Question

Consider the following statements $S_{1}and{S}_2$
$S_1$: At the resonant frquency the impedance of a series R-L-C circuit is zero.
$S_2$: In a parallel G-L-C circuit, increasing the conductance G results in increase in its Q factor.
Which one of the following is correct?

• A. $S_1$ is FALSE and $S_2$ is TRUE
• B. Both $S_1$ and $S_2$ are TRUE
• C. $S_1$ is TRUE and $S_2$ is FALSE
• D. Both $S_1$ and $S_2$ are FALSE

Answer 1

The correct option is D Both $S_1$ and $S_2$ are FALSE

$S_1$ Impedance of series RLC circuit at resonant frequency is minimum

$Z=R+j(\omega L-\frac{1}{\omega C})$

$\omega L-\frac{1}{\omega C}=0$

Z = R (Purely resistive)

$S_2:Q=R\sqrt{\frac{C}{L}}$

$G=\frac{1}{R}\Rightarrow Q=\frac{1}{G}\sqrt{\frac{C}{L}}$

$G\uparrow thenQ\downarrow$if C & L are same