In the circuit shown,  $L=1\mu H,C=1\mu F and \text{\hspace{0.33em}}R=1k\Omega$. They are connected in series with an a.c. source  $V=V_0$ $\sin \omega t$   as shown. Which of the following options is/are correct?

(A) $\omega ~0\Rightarrow V_0\sin \omega t\approx 0$ so no current and option A is correct
(B) current in phase with voltage implies resonance so,$\omega L=\frac{1}{\omega C}$ or ${\omega }_0=\frac{1}{\sqrt{LC}}$

$\Rightarrow$ frequency depends on capacitance and inductance not on resistance. (B) is correct 

(C) $\omega ={\omega }_0=\frac{1}{\sqrt{{10}^{-6}\times {10}^{-6}}}={10}^{6}rad/s$  so  (C) is not correct.

(D) $\omega >>{10}^6\Rightarrow X_L>X_C$  or circuit behaves as inductive so (D) is not correct.