GATE EE 2002

Question 1
A current impulse 5\delta \left ( t \right ), is forced through a capacitor C. The voltage V_{c}\left ( t \right ), across the capacitor is given by
A
5t
B
5u(t) - C
C
\frac{5}{C}t
D
\frac{5u(t)}{C}
Signals and Systems   Introduction of C.T. and D.T. Signals
Question 1 Explanation: 
V_c(t)=\frac{1}{C}\int_{-\infty }^{t}i(t)dt=\frac{1}{C}\int_{-\infty }^{t}5\delta (t)dt=\frac{5}{C}u(t)
Question 2
Fourier Series for the waveform, f(t) shown in figure is
A
\frac{8}{\pi ^{2}}\left [ \sin \left ( \pi t \right )+\frac{1}{9}\sin \left ( 3\pi t \right )+\frac{1}{25}\sin \left ( 5\pi t \right )+.... \right ]
B
\frac{8}{\pi ^{2}}\left [ \sin \left ( \pi t \right )-\frac{1}{9}\cos \left ( 3\pi t \right )+\frac{1}{25}\sin \left ( 5\pi t \right )+.... \right ]
C
\frac{8}{\pi ^{2}}\left [ \cos \left ( \pi t \right )+\frac{1}{9}\cos \left ( 3\pi t \right )+\frac{1}{25}\cos \left ( 5\pi t \right )+.... \right ]
D
\frac{8}{\pi ^{2}}\left [ \cos \left ( \pi t \right )-\frac{1}{9}\sin \left ( 3\pi t \right )+\frac{1}{25}\sin \left ( 5\pi t \right )+.... \right ]
Signals and Systems   Fourier Series
Question 2 Explanation: 
\because f(t) is an even function with half waves symmetry,
\therefore dc term as well as sine terms=0
Only the cosine terms with odd harmonics will be present.
Question 3
The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by
A
B - N + 1
B
B + N
C
N - B + 1
D
N - 2B -1
Electric Circuits   Magnetically Coupled Circuits, Network Topology and Filters
Question 3 Explanation: 
Number of links =B-(N-1) =B-N+1
Question 4
Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode?
A
A circle of unit radius
B
An ellipse
C
A parabola
D
A straight line inclined at 45^{\circ} with respect to the x-axis
Electrical and Electronic Measurements   CRO and Electronic Measurements
Question 4 Explanation: 
\therefore \;\; \text{Phase difference}=0^{\circ} \text{also} f_x=f_y.
Question 5
Given a vector field \vec{F}, the divergence theorem states that
A
\int _S\vec{F}\cdot d\vec{S}=\int _V\vec{\triangledown }\cdot \vec{F}dV
B
\int _S\vec{F}\cdot d\vec{S}=\int _V\vec{\triangledown }\times \vec{F}dV
C
\int _S\vec{F}\times d\vec{S}=\int _V\vec{\triangledown }\cdot \vec{F}dV
D
\int _S\vec{F}\times d\vec{S}=\int _V\vec{\triangledown }\times \vec{F}dV
Electromagnetic Fields   Coordinate Systems and Vector Calculus
Question 6
If a 400V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated current from the supply?
A
reduces
B
increases
C
remains the same
D
increase or reduces depending upon the rotor resistance
Electrical Machines   Three Phase Induction Machines
Question 6 Explanation: 
T=3 I^2\frac{R_2}{s}\frac{60}{2 \pi N_s}
As the motor is drawing rated current from the supply.
\begin{aligned} T &=\propto \frac{1}{N_s} \\ T & \propto \frac{1}{\text{frequency}} \;\;\left [ \because \; N_s=\frac{120f}{P} \right ] \end{aligned}
Hence as frequency increases, torque decreases.
Question 7
A dc series motor fed from rated supply voltage is overloaded and its magnetic circuit is saturated. The torque-speed characteristic of this motor will be approximately represented by which curve of below figure?
A
Curve A
B
Curve B
C
Curve C
D
Curve D
Electrical Machines   DC Machines
Question 7 Explanation: 
At saturation , linear characteristic are observed.
Question 8
A 1 kVA, 230V/100V, single phase, 50 Hz transformer having negligible winding resistance and leakage inductance is operating under saturation, while 250 V, 50 Hz sinusoidal supply is connected to the high voltage winding. A resistive load is connected to the low voltage winding which draws rated current. Which one of the following quantities will not be sinusoidal?
A
Voltage induced across the low voltage winding
B
Core flux
C
Load current
D
Current drawn from the source
Electrical Machines   Transformers
Question 9
A 400V/200V/200V, 50 Hz three winding transformer is connected as shown in figure. The reading of the voltmeter, V, will be
A
0V
B
400V
C
600V
D
800V
Electrical Machines   Transformers
Question 9 Explanation: 
The two 200 turns winding are connected in additive polarity. Hence the output voltage will be 400V. The difference of this 400 V and the voltage induced in first winding (i.e. 400 turn) is same.
Question 10
The frequency of the clock signal applied to the rising edge triggered D flip-flop shown in figure is 10 kHz. The frequency of the signal available at Q is
A
10 kHz
B
2.5 kHz
C
20 kHz
D
5 kHz
Digital Electronics   Sequential Logic Circuits
Question 10 Explanation: 
In toggle mode
f_{out}=\frac{f_{in}}{2}=\frac{10kHz}{2}=5kHz
There are 10 questions to complete.
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