In the circuit shown, $L=1\mu H,C=1\mu Fand\text{\hspace{0.17em}}R=1k\Omega .$ They are connected in series with an a.c. source $V=V_0\text{\hspace{0.17em}}$ sin $\omega t$ as shown. Which of the following options is /are correct?
 

 

We know $X_L=\omega Land{X}_C=\frac{1}{\omega C}$ At $\omega ~0, X_L~0and{X}_c\to \infty$

$\therefore$Current will be nearly zero. For $\omega ={10}^6,X_L=\omega L={10}^6\times {10}^{-6}=1\Omega$ and $X_C=\frac{1}{\omega C}=\frac{1}{{10}^6\times {10}^{-6}}=1\Omega$

For $\omega >>{10}^6,X_L>>1\Omega and{X}_C<<1\Omega \text{\hspace{0.17em}\hspace{0.17em}}or{X}_C\to 0$

Hence circuit does not behave like a capacitor. At resonance frequency (${\omega }_B$) i.e. when $X_C=X_L$ current        
will be in phase with voltage and frequency is independent of R. Resonant frequency. ${\omega }_R=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{{10}^{-6}{10}^{-6}}}={10}^{6}rad{s}^{-1}$