Question

Answer in brief:
What is the natural frequency of the LC circuit? What is the reactance of this circuit at this frequency?

Answer 1

$X_L=-X_C$
$\Rightarrow \omega L=\frac{1}{\omega C}$
${\omega }^{2}LC=1$

$\omega =\frac{1}{\sqrt{2C}}$

$\omega =2\pi f\Rightarrow f=\frac{\omega }{2}\pi =\frac{1}{2\pi \sqrt{LC}}$

Total reactance $=X_L+X_C$
$=-X_C+X_C$
$=0$
$V=\frac{1}{2\pi \sqrt{LC}}$
Reactance of the circuit at this frequency is zero.