1
GATE EE 1998
MCQ (Single Correct Answer)
+1
-0.3
A sinusoidal source of voltage $$V$$ and frequency $$f$$ is connected to a series circuit of variables resistance, $$R$$ and a fixed reactance, $$X.$$ The locus of the tip of the current phasor, $$I$$, as $$R$$ is varied from $$0$$ to $$\infty$$ is
A
a semicircle with a diameter of $$V/X.$$
B
a straight line with a slope of $$R/X.$$
C
an ellipse with $$V/R$$ as major axis.
D
a circle of radius $$R/X$$ and origin at $$\left( {0,\,\,\,V/2} \right).$$
2
GATE EE 1998
MCQ (Single Correct Answer)
+1
-0.3
A circuit with a resistor, inductor and capacitor in series is resonant at $${f_0}\,\,Hz.$$ If all the component values are now doubled, the new resonant frequency is
A
$$2\,\,{f_0}$$
B
still $${f_0}$$
C
$${f_0}/4$$
D
$${f_0}/2$$
3
GATE EE 1996
MCQ (Single Correct Answer)
+1
-0.3
In the circuit shown in Fig. $$X$$ $$-$$ is an element which always absorbs power. During a particular operation, it sets up a current of $$1$$ $$amp$$ in the direction shown and absorbs a power $${P_{x}}.$$ It is possible that $$X$$ can absorb the same power $${P_x}$$ for another current $$i.$$ Then the value of this current is
A
$$\left( {3 - \sqrt {14} } \right)\,\,amps$$
B
$$\left( {3 + \sqrt {14} } \right)\,\,amps$$
C
$$5$$ $$amps$$
D
None of these
4
GATE EE 1995
Numerical
+1
-0
A series $$R-L-C$$ circuit has the following parameter values:
$$R = 10\Omega ,\,\,L = 0.01\,H,\,\,C = 100\,\,m\,\,F.$$
The $$Q$$ factor of the circuit at resonance is