 Explanation: 
The condition for balanced bridge
\begin{aligned} R_{AB}R_{CD}&=R_{DA}R_{BC} \\ R_{CD} &=\frac{300 \times 100}{1000}=30\Omega \\ %Error &=\pm (2.1+0.5+0.4)=\pm 3% \\ \therefore \; R_{CD}&=30\pm 30 \times \frac{3}{100}=30\pm 0.9\Omega \end{aligned}
Question 9
The open loop transfer function of a unity gain negative feedback system is given by G(s)=\frac{k}{s^2+4s-5}.
The range of k for which the system is stable, is
A
k \gt 3
B
k \lt 3
C
k \gt 5
D
k \lt 5
Control Systems   Root Locus Techniques
Question 9 Explanation: 
Characteristic equation:
\begin{aligned} 1+G(s)H(s)&=0\\ 1+\frac{k}{s^2+4s-5}&=0\\ s^2+4s+k-5&=0 \end{aligned}
R-H criteria:
\left.\begin{matrix} s^2\\ s^1\\ s^0 \end{matrix}\right| \begin{matrix} 1 & k-5\\ 4 & 0\\ k-5 & \end{matrix}
Hence, for stable system,
k-5 \gt 0 \;\; \Rightarrow \; k \gt 5
Question 10
Consider a 3 x 3 matrix A whose (i,j)-th element, a_{i,j}=(i-j)^3. Then the matrix A will be
A
symmetric.
B
skew-symmetric.
C
unitary
D
null.
Engineering Mathematics   Linear Algebra
Question 10 Explanation: 
for \; i=j\Rightarrow a_{ij}=(i-i)^3=0\forall i
for \; i\neq j\Rightarrow a_{ij}=(i-j)^3=(-(j-i))^3=-(j-i)^3=-a_{ji}
\therefore \; A_{3 \times 3 } is skew symmetric matrix.
There are 10 questions to complete.

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