In the circuit shown, $\mathrm{L}=1 \mu \mathrm{H}, \mathrm{C}=1 \mu \mathrm{~F}$ and $\mathrm{R}=1 \mathrm{k} \Omega$. They are connected in series with an a.c. source $\mathrm{V}=\mathrm{V}_0 \sin \omega t$ as shown. Which of the following options is/are correct?
Select ALL correct options:
A
The current will be in phase with the voltage if $\omega=10^4 \mathrm{rad} . \mathrm{s}^{-1}$
B
At $\omega \gg 10^6$ rad. $\mathrm{s}^{-1}$, the circuit behaves like a capacitor
C
The frequency at which the current will be in phase with the voltage is independent of R
D
At $\omega \sim 0$ the current flowing through the circuit becomes nearly zero.
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