An ac source of angular frequency $\omega$ is fed across a resistor $r$ and a capacitor $C$ in series. The current registered is $I.$ If now the frequency of the source is changed to $\frac{\omega }{3}$ (but maintaining the same voltage), then current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

• Correct answer
  A

  $\sqrt{\frac{3}{5}}$
• B

  $\sqrt{\frac{2}{5}}$
• C

  $\sqrt{\frac{1}{5}}$
• D

  $\sqrt{\frac{4}{5}}$

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