In the circuit shown, $$L = 1 \mu H, C = 1 \mu F$$ and $$R = 1 kΩ.$$ 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

The current will be in phase with the voltage if $$\omega = 10^4 rad. s^{-1}$$

B

The frequency at which the current will be in phase with the voltage is independent of 𝑅

C

At $$\omega \sim 0$$ the current flowing through the circuit becomes nearly zero

D

At $$\omega \gg 10^6 rad. s^{-1}$$, the circuit behaves like a capacitor