## Electromagnetics question for GATE ECE 2017

There will be questions related to Electromagnetics in every GATE paper. Electromagnetics is one such subject where primary focus should be on understanding Maxwell’s equations(Concepts, forms and different types of problems). One should have thorough understanding of vector calculus and integration to come out on top. Try to get the below questions right. More questions will follow in future posts.

1) An electron traveling horizontally enters a region where a uniform electric field is
directed upward. What is the direction of the force exerted on the electron once it
entered the field?
(a) To the left
(b) To the right
(c) Upward
(d) Downward

Ans: d

2) Point charges 30 nC, -20 nC, and 10 nC are located at (-1,0,2), (0,0,0), and (1,5,-1)
respectively. The total flux leaving a cube of side 6 m centered at the origin.
(a) -20 nC
(b) 10 nC
(c) 20 nC
(d) 60 nC

Ans : b

3) Plane z = 10 m carries charge 20 nC/m2 . The electric field intensity at the origin
is
(a) -10 ˆaz V/m
(b) -18π aˆz V/m
(c) -72π aˆz V/m
(d) -360π aˆz V/m

Ans : d

4) Consider the following cases:
• A point charge Q is placed at the origin. Let D1 be the flux due to this charge
over a sphere of radius b centered at the origin.
• A uniformly charged sphere of radius a(a<b) centered at the origin with a
total charge of Q. Let D2 be the flux due to this over a sphere of radius b
centered at the origin is.
Which of the following is true
(a) D1 = D2
(b) D1 is not equal to D2
(c) Under special conditions, D1 = D2

Ans: a

5) Two identical coaxial circular coils carry the same current I but in opposite directions.
The magnitude of the magnetic field −→B at a point on the axis midway
between the coil is
(a) Zero
(b) The same as that produces by one coil
(c) Twice that produced by one coil
(d) Half that produced by one coil

Ans: a

6) According to Ampere’s Law, the path integral $\oint_{C} \vec B. \vec dl$around the closed loop C is
given by

(a) µ0(I1 + I2 − I3)
(b) µ0(−I1 − I2 + I3)
(c) µ0(I1 + I2 + I3)
(d) −µ0(I1 + I2 + I3)

For any explanations , use comment section.

## GATE Signals and systems questions

1) Which of the following signal is not periodic?
a) sin 10$\pi$t
b) sin 31t
c)sin 10$\pi$t + sin 31t
d) sin(10$\pi$t +31)

2) The value of the integral $\int_{0}^{\infty} e^{-\alpha*t^2} \delta(t+10)$ dt is
a) 0
b) $e^{-100 \alpha}$
c) $e^{10 \alpha}$
d) $e^{100 \alpha}$

3) A system is defined by its input and output relationship y(t)=5x(t+3)+2 where y(t) and x(t) are the output and input respectively. The system is
a) Linear and Casual
b)Linear and non-casual
c) non-linear and casual
d) non-linear and non-casual

4) If the input-output relation of a system is y(t)=$\int_{-\infty}^{2t} x(\tau) d\tau$ then the system is
a) Linear, time invariant and unstable
b) linear ,non-causal and unstable
c) linear, causal and time invariant
d) non-causal, time invariant and unstable

5) Evaluate te function $\int_{0}^{\infty} t^2 \delta(t-3)$ dt
a) $e^{-t^2}$
b) $t^3/3$
c) $t^2(t-3)$
d) 9

## GATE : Previous questions on Feedback Amplifier

GATE 1993
1) Negative feedback in Amplifiers

a) Improves the Signal to Noise ratio at I/p
b) Improves the Signal to Noise ratio at O/p
c) Does not improvee signal to noise ratio at I/o
d) Reduces distortion

Ans : d

GATE 1995
2) To obtain very high input impedance and output impedances in a feedback Amplifier , which is the suitable configuration

a) Voltage – Series
b) Current – Series
c) Voltage – Shunt
d) Current – Shunt

Ans : b

Note: Explanation is given after 3rd question.

GATE 1998
3) In a shunt-shunt negative feedback Amplifier, as compared to the basic Amplifer.

a) Both input and output impedance increases
b) Input impedance decreases, but output impedance increases
c) Input impedance increases, but output impedance decreases
d) both input and output impedance increases

Hint : Feedback topology naming convention goes this way

Shunt(I/P) – Shunt(O/P). Remember Shunt-Shunt is also called as Voltage – Shunt. You can read that HERE
Impedance at input or output side depends on the word Series/Shunt. If Series then impedance increases
and if Shunt, then impedance decrease. In this question, the feedback topology is shunt-shunt, hence the correct answer is option d.

Ans : d

GATE 1991

4) Two non-inverting amplifiers, one having a unity gain and other having a gain of twenty, are made using identical operational amplifiers. As compared to the unity gain amplifier, the amplifier with gain twenty has

a) less negative feedback
b) More input impedance
c) Less Bandwidth
d) None of the above

Ans : c

Try to dissolve the above question.

## GATE : Transmission lines questions

1) Two very long loss-less cables of characteristic impedances of 50 $\Omega$ and 100 $\Omega$ respectively are to be joined for reflection less transmission. If the quarter wave transformer is used for matching, what should be the value of its impedance(in ohms)?

a) 70.7
b) 35.7
c) 50
d) 2

2) A transmission line with a characteristic impedance of 100 $\Omega$ is used to match a 50 $\Omega$ section to a 200 $\Omega$ section. If the matching is to be done both at 429MHz and 1GHz, the length of the transmission line can be approximately

a) 82.5cm
b) 1.05m
c) 1.58m
d) 1.75m

3) Impedance of a transmission line repeats itself every

a) $\lambda$/4
b) $\lambda$/2
c) $\lambda$
d) 2$\lambda$

4) If $Z_{open}$ is the impedance of a open circuited transmission line and $Z_{short}$ is the impedance of a short circuited transmission line whose characteristic impedance is $Z_o$. Then which of the following relationship is true?

a) $Z_o$ =$\frac{Z_{open}}{Z_{short}}$
b) $Z_o$ =$Z_{open}$ * $Z_{short}$
c) $Z_o$ =$\sqrt{\frac{Z_{open}}{Z_{short}}}$
d) $Z_o$ =$\sqrt {Z_{open}*Z_{short}}$

5) A transmission line of characteristic impedance 50 $\Omega$ is terminated by a 50 $\Omega$ load. When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm
apart on the line is found to be π/4 radians. The phase velocity of the wave along the line is

a) 0.8* $10^8$ m/s
b) 1.2*$10^8$ m/s
c) 1.6*$10^8$ m/s
d) 3*$10^8$ m/s

A transmission line of characteristic impedance 50 $\Omega$ is terminated in a load impedance . The
VSWR of the line is measured as 5 and the first of the voltage maxima in the line is observed at a
distance of $\lambda$/4 from the load. The value of $Z_L$ is
(A) 10 $\Omega$
(B) 250 $\Omega$
(C) (19.23 + j46.15) $\Omega$
(D) (19.23 – j46.15) $\Omega$

….

1-a, 2-c , 3-b, 4-d

## Waveguide Questions for GATE EC

1) Which is the dominant mode in TM?
a) $TM_{10}$
b) $TM_{21}$
c) $TM_{01}$
d) $TM_{11}$

2) Dominant mode in Waveguides usually refers to ?

a) $TE_{10}$
b) $TM_{10}$
c) $TM_{01}$
d) $TM_{11}$

3) The cut-off wavelength of rectangular waveguide was measured to be 8 cm and 4.8 cm when excited in $TE_{10}$ and $TE_{11}$ modes respectively. Determine the dimensions of a waveguide

a= ______
b= ______

4) A rectangular waveguide has dimensions a=2.5 cm and b=1 cm. A microwave signal at a frequency if 8.6 GHz is to be propagated through this waveguide.Which of the following mode can exist in rectangular waveguide?

a) $TE_{10}$
b) $TM_{10}$
c) $TM_{01}$
d) $TM_{11}$

5) The modes in a rectangular waveguide are denoted by $TE_{mn}$/$TM_{mn}$ where m and n are the Eigen
numbers along the larger and smaller dimensions of the waveguide respectively. Which one of
the following statements is TRUE?

a) The mode $TM_{10}$ of the waveguide does not exist
b) The mode $TE_{10}$ of the waveguide does not exist
c) The $TE_{10}$ and $TM_{10}$ the modes both exist and have the same cut – off frequencies
d) The $TM_{10}$ and $TM_{01}$ the modes both exist and have the same cut – off frequencies

6) If $\lambda_c$ is the cut off wavelength of a rectangular waveguide and $\lambda_o$ is a free space wavelength. Then the condition for wave propagation is

a) $\lambda_c$ > $\lambda_o$
b) $\lambda_c$ < $\lambda_o$
c) $\lambda_c$ = $\lambda_o$
d) $\lambda_c$ = 0

7)

TE(02) means the wave exists only in the Y direction. So look out for Electric field lines which are originating or ending at Y axis. In this case, options A and C are eliminated. Now we are left with option b and d.

Here as you can see, TE(02) means n=2 (Mode is 2) . So the E field equation will be of the following form

$E_y$= K $sin(\frac{2\pi y}{b})$

Y axis range is from 0 to b.

At

y=0 and y=b, value of sin is 0.

At y=b/4,  value of sin is 1

At y=3b/4, value of sin is -1

So, the correct answer is option “d” , where E field lines are pointing towards positive x axis below b/2 and towards negative x axis above b/2

…………………………………………………………………………………………………….

1-d, 2-a ,3 => a=4, b=3 ,4-a,5-a, 7-d

## Lead – Lag compensator previous GATE questions

GATE EC-2012

The transfer function of  a compensator is given by  $G_c(s)$=$\frac{s+a}{s+b}$

1.  $G_c(s)$ is a lead compensator if

A) a=1, b=2     B) a=3,b=2       C) a=-3 b=-1        d) a=3, b=1

2. The phase of the above lead compensator is maximum at

a)  $\sqrt{3}$              b) $\sqrt{2}$          c) $\sqrt{6}$    d) $\sqrt{1/3}$

3) The open loop transfer function of a plant is given as G(s)=$\frac{1}{s^2-1}$. If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

a) 10 $\frac{s-1}{s+2}$                                b) 10 $\frac{s-1}{s+2}$

c) 10 $\frac{s+2}{s+10}$                                       d) 2 $\frac{s+2}{s+10}$

4) The transfer function of a phase lead compensator is given by $G_c(s)$= $\frac{1+3Ts}{1+Ts}$ where T>0 . The maximum phase shift produced by such compensator is(in degrees)

a) 90             b) 30          c) 45            d) 60

## Steady state error questions for GATE ECE

1) The transfer system of the system which will have more steady error for unit step input is
a) 80/(s+1)(s+2)(s+3)
b)120/s(s+1)(s+15)
c) 60/(s+0.5) (s+3)(s+5.5)
d)120/(s+1)(s+4)(s+15)

2)A unity feedback system has forward path transfer function G(s)=K/s(s+2). If the design specification is that the steady state error due to ramp input is 0.05,the value of K allowed is
a)20
b)40
c)10
d)80

3) When the gain  of the system is increased, the steady state error of the system
a)Increases
b) Decreases
c) Remains unchanged
d) May Increase or decrease

4) A unity feedback system has open loop transfer function G(s). The steady state error is zero for

a) Step input and type-1 G(s)                      b) Ramp input and type 1 G(s)

c) Step input and type -0 G(s)                     d) Ramp input and type 0 G(s)

5) A dc motor model G(s)= $\frac{1}{s(s+1)}$ is to obtain a steady state error of less than 0.1 for a unit ramp input. The above design specification can be achieved by a feed forward lead compensator whose steady state gain must be greater than

a) 100            b) 10       c) 1        d) 0.1

6) A unity feedback closed loop second order system has a transfer function  $\frac{81}{s^2+0.6s+9}$ and is excited by step input of 1 unit. The steady state error of the output is

a) 10       b) 0         c ) 1         d) 0.1

……………………..

1-d , 2-b, 3-b,4-a,5-b,6-d