1
GATE ECE 1997
Subjective
+5
-0
In the circuit of Fig., all currents and voltage are sinusoids of frequency $$\omega$$ rad/sec.

(a) Find the impedance to the right of $$\left( {A,\,\,\,\,\,\,B} \right)$$ at $$\omega \,\,\, = \,\,\,\,0$$ rad/sec and $$\omega \,\,\, = \,\,\,\,\infty$$ rad/sec.

(b) If $$\omega \,\,\, = \,\,\,\,{\omega _0}$$ rad/sec and $${i_1}\left( t \right) = \,\,{\rm I}\,\,\,\sin \,\left( {{\omega _0}t} \right)\,{\rm A},$$ where $${\rm I}$$ is positive, $${{\omega _0}\,\, \ne \,\,0}$$, $${{\omega _0}\,\, \ne \,\,\infty }$$, then find $${\rm I}$$, $${{\omega _0}}$$ and $${i_2}\left( t \right)$$

2
GATE ECE 1997
MCQ (More than One Correct Answer)
+2
-0.6
In the circuil of Fig. the equivalent impedance seen across terminals A. B is
A
(16/3) $$\Omega$$
B
(8/3) $$\Omega$$
C
(8/3 + 12 j ) $$\Omega$$
D
None of the above
3
GATE ECE 1997
MCQ (Single Correct Answer)
+1
-0.3
The function f(t) has the Fourier Transform g($$\omega$$). The Fourier Transform of $$g(t) = \left( {\int\limits_{ - \infty }^\infty {g(t){e^{ - j\omega t}}} } \right)\,is$$\$
A
$${1 \over {2\pi }}f(\omega )$$
B
$${1 \over {2\pi }}f( - \omega )$$
C
$$2\pi \,f( - \omega )$$
D
none of the above
4
GATE ECE 1997
MCQ (Single Correct Answer)
+2
-0.6
The power spectral density of a deterministic signal is given by $${\left[ {\sin (f)/f} \right]^2}$$, where 'f' is frequency. The autocorrelation function of this signal in the time domain is
A
a rectangular pulse
B
a delta function
C
a sine pulse
D
a triangular pulse
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