GATE Questions & Answers of Resonance

An inductor is connected in parallel with a capacitor as shown in the figure.

As the frequency of current i is increased, the impedance (Z) of the network varies as

•  (A) 
•  (B) 
•  (C) 
•  (D) 

A series RLC circuit is observed at two frequencies. At ω₁=1 krad/s, we note that source voltage $V_1=100\angle 0^{o}V$ results in a current $I_1=0.03\angle {31}^{o}A$. At ${\omega }_2=2$ krad/s, the source voltage $V_2=100\angle 0^{o}V$ results in a current $I_1=2\angle {31}^{o}A$. The closest values for R,L,C out of the following options are

•  (A) R=50 Ω;L =25 mH;C=10 μF;
•  (B) R=50 Ω;L =10 mH;C=25 μF;
•  (C) R=50 Ω;L =50 mH;C=5 μF;
•  (D) R=50 Ω;L =5 mH;C=50 μF;

The resonant frequency for the given circuit will be

•  (A) 1 rad/s
•  (B) 2 rad/s
•  (C) 3 rad/s
•  (D) 4 rad/s

The R-L-C series circuit shown in figure is supplied from a variable frequency voltage source. The admittance - locus of the R-L-C network at terminals AB for increasing frequency $\omega$ is