# GATE EE 2006

 Question 1
Which of the following is true?
 A A finite signal is always time bounded B A time bounded signal always possesses finite energy C A bounded signal is always zero outside the interval [$-t_0,t_0$ ] for some $t_0$ D A time bounded signal is always finite
Signals and Systems   Introduction of C.T. and D.T. Signals
 Question 2
x(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency $\omega = 2\pi$(2k)/T; k=1,2... Also, no sine terms are present. Then x(t) satisfies the equation
 A $x(t)=-x(t-T)$ B $x(t)=x(T-t)=-x(-t)$ C $x(t)=x(T-t)=-x(t-T/2)$ D $x(t)=x(t-T)=x(t-T/2)$
Signals and Systems   Fourier Series
Question 2 Explanation:
Since trigonometric fourier series has no sine terms and has only cosine terms therefore this will be an even signal i.e. it will satisfy.
$x(t)=x(-t)$
or, we can write,
$x(t-T)=x(-t+T)$
but signal is periodic with period T.
therefore $x(t-T)=x(t)$
therefore, $x(t)=x(T-t)\;\;...(i)$
Now, since signal contains only odd harmonics i.e. no terms of frequency
$\omega =\frac{2 \pi \times 2k}{T},\;\;\;k=1,2,3,4$
i.e. no even harmonics.
This means signal contains half wave symmetry
this implies that,
$x(t)=-x\left ( t-\frac{T}{2} \right )\;\;...(ii)$
From eq. (i) and (ii),
$x(t)=x(T-t)=-x\left ( t-\frac{T}{2} \right )$
 Question 3
In the figure the current source is $1\angle 0$ A, R=1$\Omega$, the impedances are $Z_{C} =-j \Omega$ and $Z_{L}= 2j \Omega$. The Thevenin equivalent looking into the circuit across X-Y is
 A $\sqrt{2}\angle 0V , (1+2j)\Omega$ B $2\angle 45^{\circ}V , (1-2j)\Omega$ C $2\angle 45^{\circ}V , (1+j)\Omega$ D $\sqrt{2}\angle 45^{\circ}V , (1+j)\Omega$
Electric Circuits   Network Theorems
Question 3 Explanation:
To calculate Thevenin's impedance, current-souce is open-circuited

$Z_{th}=R+Z_L+Z_c$
$\;\;=1+2j-j$
$\;\;=1+j \Omega$
Open-circuit voltage at terminals X-Y
$=I \times Z_{th}$
$\;\;=1\angle 0 \times (1+j)$
$\;\;=\sqrt{2}\angle 15^{\circ} volts$
 Question 4
The three limbed non ideal core shown in the figure has three windings with nominal inductances L each when measured individually with a single phase AC source. The inductance of the windings as connected will be
 A very low B L/3 C 3L D very high
Electrical Machines   Transformers
 Question 5
Which of the following statement holds for the divergence of electric and magnetic flux densities ?
 A Both are zero B These are zero for static densities but non zero for time varying densities. C It is zero for the electric flux density D It is zero for the magnetic flux density
Electromagnetic Fields   Magnetostatic Fields
Question 5 Explanation:
The divergence of magnetic field is always zzero because magnetic flux makes always a closed path.
So, $\bigtriangledown \cdot B=0$ (Maxweel's equation)
while divergence of electric field,
$\bigtriangledown \cdot \vec{E}=\frac{\rho _v}{\in}$
 Question 6
In transformers, which of the following statements is valid ?
 A In an open circuit test, copper losses are obtained while in short circuit test, core losses are obtained B In an open circuit test, current is drawn at high power factor C In a short circuit test, current is drawn at zero power factor D In an open circuit test, current is drawn at low power factor
Electrical Machines   Transformers
Question 6 Explanation:

Circuit model in open-circuit test:
In open-circuit test, the transformer draws only exciting current. The exciting current is only magnetizing in nature and is proportional to the sinusoidal flux and in phase with it. This is represnted by $I_m$ lagging the induced emf by $90^{\circ}$. However, the presence of eddy-current, and hysteresis, both demad the flow of active power into the system and as a consequence the exciting current $I_0$ has another component $I_i$ in phase with $E_1$. Thus the exciting current lags the induced emf by an angle slightly less than $90^{\circ}$ making power factor very low.
 Question 7
For a single phase capacitor start induction motor, which of the following statements is valid ?
 A The capacitor is used for power factor improvement B The direction of rotation can be changed by reversing the main winding terminals C The direction of rotation cannot be changed D The direction of rotation can be changed by interchanging the supply terminals
Electrical Machines   Single Phase Induction Motors, Special Purpose Machines and Electromechanical Energy Conversion System
Question 7 Explanation:

Start capacitor is used to provide $90^{\circ}$ phase difference between $I_m$ and $I_a$.
If supply terminals are interchanged, $I_a$ and $I_m$ will flow in the opposite direction. So, toque will act in the smae direction. Therefore, the direction of rotation will remainsame.
 Question 8
In a DC machine, which of the following statements is true ?
 A Compensating winding is used for neutralizing armature reaction while interpole winding is used for producing residual flux B Compensating winding is used for neutralizing armature reaction while interpole winding is used for improving commutation C Compensating winding is used for improving commutation while interpole winding is used for neutralizing armature reaction D Compensation winding is used for improving commutation while interpole winding is used for producing residual flux
Electrical Machines   DC Machines
Question 8 Explanation:
Compensating winding is placed in slots cut out in pole faces such that the axis of this winding coincides with the brish axis. The compensating winding neutralizes the armature mmf directly under the pole while in the interpolar region, there is incomplete neutralization.
To speed up the commutation process, the reactance voltage must be neutralized by injecting a suitable polarity dynamical (speed) voltage into the commutating coil. In rder that this injection is restricted to commutating coils, narrow iterpolar are provided in the interpolar region.
 Question 9
The concept of an electrically short, medium and long line is primarily based on the
 A nominal voltage of the line B physical length of the line C wavelength of the line D power transmitted over the line
Power Systems   Performance of Transmission Lines, Line Parameters and Corona
Question 9 Explanation:
$L=$ length of line
If $L \leq 80$ km
The line id short line.
If $80km \lt L \leq 250km$
The line is medium line.
If $L \gt 250km$
The line is long line.
 Question 10
Keeping in view the cost and overall effectiveness, the following circuit breaker is best suited for capacitor bank switching
 A vacuum B air blast C $SF_{6}$ D oil
Power Systems   Switch Gear and Protection
Question 10 Explanation:
The arc time constant is the least (a few $\mu s$) in vaccum circuit breakers as compared to other breaker types. The rapid building up of dielectric strength after final arc extinction ($20kV/\mu s$) is unique feature of VCBs. These arc, therefore, ideally suited for capacitor switching.
There are 10 questions to complete.