Consider the circuit diagram as shown in the figure. The source has a voltage $V=V_0 \sin \omega t$. Both the resistors A and B have the same resistance. The capacitor and the inductor have capacitance $C$ and inductance $L$, respectively. For some frequency $\omega$, and certain initial charge in the capacitor, the current through the resistor A is in phase with the source. What is the value of $\omega$ ?

• Correct answer
  A

  $\frac{1}{\sqrt{2 L C}}$
• B

  $\frac{1}{\sqrt{L C}}$
• C

  $\frac{1}{2 \sqrt{L C}}$
• D

  $\frac{1}{\sqrt{3 L C}}$

Hence, the correct answer is option: 'A'.