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


There are 5 questions to complete.